// LabEdgeConsSpecs.swift. 11/13/2020. // MicroEconLab import Foundation class LabEdgeProdPossSpecs { let strLabEWBoxFirstTheorem :String = """ `` Lab Specs // Names of households and goods Smith Jones // 0: Household full names S J // 1: Household abbreviated names Good_X Good_Y // 2: Good full names X Y // 3: Good abbreviated names // Household utility function sliders 0.20 0.80 0.10 0.70 // 4: Smith Cobb-douglas production exponents 0.20 0.80 0.10 0.30 // 5: Jones Cobb-douglas production exponents // Household endowment sliders 20 240 20 220 // 6: Smith Good X endowments 20 240 20 40 // 7: Smith Good Y endowments 20 240 20 80 // 8: Jones Good X endowments 20 240 20 160 // 9: Jones Good Y endowments `` Prob Specs ` ****** Problem 0 Start Screen 1 - Edgeworth Box Geometry: Smith // 0: Title // Type of lab C // 1: Contract curve, First theorem, Second theorem // Slider scrollbar and slider label visibility N N L // 2: Smith utility, Jones utility, Endowments // Point visibility F T F // 3: Endowment point, mouse point Smith, mouse point Jones // Curve visibility F F F F F // 4: Contract curve, EndowSmith isoquant, EndowJones isoquant // MouseSmith isoquant, MouseJones isoquant // Better than set visibility F F F F // 5: Endowment base Smith, Endowment base Smith // Mouse base Smith, Mouse base Smith ` Text Start // 6: Text `RED`BLDObjective:`BLD Show how a point in the Edgeworth box represents an allocation of good X and good Y for Smith.`BLK `BLDSetting the stage:`BLD The width of the box is 200 and the height 300. This reflects the endowments of Smith and Jones: `0x2022 Good X endowments: Smith 220 units, Jones 80 units - a total of 300 units. `0x2022 Good Y endowments: Smith 40 units, Jones 160 units - a total of 200 units. Using your mouse's left button, drag Smith's red allocation point around the Edgeworth box. Observe how the quantities of good X and good Y allocated to Smith change as you drag the point around the box. ` ****** Problem 0 End ` ****** Problem 1 Start Screen 2 - Edgeworth Box Geometry: Jones // 0: Title // Type of lab C // 1: Contract curve, First theorem, Second theorem // Slider visibility // Slider scrollbar and slider label visibility N N L // 2: Smith utility, Jones utility, Endowments // Point visibility F F T // 3: Endowment point, mouse point Smith, mouse point Jones // Curve visibility F F F F F // 4: Contract curve, EndowSmith isoquant, EndowJones isoquant // MouseSmith isoquant, MouseJones isoquant // Better than set visibility F F F F // 5: Endowment base Smith, Endowment base Smith // Mouse base Smith, Mouse base Smith ` Text Start // 6: Text `RED`BLDObjective:`BLD Show how a point in the Edgeworth box represents an allocation of good X and good Y for Jones.`BLK Note that Jones's origin is the upper right hand corner of the Edgeworth box rather than the lower left. While this may seem a little strange, we will see that it serves a good purpose. Using your mouse's left button, drag Jones's blue allocation point around the Edgeworth box. Remember that the upper right hand corner of the box represents Jones's origin. Observe how the quantities of good X and good Y allocated to Jones change as you drag the point around the box. ` ****** Problem 1 End ` ****** Problem 2 Start Screen 3 - Edgeworth Box Geometry: Smith and Jones Together // 0: Title // Type of lab C // 1: Contract curve, First theorem, Second theorem // Slider visibility // Slider scrollbar and slider label visibility N N L // 2: Smith utility, Jones utility, Endowments // Point visibility F T T // 3: Endowment point, mouse point Smith, mouse point Jones // Curve visibility F F F F F // 4: Contract curve, EndowSmith isoquant, EndowJones isoquant // MouseSmith isoquant, MouseJones isoquant // Better than set visibility F F F F // 5: Endowment base Smith, Endowment base Smith // Mouse base Smith, Mouse base Smith ` Text Start // 6: Text `RED`BLDObjective:`BLD Show how each point in the Edgeworth box represents one way to divide 200 units of good X and 300 units of good Y between Smith and Jones. That is, each point represents one allocation of good X and good Y for Smith and Jones.`BLK Using your mouse's left button, drag the black allocation