// LabOptimizeSpecs.swift. 12/11/2020. class LabOptimizeSpecs { // Utility Maximization let strLabIndiffCurveIntroSpecs :String = """ `` Lab Specs // Lab mode: Utility Cost Work Savings Lump Utility // 0: Lab mode: Utility // Utility Parameters X Y // 1: Good X and good Y names .1 .9 .05 .4 // 2: Utility slider specs: Alpha 0 5.0 .2 0.8 // 3: Utility slider specs: Elasticity of substitution // Price and income parameters Px Py Inc // 4: Good price and income names 1.50 4.00 .50 2.00 // 5: Price of X slider specs .75 2.00 .25 1.00 // 6: Price of Y slider specs 10.00 40.00 2.50 40.00 // 7: Income slider specs // Use elasticity of substitution sigma or FW's substitutability parameter // NB: Not implemented E // 8: E or S // Demand elasticity/tax slider specs; used only by cost min and taxes DemElast= // 9: Slider prefix -1.5 -.25 .25 -1.00 // 10: Demand elasticity/tax slider specs // Graph parameters 0 0 30 30 // 11: Graph Data range: x0 y0 x1 y1 X Y // 12: Graph axis names `` Prob Specs ` ******** Problem 0 Start Screen 1 - Construct a Household's Indifference Curve // 0: Title // Problem mode: IndiffCurve ContourLine LinearLine Optimize Sub/IncEffects Indiff // 1: Problem mode: Contour line // Visibility of utility coefficient and elasticity sliders N N // 2: Both, Slider, Label, Neither // Visibility of initial and new prices and income sliders N N N // 3: Both, Slider only, Label only, None // Result parameters Utility= _ _ _ _ // 4: Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map F F T // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes N -1.00 // 7: Initial value // Slider or mouse input M // 8: Slider, Mouse, None 0 30 1 15 // 9: Search slider specs Utility= // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Illustrate the construction of a household's indifference curve.`BLK The household's initial bundle is comprised of 12 units of good X and 16 units of good Y. The initial bundle generates 13.5 units of utility. We will now construct the household's indifference curve representing 13.5 units of utility. Using the mouse, point to a bundle on the graph that is northeast of the initial bundle and click. The new bundle includes more of both good X and good Y. `IND`BLDQuestion:`BLD Why does the new bundle generate more utility than the initial bundle? `INDThe new bundle is in the initial bundle's better than set. Focus you attention on the utility generated by the new bundle, the bottom line in the table. SLOWLY, drag the new bundle due west toward the Y-axis. `IND`BLDQuestion:`BLD Why does the new bundle now generate less utility? `INDContinue to move the bundle slowly due west until the utilities of the new and initial bundles are equal. The household is now indifference between the new and initial bundles. The initial and new bundles lie on the same indifference curve, the indifference curve representing 13.5 units of utility. The curve connecting the two bundles represent all the bundles between the initial and new bundles to which the household is indifferent. Next, click on a point southwest of the initial bundle to produce a second new bundle. This new bundle includes less of both good X and good Y. `IND`BLDQuestion:`BLD Why does the new bundle generate less utility than the initial bundle? `INDThis new bundle is in the initial bundle's worse than set. SLOWLY, drag the new bundle due east away from the Y-axis. `IND`BLDQuestion:`BLD Why does the new bundle now generate more utility? `INDContinue to move the bundle slowly due east until the utilities of the new and initial bundles are equal. The household is now indifference between the new and initial bundles. The initial and new bundles lie on the same indifference curve, the indifference curve representing 13.5 units of utility. Continue to use this procedure to trace out the household's indifference curve representing 13.5 units of utility. ` Prob End ` ******** Problem 1 Start Screen 2 - Utility Functions and Indifference Curve Maps // 0: Title // Problem mode: IndiffCurve ContourLine LinearLine Optimize Sub/IncEffects Contour // 1: Problem mode: Contour line // Visibility of utility coefficient and elasticity sliders N N // 2: Both, Slider, Label, Neither // Visibility of initial and new prices and income sliders N N N // 3: Both, Slider only, Label only, None // Result parameters Utility= _ _ _ _ // 4: Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map F F T // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes N -1.00 // 7: Initial value // Slider or mouse input S // 8: Slider, Mouse, None 0 25 1 15 // 9: Search slider specs Utility= // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Illustrate the relationship between indifference curves and utility.`BLK Use the scrollbar immediately below the graph to vary the level of utility from 1 to 25. `IND`BLDQuestions:`BLD How does the indifference curve shift as utility `0x2022 decreases? `0x2022 increases? `IND There is an indifference curve depicting each level of utility. The graph depicts a utility map illustrating the indifference curves for various utilities. ` Prob End ` ******** Problem 2 Start Screen 3 - Elasticity of Substitution and Indifference Curves // 0: Title // Problem mode: Contour line, Linear line, Optimize, Sub/Inc effects Contour // 1: Problem mode: Contour line // Visibility of utility coefficient and elasticity sliders N B // 2: Both, Slider, Label, Neither // Visibility of initial and new prices and income sliders N N N // 3: Both, Slider only, Label only, None // Result parameters Utility= _ _ _ _ // 4: Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map F F F // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes N -1.00 // 7: Initial value // Slider or mouse input N // 8: Slider, Mouse, None 0 30 .25 10 // 9: Search slider specs Utility= // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Illustrate the relationship between the shape of indifference curves and the elasticity of substitution?`BLK Use the elasticity of substitution scrollbar, near the top of the window, to vary the elasticity of substitution. `IND`BLDQuestion:`BLD How does the shape of an indifference curve change as the elasticity of substitution `0x2022 increases? `0x2022 decreases? `IND ` Prob End ` ******** Problem 3 Start Screen 4 - Marginal Rate of Substitution and the Indifference Curve's Slope // 0: Title // Problem mode: Contour line, Linear line, Optimize, Sub/Inc effects Contour // 1: Problem mode: Contour line // Visibility of utility coefficient and elasticity sliders N N // 2: Both, Slider, Label, Neither // Visibility of initial and new prices and income sliders N N N // 3: Both, Slider only, Label only, None // Result parameters Utility= _ _ _ _ // 4: Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map F T F // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes N -1.00 // 7: Initial value // Slider or mouse input S // 8: Slider, Mouse, None 0 30 0.5 12 // 9: Search slider specs X= // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Show that the marginal rate of substitution equals the negative of the indifference curve's slope.`BLK Initially, the household consumes 12 units of good X and 16 units of good Y. Also, the slope of the indifference curve's tangent line equals -2.00 as reported above. Confirm this by choosing two points on the tangent line and calculating its slope. (Hint: The best points to choose are (12, 16) and (20, 0).) `BLDDefinition:`BLD The `BLDmarginal rate of substitution (MRS)`BLD equals the rate at which a household can substitute good Y for very small changes in good X while remaining equally well off. `BLDClaim:`BLD The marginal rate of substitution equals the negative of the slope of the indifference curve's tangent line: MRS = Negative of the indifference curve's slope More specifically, we claim that since the slope of the indifference curve's tangent line equals -2.00, the marginal rate of substitution equals 2.00: `BLDCritical Point:`BLD To remain equally well off the household must remain on the same indifference curve. The scrollbar immediately below the graph allows you to move along the indifference curve. The scrollbar allows you to trace out all the bundles of good X and good Y which keep the household equally well off. We begin with the household consuming 12.0 units of good X and 16.0 units of good Y. Adjust the scrollbar to increase the amount of good X by 10.0, from 12.0 to 22.0. `IND`BLDQuestion:`BLD By how much does good Y decrease? `IND`BLDQuestion:`BLD What is the ratio of the change in good Y to the change in good X that keeps the household equally well off? Now, recall that the marginal rate of substitution is concerned with very small increases in good X? With is in mind, increase good X by smaller and smaller amounts. Instead of increasing good X by 10, only increase it only by `0x2022 5.0 from 12.0 to 17.0. `0x2022 1.0 from 12.0 to 13.0. `0x2022 0.5 from 12.0 to 12.5. `BLDQuestions: `BLDIn each case, what is the ratio of the change in good Y to the change in good X that keeps the household equally well off. `BLDQuestion:`BLD As the change in good X becomes smaller and smaller, from 10.0 to 5.0 to 1.0 to 0.5, does the ratio of the change in good Y to the change in good X get closer and closer to 2.00? Next, instead of increasing the amount of good X above 12.0, decrease it below 12.0. Decrease it by `0x2022 4.0 from 12.0 to 8.0. `0x2022 3.0 from 12.0 to 11.0. `0x2022 0.5 from 12.0 to 11.5. `BLDQuestions: `BLDIn each case, what is the ratio of the change in good Y to the change in good X that keeps the household equally well off. `BLDQuestion:`BLD As the change in good X becomes smaller and smaller, from 4.0 to 3.0 to 0.5, does the ratio of the change in good Y to the change in good X get closer and closer to 2.00? `BLDGeneralization:`BLD Whether the change in good X is positive or negative, as the change in good X becomes smaller and smaller, the ratio of the change in good Y to the change in good X that keeps the household equally well off approaches 2.00. Consequently, when the household consumes 12.0 units of good X and 16.0 units of good Y, what does the marginal rate of substitution equal? Now, recall our claim: The marginal rate of substitution equals the negative of the slope of the indifference curve's tangent line: MRS = Negative of the indifference curve's slope `BLDQuestions:`BLD `0x2022 What does the slope of the indifference curve's tangent line equal? `0x2022 What does the marginal rate of substitution equal? `BLDGeneralization:`BLD The marginal rate of substitution equals the negative of the indifference curve's slope. ` Prob End ` ******** Problem 4 Start Screen 5 - Diminishing Marginal Rate of Substitution // 0: Title // Problem mode: Contour line, Linear line, Optimize, Sub/Inc effects Contour // 1: Problem mode: Contour line // Visibility of utility coefficient and elasticity sliders N N // 2: Both, Slider only, Label only, None // Visibility of initial and new prices and income sliders N N N // 3: Both, Slider only, Label only, None // Result parameters Utility= _ _ _ _ // 4: Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map T F F // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes N -1.00 // 7: Initial value // Slider or mouse input S // 8: Slider, Mouse, None 0 30 1.0 12 // 9: Search slider specs X= // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Illustrate the principle of diminishing marginal rate of substitution: When we move along an indifference curve by increasing the consumption of good X, the marginal rate of substitution decreases.`BLK We have just shown that the marginal rate of substitution equals the negative of the indifference curve's slope. As before, the scrollbar immediately below the graph allows us to move along the indifference curve. Use the scrollbar to increase the consumption of good X. `BLDQuestions:`BLD What happens to `0x2022 the slope of the indifference curve? `0x2022 the marginal rate of substitution? ` Prob End """ // Utility Maximization let strLabOptimizeUtilMaxSpecs :String = """ `` Lab Specs // Lab mode: Utility Cost Work Savings Lump Utility // 0: Lab mode: Utility // Utility Parameters X Y // 1: Good X and good Y names .1 .9 .05 .4 // 2: Utility slider specs: Alpha 0 5.0 .2 0.8 // 3: Utility slider specs: Elasticity of substitution // Price and income parameters Px Py Inc // 4: Good price and income names 1.50 4.00 .50 2.00 // 5: Price of X slider specs .75 2.00 .25 1.00 // 6: Price of Y slider specs 10.00 20.00 2.50 20.00 // 7: Income slider specs // Use elasticity of substitution sigma or FW's substitutability parameter // NB: Not implemented E // 8: E or S // Demand elasticity/tax slider specs; used only by cost min and taxes DemElast= // 9: Slider prefix -1.5 -.25 .25 -1.00 // 10: Demand elasticity/tax slider specs // Graph parameters 0 0 12 20 // 11: Graph Data range: x0 y0 x1 y1 X Y // 12: Graph axis names `` Prob Specs ` ******** Problem 0 Start Screen 1 - Interpreting the Budget Constraint // 0: Title // Problem mode: Contour line, Linear line, Optimize, Sub/Inc effects Linear // 1: Problem mode: Linear // Visibility of utility coefficient and elasticity sliders N N // 2: Both, Slider only, Label only, None // Visibility of initial and new prices and income sliders L L L // 3: Both, Slider only, Label only, None // Result parameters Utility= _ _ _ _ // 4: Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map F F F // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes N -1.00 // 7: Initial value // Slider or mouse input N // 8: Slider, Mouse, None 0 30 .25 10 // 9: Search slider specs Utility= // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Interpret the budget constraint's intercepts and slope.`BLK `BLDQuestions:`BLD What does the `0x2022 X-intercept equal? Interpret it. `0x2022 Y-intercept equal? Interpret it. `0x2022 slope equal? Interpret the price ratio, Px/Py. Hint: If the household were to purchase one additional unit of good X, how many units of good Y must it forego? `BLDQuestion:`BLD How is the price ratio related to the slope of the budget constraint? ` Prob End ` ******** Problem 1 Start Screen 2 - Households's Utility Maximizing Bundle of Goods // 0: Title // Problem mode: Contour line, Linear line, Optimize, Sub/Inc effects Optimize // 1: Problem mode: Optimize // Visibility of utility coefficient and elasticity sliders N N // 2: Both, Slider only, Label only, None // Visibility of initial and new prices and income sliders L L L // 3: Both, Slider only, Label only, None // Result parameters X= Y= Utility= MRS= Price_ratio= // 4: Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map T F F // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes N -1.00 // 7: Initial value // Slider or mouse input S // 8: Slider, Mouse, None 0 12 .25 3 // 9: Search slider specs More_X Best_Possible Less_X // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Illustrate the household's utility maximizing decision.`BLK We begin by setting the stage: `0x2022 The household consumes 3 units of good X and 14 units of good Y. `0x2022 The household's marginal rate of substitution (MRS) equals 9.57. `0x2022 The price ratio equals 2.00. `BLDClaim:`BLD The household should purchase more good X because the marginal rate of substitution is greater than the price ratio. To justify this claim, we review the marginal rate of substitution and the price ratio. `BLDMarginal rate of substitution:`BLD Negative of the indifference curve's slope. The rate at which a household can substitute good Y for very small changes in good X while remaining equally well off. The marginal rate of substitution is 9.57. When the household purchases one more unit of good X it could forego about 9.57 units of good Y and remain equally well off. `BLDPrice ratio:`BLD Negative of the budget constraint's slope. The amount of good Y the household must forego to purchase an additional unit of good X. The price ratio is 2.00; when the household purchases an additional unit of good X it must forego 2.00 unit of good Y. `BLDSummary:`BLD When the household purchases one additional unit of good X: `0x2022 It could forego about 9.57 units of good Y and remain equally well off. `0x2022 It would forego only 2.00 unit of good Y. Therefore, when the household purchases one additional unit of good X, it becomes better off. In some sense, it would be about 7.57 units of good Y ahead. We've shown that when the marginal rate of substitution is greater than the price ratio, the household would become better off by purchasing more X. Using similar logic, we can show that when the marginal rate of substitution is less than the price ratio, the household would become better off by purchasing less X. Adjust the scrollbar immediately below the graph to move the bundle along the budget line to find the utility maximizing bundle of good X and good Y. `BLDGeneralization:`BLD When utility is maximized how are the marginal rate of substitution and the price ratio related? ` Prob End """ // Income and Substitution Effects let strLabOptimizeSubIncSpecs :String = """ `` Lab Specs // Lab mode: Utility, Cost, Work, Save Utility // 0: Problem mode // Utility Parameters X Y // 1: Good X and good Y names .1 .9 .05 .4 // 2: Utility slider specs: Alpha 0 5.0 .2 0.8 // 3: Utility slider specs: Elasticity of substitution // Price and income parameters Px Py Inc // 4: Good price and income names 1.50 4.00 .50 2.00 // 5: Price of X slider specs .75 2.00 .25 1.00 // 6: Price of Y slider specs 10.00 20.00 2.50 20.00 // 7: Income slider specs // Use elasticity of substitution sigma or FW's substitutability parameter // NB: Not implemented E // 8: E or S // Demand elasticity/tax slider specs; used only by cost min and taxes DemElast= // 9: Slider prefix -1.5 -.25 .25 -1.00 // 10: Demand elasticity/tax slider specs // Graph parameters 0 0 12 20 // 11: Graph Data range: x0 y0 x1 y1 X Y // 12: Graph axis names `` Prob Specs ` ******** Problem 0 Start Screen 1 - Budget Constraint and the Income // 0: Title // Problem mode: Contour line, Linear line, Optimize, Sub/Inc effects Linear // 1: Problem mode: Linear // Visibility of utility coefficient and elasticity sliders N N // 2: Both, Slider only, Label only, None // Visibility of initial and new prices and income sliders L L B // 3: Both, Slider only, Label only, None // Result parameters Utility= _ _ _ _ // 4: Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map F F F // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes N -1.00 // 7: Initial value // Slider or mouse input N // 8: Slider, Mouse, None 0 30 .25 10 // 9: Search slider specs Utility= // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Illustrate the effect of a change in income on the household's budget constraint.`BLK Using the income scrollbar, decrease the household's new income from 20 to 10. The initial budget constraint now appears in light green and the new budget line in a darker green. `BLDQuestions:`BLD How does the change in income affect the budget constraint's `0x2022 X-intercept? `0x2022 Y-intercept? `0x2022 slope? Since the household's income falls and the prices remain the same, the household's purchasing power decreases. `BLDQuestion:`BLD Does the budget line shift in a parallel fashion? Explain. `BLDGeneralization:`BLD A change in purchasing power causes the budget line to shift in a parallel fashion. ` Prob End ` ******** Problem 1 Start Screen 2 - Household's Income Effect // 0: Title // Problem mode: Contour line, Linear line, Optimize, Sub/Inc effects Substitution // 1: Problem mode: Sub/Inc effects // Visibility of utility coefficient and elasticity sliders N N // 2: Both, Slider only, Label only, None // Visibility of initial and new prices and income sliders L L B // 3: Both, Slider only, Label only, None // Result parameters Initial= Sub_Effect= Price_Comp= Inc_Effect New= // 4: Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map F F F // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes N -1.00 // 7: Initial value // Slider or mouse input N // 8: Slider, Mouse, None 0 30 .1 10 // 9: Search slider specs More_comp_income Just_right Less_comp_income // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Illustrate the income effect.`BLK Once again, decrease new income from 20 to 10. Since both prices have remained the same, the household's purchasing power as decreased. The depiction of the initial utility maximizing state of affairs remains on the graph, but now appears in lighter colors. The gray and black bundles represent the household's utility maximizing bundles at the initial and new prices: `0x2022 `BLDGray bundle:`BLD The initial utility maximizing bundle. `0x2022 `BLDBlack bundle:`BLD The new utility maximizing bundle. `BLDDefinition:`BLD The income effect reflects the change in the household's utility maximizing bundle resulting from a change in purchasing power. The movement from the initial gray bundle to the new black bundle illustrates the income effect, the effect of the decrease in purchasing power. The effect resulting from a parallel shift of the budget line. The coordinates of the initial gray and the new black utility maximizing bundles are reported above along with the values of the income effect: `BLD`GRYInitial `BLK`0x2192 `MGRInc Effect `BLK`0x2192 New`BLK`BLD `BLDIncome Effect:`BLD `0x2022 Reduces good X consumption by 3.00 from 6.00 to 3.00. `0x2022 Reduces good Y consumption by 4.00 from 8.00 to 4.00. ` Prob End ` ******** Problem 2 Start Screen 3 - Budget Constraint and the Price of Good X // 0: Title // Problem mode: Contour line, Linear line, Optimize, Sub/Inc effects Linear // 1: Problem mode: Linear // Visibility of utility coefficient and elasticity sliders T T // 2: Both, Slider only, Label only, None // Visibility of initial and new prices and income sliders B L L // 3: Both, Slider only, Label only, None // Result parameters Utility= _ _ _ _ // 4: Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map F F F // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes N -1.00 // 7: Initial value // Slider or mouse input N // 8: Slider, Mouse, None 0 30 .25 10 // 9: Search slider specs Utility= // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Illustrate the effect of a change in the price of good X on the household's budget constraint.`BLK Using the price X (Px) scrollbar, increase the price of good X from 2.00 to 4.00. `BLDQuestions:`BLD How does a change in the price of good X affect the budget constraint's: `0x2022 X-intercept? `0x2022 Y-intercept? `0x2022 slope? `BLDQuestion:`BLD Why does the budget line rotate around the Y-intercept? `BLDQuestion:`BLD How are the slope of the budget line and relative price ratio (Px/Py) related? `BLDGeneralizations:`BLD A change in the relative price ratio changes the budget line's slope. ` Prob End ` ******** Problem 3 Start Screen 4 - Household's Substitution and Income Effects // 0: Title // Problem mode: Contour line, Linear line, Optimize, Sub/Inc effects Substitution // 1: Problem mode: Sub/Inc effects // Visibility of utility coefficient and elasticity sliders N N // 2: Both, Slider only, Label only, None // Visibility of initial and new prices and income sliders B L L // 3: Both, Slider only, Label only, None // Result parameters Initial= Sub_Effect= Price_Comp= Inc_Effect= New= // 4: Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map F F F // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes N -1.00 // 7: Initial value // Slider or mouse input S // 8: Slider, Mouse, None 0 12 .1 3 // 9: Search slider specs More_comp_income Just_right Less_comp_income // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Illustrate the substitution and income effects.`BLK Again, increase the price of good X from 2.00 to 4.00. The depiction of the initial utility maximizing state of affairs remains on the graph, but now appears in lighter colors. The gray and black bundles represent the household's utility maximizing bundles at the initial and new prices: `0x2022 `BLDGray bundle:`BLD The initial utility maximizing bundle. `0x2022 `BLDBlack bundle:`BLD The new utility maximizing bundle. The increase in the price of X affects the household in two ways: `0x2022 Since the price of Y remains the same, good X is now more expensive relative to good Y. `0x2022 Since income remains the same, the household's purchasing power decreases. The movement from the initial gray bundle to the new black bundle combines these two effects: the substitution effect and the income effect. `IND`BLDDefinition:`BLD The substitution effect reflects the change in the household's utility maximizing bundle resulting from a change in the relative prices. `BLDDefinition:`BLD The income effect reflects the change in the household's utility maximizing bundle resulting from a change in purchasing power. `IND `BLDSummary:`BLD `0x2022 `BLD`PNKSubstitution effect`BLK`BLD reflects the change in relative prices. `0x2022 `BLD`MGRIncome effect`BLK`BLD reflects the change in purchasing power. The movement from the gray to the black bundle reflects both the substitution and income effects. `0x2022 `BLD`GRYGray`BLK `0x2192 Both `PNKsubstitution effect`BLK and `MGRincome effect`BLK `0x2192 Black`BLD We would like to separate these two effects. To do so, note that the household is made worse off by the increase in the price of X. However, suppose that we do not want the household to suffer from the price increase. We could give the household more income to compensate it for the decrease in purchasing power caused by the higher good X price. After doing so, only the substitution effect remains. `BLDStrategy:`BLD After the price of X increases: `0x2022 Give the household additional income to compensate it for the loss in purchasing power. `0x2022 Now, only the substitution effect remains. Provide the household with additional income by moving the compensation scrollbar (the scrollbar immediately below the graph) slowly to the right. A new purple budget line appears on the graph which includes the additional income. Continue to move the compensation scrollbar rightward until the purple budget line just touches the initial light red indifference curve. A new purple bundle appears at the point of contact; it's called the price compensated bundle. The purple budget line is called the price compensated budget line. We have achieved our objective. The household is just as well off as it was initially. We have given the household just enough additional income to compensate it for the reduction in purchasing power caused by the higher good X price. The movement from the gray bundle to the purple bundle reflects the substitution effect only: `BLD`GRYGray`BLK `0x2192 `PNKSubstitution effect only`BLK `0x2192 `PURPurple`BLK`BLD So, here's where we stand: `IND`0x2022 The movement from the gray to the black bundle reflects both the income and substitution effects: `BLD`GRYGray`BLK `0x2192 Both `PNKSubstitution effect`BLK and `MGRincome effect`BLK `0x2192 Black`BLD `0x2022 The movement from the gray to the purple bundle reflects the substitution effect only. `BLD`GRYGray`BLK `0x2192 `PNKSubstitution effect only`BLK `0x2192 `PURPurple`BLK`BLD `0x2022 Therefore, the movement from the purple to the black bundle reflects the income effect only. `BLD`PURPurple`BLK `0x2192 `MGRIncome effect only`BLK `0x2192 Black`BLD `IND The above table quantifies the substitution and income effects: `IND`0x2022 `BLD`PNKSubstitution Effect:`BLK`BLD `0x25E6 Reduces good X consumption by 1.15 from 6.00 to 4.85. `0x25E6 Increases good Y consumption by 3.26 from 8.00 to 11.26. `0x2022 `BLD`MGRIncome Effect:`BLK`BLD `0x25E6 Reduces good X consumption by 1.69 from 4.85 to 3.16. `0x25E6 Reduces good Y consumption by 3.92 from 11.26 to 7.34. ` Prob End """ // ********** Cost Minimization ************* // Cost Minimization let strLabIsoquantIntroSpecs :String = """ `` Lab Specs // Lab mode: Utility Cost Work Savings Lump Cost // 0: Lab mode: Cost // Contour Function Parameters L K // 1: Labor and captial names .1 .9 .05 .4 // 2: Production function slider specs: Alpha 0 5.0 .2 1.6 // 3: Production function slider specs: Elasticity of substitution // Price and income parameters w v Q // 4: Input price and income names 1.50 4.00 .50 2.00 // 5: Price of X slider specs .75 2.00 .25 1.00 // 6: Price of Y slider specs 10.00 50.00 5.00 50.00 // 7: Output slider specs // Use elasticity of substitution sigma or FW's substitutability parameter // Not implemented E // 8: E or S // Demand elasticity/tax slider specs; used only by cost min and taxes DemElast= // 9: Slider prefix -1.5 -.25 .25 -1.00 // 10: Demand elasticity/tax slider specs // Graph parameters 0 0 150 150 // 11: Graph Data range: x0 y0 x1 y1 L K // 12: Graph axis names `` Prob Specs ` ******** Problem 0 Start Screen 1 - Production Functions and Isoquants // 0: Title /// Problem mode: Contour line, Linear line, Optimize, Sub/Inc effects Contour // 1: Problem mode: Contour line // Visibility of utility coefficient and elasticity sliders N N // 2: Both, Slider only, Label only, None // Visibility of initial and new prices and income sliders N N N // 3: Both, Slider only, Label only, None // Result parameters Production= _ _ _ _ // 4: Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map F F T // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes N -1.00 // 7: Initial value // Slider or mouse input S // 8: Slider, Mouse, None 0 125 5 50 // 9: Search slider specs Production= // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Illustrate a firm's isoquant to understand the relationship between isoquants and production.`BLK Use the production scrollbar to vary the level of production. `BLDQuestion:`BLD As production increases what happens to the isoquant? ` Prob End ` ******** Problem 1 Start Screen 2 - Elasticity of Substitution and Isoquants // 0: Title // Problem mode: Contour line, Linear line, Optimize, Sub/Inc effects Contour // 1: Problem mode: Contour line // Visibility of utility coefficient and elasticity sliders N B // 2: Both, Slider only, Label only, None // Visibility of initial and new prices and income sliders N N N // 3: Both, Slider only, Label only, None // Result parameters Production= _ _ _ _ // 4: Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map F F F // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes N -1.00 // 7: Initial value // Slider or mouse input N // 8: Slider, Mouse, None 0 150 1 50 // 9: Search slider specs Production= // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Illustrate the relationship between the shape of isoquants and the elasticity of substitution?`BLK Use the elasticity of substitution scrollbar to vary the elasticity of substitution. `BLDQuestion:`BLD What happens to the shape of the isoquant as the elasticity of substitution `0x2022 increases? `0x2022 decreases? ` Prob End ` ******** Problem 2 Start Screen 3 - Rate of Technical Substitution and Isoquants // 0: Title // Problem mode: Contour line, Linear line, Optimize, Sub/Inc effects Contour // 1: Problem mode: Contour // Visibility of coefficient and elasticity sliders N N // 2: Both, Slider only, Label only, None // Visibility of initial and new prices and income sliders N N N // 3: Both, Slider only, Label only, None // Result parameters Production= _ _ _ _ // 4: Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map F T F // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes N -1.00 // 7: Initial value // Slider or mouse input S // 8: Slider, Mouse, None 0 150 1 50 // 9: Search slider specs Labor= // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Show that the rate of technical substitution equals the negative of the isoquant's slope.`BLK Initially, the firm uses 50 units of labor and 50 units of capital. Also, the slope of the isoquant's tangent line equals -1.50 as reported above. Confirm this by choosing two points on the tangent line and calculating its slope. (Hint: The best points to choose are (0, 125) and (50, 50).) `BLDDefinition:`BLD The rate of technical substitution (RTS) equals the rate at which a firm substitutes capital (K) for small changes in labor (L) to keep production constant. `BLDClaim:`BLD The negative of the iosquant's tangent line equals the rate of technical substitution: Negative of the isoquant's slope = RTS More specifically, we claim that since the slope of the isoquant's tangent line equals -1.50, the rate of technical substitution equals 1.50: `BLDCritical point:`BLD To keep production constant, the firm must remain on the same isoquant. The scrollbar immediately below the graph allows you to move along the isoquant. The scrollbar allows you to trace out all the combinations of labor (L) and capital (K) which keep production constant. Adjust the scrollbar to increase the amount of labor by 50, from 50 to 100. By how much does capital decrease? What is the ratio of the change in capital to the change in labor that keeps production constant? In each of the following cases, what is the ratio of the change in capital to the change in labor that keeps production constant when labor increases by `0x2022 25 from 50 to 75? `0x2022 10 from 50 to 60? `0x2022 5 from 50 to 55? `0x2022 1 from 50 to 51? `BLDQuestion:`BLD As the change in good X becomes smaller and smaller, from 50 to 25 to 10 to 5 to 1, does the ratio of change in capital to the change in labor get closer and closer to 1.50? If so, what does the rate of technical substitution equal? Now, recall our claim: The negative of the iosquant's tangent line equals the rate of technical substitution: Negative of the isoquant's slope = RTS Questions: `0x2022 What does the slope of the isoquant's tangent line equal? `0x2022 What does the rate of technical substitution equal? `BLDGeneralization:`BLD The rate of technical substitution equals the negative of the isoquant curve's slope. ` Prob End ` ******** Problem 3 Start Screen 4 - Diminishing Rate of Technical Substitution // 0: Title // Problem mode: Contour line, Linear line, Optimize, Sub/Inc effects Contour // 1: Problem mode: Contour line // Visibility of utility coefficient and elasticity sliders N N // 2: Both, Slider only, Label only, None // Visibility of initial and new prices and income sliders N N N // 3: Both, Slider only, Label only, None // Result parameters Production= _ _ _ _ // 4: Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map T F F // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes N -1.00 // 7: Initial value // Slider or mouse input S // 8: Slider, Mouse, None 0 150 1 50 // 9: Search slider specs Production= // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Illustrate the principle of diminishing rate of technical substitution: As the firm uses more labor and moves along an isoquant, the rate of technical substitution decreases.`BLK `BLDDefinition`BLD The rate of technical substitution (RTS) equals the rate at which a firm substitutes capital for small changes in labor to keep production constant. Adjust the scrollbar below the graph to increase the labor used by the firm to move along the isoquant. `BLDQuestion:`BLD As the firm uses more labor and moves along an isoquant, what happens to the rate of technical substitution? ` Prob End """ let strLabOptimizeCostMinSpecs :String = """ `` Lab Specs // Lab mode: Utility Cost Work Savings Lump Cost // 0: Lab mode: Cost // Utility Parameters L K // 1: Labor and captial names .1 .9 .05 .4 // 2: Production function slider specs: Alpha 0 5.0 .2 1.6 // 3: Production function slider specs: Elasticity of substitution // Price and income parameters w v Q // 4: Input price and income names .75 3.00 .25 1.50 // 5: Price of L slider specs .75 3.00 .25 1.00 // 6: Price of K slider specs 10.00 50.00 5.00 50.00 // 7: Output slider specs // Use elasticity of substitution sigma or FW's substitutability parameter // Not implemented E // 8: E or S // Demand elasticity/tax slider specs; used only by cost min and taxes DemElast= // 9: Slider prefix -1.5 -.25 .25 -1.00 // 10: Demand elasticity/tax slider specs // Graph parameters 0 0 150 150 // 11: Graph Data range: x0 y0 x1 y1 L K // 12: Graph axis names `` ProbSpecs ` ******** Problem 0 Start Screen 1 - Firm's Isocost Curve // 0: Title // Problem mode: Contour line, Linear line, Optimize, Sub/Inc effects Lin // 1: Problem mode: Optimization // Visibility of utility coefficient and elasticity sliders N N // 2: Both, Slider only, Label only, None // Visibility of initial and new prices and income sliders L L N // 3: Both, Slider only, Label only, None // Result parameters Labor= Capital= Cost= RTS= w/v= // 4: Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map F F T // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes N -1.00 // 7: Initial value // Slider or mouse input N // 8: Slider, Mouse, None 0 300 10 150 // 9: Search slider specs Cost= // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Interpret the isocost curve's intercepts and slope.`BLK `BLDQuestion:`BLD What does the `0x2022 firm's cost equal? `0x2022 L-intercept equal? Interpret it. `0x2022 K-intercept equals? Interpret it. `0x2022 slope equal? Interpret the wage-rental ratio (w/v). Hint: If the firm were to hire an additional unit of labor, how many units of capital must it forego? `BLDQuestion:`BLD How is the wage-rental ratio related to the slope of the isocost curve? ` Prob End ` ******** Problem 1 Start Screen 2 - Firm's Cost Minimizing Combination of Labor and Capital // 0: Title // Problem mode: Contour line, Linear line, Optimize, Sub/Inc effects Optimize // 1: Problem mode: Optimization // Visibility of utility coefficient and elasticity sliders N N /// 2: Both, Slider only, Label only, None // Visibility of initial and new prices and income sliders L L L // 3: Both, Slider only, Label only, None // Result parameters Labor= Capital= Cost= RTS= w/v= // 4 Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map T F F // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes N -1.00 // 7: Initial value // Slider or mouse input S // 8: Slider, Mouse, None 0 150 1 30 // 9: Search slider specs More_Labor Best_Possible Less_Labor // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Illustrate the combination of labor and capital needed to produce a given quantity of output that minimizes the firm's total cost.`BLK We begin by setting the stage: `0x2022 The firm produces 50 units of output using 30.00 units of labor and 92.90 units of capital. `0x2022 The firm's rate of technical substitution (RTS) equals 3.04. `0x2022 The wage-rental ratio equals 1.50. `BLDClaim:`BLD The firm should use more labor and less capital to produce the 50 units of output because the rate of technical substitution is greater than the wage-rental ratio. `BLDRate of technical substitution:`BLD Negative of the isoquant curve's slope. The rate at which the firm substitutes capital for very small changes of labor to keep production constant. The rate of technical substitution is 3.04; when the firm uses one more unit of labor it could forego about 3.04 units of capital and still produce 50 units of output. `BLDPrice ratio:`BLD Negative of the isocost curve's slope. The amount of capital the firm must forego to keep costs constant when it hires an additional unit of labor. The wage-rental ratio is 1.50; to keep costs constant the firm must forego 1.50 units of capital when the firm hires an additional unit of labor. `BLDSummary:`BLD When the firm hires one additional unit of labor, it `0x2022 can keep output constant by foregoing about 3.04 units of capital. `0x2022 only needs forego 1.50 units of capital to keep cost constant. When the firm hires one additional unit of labor, it keeps output constant by hiring 3.04 fewer units of capital and its cost falls. We've shown that when the rate of technical substitution is greater than the wage-rental ratio, the firm can continue to produce the same quantity of output and reduce its cost by hiring more labor. Using similar logic, we can show that when the rate of technical substitution is less than the wage-rental ratio, the firm can continue to produce the same quantity of output and reduce its cost by hiring less labor. Adjust the scrollbar immediately below the graph to move along the firm's isoquant to find the cost minimizing combination of labor and capital needed to produce 50 units of output. `BLDQuestion:`BLD When cost is minimized how are the rate of technical substitution and the wage-rental ratio related? ` Prob End """ let strLabOptimizeSubOutSpecs :String = """ `` Lab Specs // Lab mode: Utility Cost Work Savings Lump Cost // 0: Lab mode: Cost // Utility Parameters L K // 1: Labor and captial names .1 .9 .05 .4 // 2: Production function slider specs: Alpha 0 5.0 .2 1.6 // 3: Production function slider specs: Elasticity of substitution // Price and income parameters w v Q // 4: Input price and income names .75 3.00 .25 1.50 // 5: Price of L slider specs .75 3.00 .25 1.00 // 6: Price of K slider specs 10.00 50.00 5.00 50.00 // 7: Output slider specs // Use elasticity of substitution sigma or FW's substitutability parameter // Not implemented E // 8: E or S // Demand elasticity/tax slider specs; used only by cost min and taxes DemElast= // 9: Slider prefix -1.5 -.25 .25 -1.00 // 10: Demand elasticity/tax slider specs // Graph parameters 0 0 150 150 // 11: Graph Data range: x0 y0 x1 y1 L K // 12: Graph axis names `` ProbSpecs ` ******** Problem 0 Start Screen 1 - The Wage and the Firm's Isocost Curve // 0: Title // Problem mode: Contour line, Linear line, Optimize, Sub/Inc effects Lin // 1: Problem mode: Optimization // Visibility of utility coefficient and elasticity sliders N N // 2: Both, Slider only, Label only, None // Visibility of initial and new prices and income sliders B L L // 3: Both, Slider only, Label only, None // Result parameters Labor= Capital= Cost= RTS= w/v= // 4: Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map F F T // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes N -1.00 // 7: Initial value // Slider or mouse input N // 8: Slider, Mouse, None 0 300 10 150 // 9: Search slider specs Cost= // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Show that a change in the wage changes the slope of the isocost curve.`BLK Use the new wage scrollbar to increase the wage from $1.50 to $3.00. `BLDQuestion:`BLD What happens to the `0x2022 L-intercept? Explain. `0x2022 K-intercept? Explain. `0x2022 slope? ` Prob End ` ******** Problem 1 Start Screen 2 - Firm's Substitution and Output Effects // 0: Title // Problem mode: Contour line, Linear line, Optimize, Sub/Inc effects Substitution // 1: Problem mode: Sub/Inc effects // Visibility of utility coefficient and elasticity sliders N N // 2: Both, Slider only, Label only, None // Visibility of initial and new prices and income sliders B L B // 3: Both, Slider only, Label only, None // Result parameters Initial= Sub_Effect= Price_Comp= Output_Effect= New= // 4: Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map F F F // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes N -1.00 // 7: Initial value // Slider or mouse input S // 8: Slider, Mouse, None 0 30 .1 10 // 9: Search slider specs Not_used // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Illustrate the firm's substitution and output effects.`BLK Initially, the firm produces 50 units of output using 50.00 units of labor and 50.00 units of capital. Use the new wage scrollbar to increase the wage from $1.50 to $3.00. `BLDQuestions:`BLD `IND`0x2022 Has labor become more or less expensive relative to capital? `0x2022 What happens to the combination of labor and capital the firm uses to minimize the total cost of producing 50 units of output? Explain why the firm now substitutes capital for labor? `IND But would this be the end of the story? What's your intuition? Wouldn't you expect the profit maximizing firm to produce less output when its labor costs rise? Use the new quantity scrollbar to reduce the firm's new output from 50 to 20. `BLDQuestions:`BLD `IND`0x2022 What happens to the firm's isoquant? `0x2022 What happens to the combination of labor and capital that minimizes the firm's costs when it produces less output? `INDThis is called the output effect. Summarizing the substitution and output effects when the price of labor rises: `IND `BLDSubstitution effect:`BLD Movement from the initial light gray combination of labor and capital to the purple combination. The firm substitutes capital for labor because labor is now more expensive relative to capital. `BLDOutput effect:`BLD Movement from the purple combination of labor and capital to the black combination. The firm produces less output because its labor costs have risen. ` Prob End """ // Work leisure decision let strLabOptimizeWorkLeisSpecs :String = """ `` Lab Specs // Lab mode: Utility Cost Work Savings Lump Work // 0: Lab mode: Work/Leisure // Utility Parameters Leis Cons // 1: Good X and good Y names .1 .9 .05 .3 // 2: Utility slider specs: Alpha 0 5.0 .2 1.6 // 3: Utility slider specs: Elasticity of substitution // Price and income parameters Wage PRTax LSTax // 4: Good price and income names 10.00 25.00 5.00 15.00 // 5: Wage slider specs -.5 .50 .10 .00 // 6: Proportional tax slider specs -80 80 20 0 // 7: Lump sum tax slider specs // Use elasticity of substitution sigma or FW's substitutability parameter // Not implemented E // 8: E or S // Demand elasticity/tax slider specs; used only by cost min and taxes DemElast= // 9: Slider prefix -1.5 -.25 .25 -1.00 // 10: Demand elasticity/tax slider specs // Graph parameters 0 0 24 600 // 11: Graph Data range: x0 y0 x1 y1 Leis_(hours) Cons_($) // 12: Graph axis names `` Prob Specs ` ******** Problem 0 Start Screen 1 - Households's Work-Leisure Constraint // 0: Title // Problem mode: Contour line, Linear line, Optimize, Sub/Inc effects Linear // 1: Problem mode: Optimize // Visibility of utility coefficient and elasticity sliders N N // 2: Both, Slider only, Label only, None // Visibility of initial and new prices and income sliders B N N // 3: Both, Slider only, Label only, None // Result parameters Leis= Cons= Utility= MRS= Wage= // 4: Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map T T T // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes N -1.00 // 7: Initial value // Slider or mouse input N // 8: Slider, Mouse, None 0 25 .1 10 // 9: Search slider specs More_Leis Best_Possible Less_Leis // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Illustrate the household's work-leisure constraint and show how the wage affects the constraint.`BLK The diagram depicts the work-leisure constraint reflecting a 24 hour day. Initially, the wage is specified as $15.00 per hour. `BLDQuestions:`BLD What does the `0x2022 Leis-intercept equal? Interpret it. `0x2022 Cons-intercept equal? Interpret it. `0x2022 slope equal? Use the new wage scrollbar to decrease the wage from $15.00 per hour to $10.00. `BLDQuestions:`BLD What does the new `0x2022 Leis-intercept equal? Interpret it. `0x2022 Cons-intercept equal? Interpret it. `0x2022 slope equal? Use the new wage scrollbar to increase the wage to $25.00 per hour. `BLDQuestions:`BLD What does the new `0x2022 Leis-intercept equal? Interpret it. `0x2022 Cons-intercept equal? Interpret it. `0x2022 slope equal? ` Prob End ` ******** Problem 1 Start Screen 2 - Households's Utility Maximizing Combination of Work and Leisure // 0: Title // Problem mode: Contour line, Linear line, Optimize, Sub/Inc effects Optimize // 1: Problem mode: Optimize // Visibility of utility coefficient and elasticity sliders N N // 2: Both, Slider only, Label only, None // Visibility of initial and new prices and income sliders L N N // 3: Both, Slider only, Label only, None // Result parameters Leis= Cons= Utility= MRS= Wage= // 4: Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map T F F // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes N -1.00 // 7: Initial value // Slider or mouse input S // 8: Slider, Mouse, None 0 25 .1 10 // 9: Search slider specs More_Leis Best_Possible Less_Leis // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Illustrate the household's utility maximizing combination of leisure and work.`BLK Initially, the wage is specified as $15.00 per hour. Use the leisure scrollbar below the graph to move along the budget line. `BLDQuestions:`BLD `0x2022How much leisure will the household choose to maximize its utility? `0x2022How many hours will the household work? `BLDGeneralization:`BLD When utility is maximized how are the marginal rate of substitution and the wage rate related? ` Prob End ` ******** Problem 2 Start Screen 3 - Household's Substitution and Income Effects // 0: Title // Problem mode: Contour line, Linear line, Optimize, Sub/Inc effects Substitution // 1: Problem mode: Sub/Inc effects // Visibility of utility coefficient and elasticity sliders N N // 2: Both, Slider only, Label only, None // Visibility of initial and new prices and income sliders B N N // 3: Both, Slider only, Label only, None // Result parameters Initial= Sub_Effect= Price_Comp= Inc_Effect New= // 4: Result names 2 // 5: Output decimal places // Graph related parameters // Graph parameters: Tangent, Secant, Contour map F F F // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes N -1.00 // 7: Initial value // Slider or mouse input S // 8: Slider, Mouse, None 0 30 .1 8 // 9: Search slider specs More_compensation Just_right Less_compension // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Illustrate the household's work-leisure substitution and income effects.`BLK Use the new wage scrollbar to increase the wage from $15.00 per hour to $25.00. The diagram illustrates the initial and new utility maximizing quantities of leisure and consumption. Use the horizontal scrollbar immediately below the graph to "compensate" the household for the higher wage. `BLDQuestion:`BLD What is the `0x2022 price compensated bundle? `0x2022 substitution effect? `0x2022 income effect? ` Prob End """ // Savings decision let strLabOptimizeSavingsSpecs :String = """ `` Lab Specs // Lab mode: Utility Cost Work Savings Lump Savings Decision // 0: Lab mode: Savings // Utility Parameters C0 C1 // 1: Good X and good Y names .1 .9 .05 .4 // 2: Utility slider specs: Alpha 0 5.0 .2 1.6 // 3: Utility slider specs: Elasticity of substitution // Price and income parameters i(%) Y0 Y1 // 4: Interest rate and endowments 0.0 50.0 5.0 10.0 // 7: Interest rate slider specs 0.00 100.00 10.00 90.00 // 5: Y0 slider specs 0.00 110.00 11.00 11.00 // 6: Y1 slider specs // Use elasticity of substitution sigma or FW's substitutability parameter // Not implemented E // 8: E or S // Demand elasticity/tax slider specs; used only by cost min and taxes DemElast= // 9: Slider prefix -1.5 -.25 .25 -1.00 // 10: Demand elasticity/tax slider specs // Graph parameters 0 0 120 120 // 11: Graph Data range: x0 y0 x1 y1 C0 C1 // 12: Graph axis names `` Prob Specs ` ******** Problem 0 Start Screen 1- Households's Intertemporal Bundle // 0: Title // Problem mode: Contour line, Linear line, Optimize, Sub/Inc effects Linear // 1: Problem mode: Optimize // Visibility of utility coefficient and elasticity sliders N N // 2: Both, Slider only, Label only, None // Visibility of initial and new prices and income sliders: i Y0 Y1 B L L // 3: Both, Slider only, Label only, None // Result parameters C0= C1= Utility= MRS= Price_ratio= // 4: Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map T F F // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes N -1.00 // 7: Initial value // Slider or mouse input N // 8: Slider, Mouse, None 0 120 1 20 // 9: Search slider specs More_C0 Best_Possible Less_C0 // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Illustrate the household's intertemporal budget constraint and show how the interest rate affects the constraint.`BLK By default, the household receives $90 this period (Y0) and $11.00 next period (Y1). The gray point represents the income stream. `IND`BLDQuestion:`BLD Explain why the income stream, $90 this period and $11 next period, must lie on the household's budget constraint. `IND Initially, the interest rate equals 10 percent. We will now use two different extreme scenarios to provide an intuitive interpretation of the budget constraint's two intercepts. First, suppose that the household saved all the income it receives this period, $10. `BLDQuestions:`BLD How much `0x2022 could it consume this period (C0)? `0x2022 interest would it earn from its savings? `0x2022 could it consume next period (C1)? `BLDQuestion:`BLD What point on the diagram represents this scenario? Second, consider a second scenario. Suppose that the household uses all of its income next period, $11, as collateral in order to borrow as much as it can this period. `BLDQuestions:`BLD How much `0x2022 could it borrow this period? `0x2022 could it consumer this period (C0)? `0x2022 could it consumer next period (C1)? `BLDQuestion:`BLD What point on the diagram represents this scenario? Using the intercepts, calculate the slope of the budget constraint. `BLDQuestion:`BLD How is it related to the interest rate? Explain. Use the new new interest rate scrollbar to decrease the interest rate from 10 percent to 5 percent. Focus on the budget constraint. `BLDQuestions:`BLD Does the `0x2022 C0-intercept increase or decrease? Explain. `0x2022 C1-intercept increase or decrease? Explain. `0x2022 slope increase or decrease? Explain. Use the new new interest rate scrollbar to increase the interest rate to 20 percent. Focus on the budget constraint. `BLDQuestions:`BLD Does the `0x2022 C0-intercept increase or decrease? Explain. `0x2022 C1-intercept increase or decrease? Explain. `0x2022 slope increase or decrease? Explain. ` Prob End ` ******** Problem 1 Start Screen 2 - Households's Utility Maximizing Intertemporal Bundle // 0: Title // Problem mode: Contour line, Linear line, Optimize, Sub/Inc effects Optimize // 1: Problem mode: Optimize // Visibility of utility coefficient and elasticity sliders N N // 2: Both, Slider only, Label only, None // Visibility of initial and new prices and income sliders: i Y0 Y1 L L L // 3: Both, Slider only, Label only, None // Result parameters C0= C1= Utility= MRS= Price_ratio= // 4: Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map T F F // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes N -1.00 // 7: Initial value // Slider or mouse input S // 8: Slider, Mouse, None 0 120 1 20 // 9: Search slider specs More_C0 Best_Possible Less_C0 // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Illustrate the utility maximizing intertemporal bundle of goods this period and goods next period.`BLK Initially, the interest rate is 10 percent. Use the horizontal C0 scrollbar located immediately below the graph to move the bundle along the intertemporal budget line. `BLDQuestions:`BLD What is the households utility maximizing amount of `0x2022 consumption this period? `0x2022 consumption next period `BLDQuestion:`BLD How much does the household ave this period? `BLDGeneralization:`BLD When utility is maximized how are the marginal rate of substitution and the interest rate related? ` Prob End ` ******** Problem 2 Start Screen 3 - Household's Income and Substitution Effects // 0: Title // Problem mode: Contour line, Linear line, Optimize, Sub/Inc effects Substitution // 1: Problem mode: Sub/Inc effects // Visibility of utility coefficient and elasticity sliders N N // 2: Both, Slider only, Label only, None // Visibility of initial and new prices and income sliders: i Y0 Y1 B L L // 3: Both, Slider only, Label only, None // Result parameters Initial= Sub_Effect= Price_Comp= Inc_Effect New= // 4: Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map F F F // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes N -1.00 // 7: Initial value // Slider or mouse input S // 8: Slider, Mouse, None 0 120 1 20 // 9: Search slider specs More_compensation Just_right Less_compension // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Illustrate the household's intertemporal substitution and income effects.`BLK Use the new interest rate scrollbar to increase the interest rate from 10 percent to 50 percent. The diagram illustrates the initial and new utility maximizing quantities of consumption this period and next period. Use the horizontal scrollbar immediately below the graph to "compensate" the household for the higher interest rate. `BLDQuestion:`BLD What is the `0x2022 price compensated bundle? `0x2022 substitution effect? `0x2022 income effect? ` Prob End """ // Lump Sum Tax Principle let strLabLumpSumPrincipleSpecs :String = """ `` Lab Specs // Lab mode: Utility Cost Work Savings Lump LumpSum // 0: Lab mode: Utility // Utility Parameters X Y // 1: Good X and good Y names .1 .9 .05 .4 // 2: Utility slider specs: Alpha 0 5.0 .2 2.0 // 3: Utility slider specs: Elasticity of substitution // Price and income parameters Px Py Inc // 4: Good price and income names .75 2.00 .25 1.00 // 5: Price of X slider specs .75 2.00 .25 1.00 // 6: Price of Y slider specs 10.00 20.00 2.50 20.00 // 7: Income slider specs // Use elasticity of substitution sigma or FW's substitutability parameter // NB: Not implemented E // 8: E or S // Demand elasticity/tax slider specs; used only by cost min and taxes X UnitTax= // 9: Slider prefix 0.0 3.00 0.20 0.0 // 10: Demand elasticity/tax slider specs // Graph parameters 0 0 30 20 // 11: Graph Data range: x0 y0 x1 y1 X Y // 12: Graph axis names `` Prob Specs ` ******** Problem 0 Start Screen 1 - Lump Sum Principle // 0: Title // Problem mode: IndiffCurve ContourLine LinearLine Optimize Sub/IncEffects LumpSum // 1: Problem mode: Lump sum principle // Visibility of utility coefficient and elasticity sliders N N // 2: Both, Slider, Label, Neither // Visibility of initial and new prices and income sliders L L L // 3: Both, Slider only, Label only, None // Result parameters Utility= _ _ _ _ // 4: Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map F F F // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes B 0.0 // 7: Initial value // Slider or mouse input S // 8: Slider, Mouse, None 0 30 1 15 // 9: Search slider specs Decrease_lump_sum_tax:_Move_scrollbar_right Lump_sum_and_unit_tax_revenue_equal Increase_lump_sum_tax:_Move_scrollbar_left // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Illustrate the lump sum principle.`BLK Adjust the X UnitTax scrollbar to increase the tax on good X to $3.00 per unit. The light red curves on the diagram depict the no tax scenario and the red curves the tax case. `BLDQuestion:`BLD How much tax revenue does the government collect? Note that a new scrollbar has appeared below the graph. This new scrollbar allows you to impose a lump sum tax INSTEAD OF the unit tax. Gradually adjust the scrollbar to the left. A purple budget constraint you now see accounts for a lump sum tax. `BLDQuestion:`BLD Why is the purple budget line parallel to the original light red no tax budget line? `BLDAnswer:`BLD The lump sum tax reduces the income the household can spend. Recall that a change in income shifts the budget constraint in a parallel fashion. Continue to increase the lump sum tax by moving the scrollbar left until the revenue collected by the lump sum tax equals the revenue collected by the unit tax. Compare the utilities. `BLDQuestion:`BLD Which tax would the household prefer, unit or lump sum? Explain. ` Prob End """ } // Development specs ` ******** Problem X Start Screen - Intertemporal development // 0: Title // Problem mode: Contour line, Linear line, Optimize, Sub/Inc effects Substitution // 1: Problem mode: Sub/Inc effects // Visibility of utility coefficient and elasticity sliders N N // 2: Both, Slider only, Label only, None // Visibility of initial and new prices and income sliders: i Y0 Y1 B L L // 3: Both, Slider only, Label only, None // Result parameters Initial= Sub_Effect= Price_Comp= Inc_Effect New= // 4: Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map F F F // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes N -1.00 // 7: Initial value // Slider or mouse input S // 8: Slider, Mouse, None 0 120 1 20 // 9: Search slider specs More_compensation Just_right Less_compension // 10: Search slider advise // Text ` Text Start // 11: Text Dialogue ` Prob End // Lab mode: Utility Cost Work Savings Lump LumpSum // 0: Lab mode: Utility // Utility Parameters X Y // 1: Good X and good Y names .1 .9 .05 .4 // 2: Utility slider specs: Alpha 0 5.0 .2 0.8 // 3: Utility slider specs: Elasticity of substitution // Price and income parameters Px Py Inc // 4: Good price and income names .75 2.00 .25 1.00 // 5: Price of X slider specs .75 2.00 .25 1.00 // 6: Price of Y slider specs 10.00 20.00 2.50 20.00 // 7: Income slider specs // Use elasticity of substitution sigma or FW's substitutability parameter // NB: Not implemented E // 8: E or S // Demand elasticity/tax slider specs; used only by cost min and taxes X UnitTax= // 9: Slider prefix 0.0 3.00 0.20 0.0 // 10: Demand elasticity/tax slider specs // Graph parameters 0 0 30 20 // 11: Graph Data range: x0 y0 x1 y1 X Y // 12: Graph axis names `` Prob Specs ` ******** Problem 0 Start Screen 1 - Lump Sum Principle // 0: Title // Problem mode: IndiffCurve ContourLine LinearLine Optimize Sub/IncEffects LumpSum // 1: Problem mode: Lump sum principle // Visibility of utility coefficient and elasticity sliders N N // 2: Both, Slider, Label, Neither // Visibility of initial and new prices and income sliders L L L // 3: Both, Slider only, Label only, None // Result parameters Utility= _ _ _ _ // 4: Result names 2 // 5: Output decimal places // Graph parameters: Tangent, Secant, Contour map F F F // 6: True, False // Elasticity of demand/taxes - Used only by cost min and taxes B 0.0 // 7: Initial value // Slider or mouse input S // 8: Slider, Mouse, None 0 30 1 15 // 9: Search slider specs Decrease_lump_sum_tax:_Move_scrollbar_right Lump_sum_and_unit_tax_revenue_equal Increase_lump_sum_tax:_Move_scrollbar_left // 10: Search slider advise // Text ` Text Start // 11: Text `RED`BLDObjective:`BLD Illustrate the lump sum principle.`BLK Adjust the X UnitTax scrollbar to increase the tax on good X to $2.20 per unit. The light red curves on the diagram depict the no tax scenario and the red curves the tax case. How much tax revenue does the government collect? Note that a new scrollbar now appears below the graph. This new scrollbar allows you to impose a lump sum tax BEFORE the unit tax was imposed. Gradually adjust the scrollbar to the left. A purple budget constraint you now see accounts for a lump sum tax. The lump sum tax reduces the income the household can spend. Recall that a change in income shifts the budget constraint in a parallel fashion. As you can see, the purple budget constraint which accounts for the lump sum tax is parallel to the original light red no tax budget constraint. Continue to increase the lump sum tax by moving the scrollbar left until the revenue collected by the lump sum tax equals the revenue collected by the unit tax. Compare the utilities. Which tax would the household prefer? ` Prob End Household's Income and Substitution Effects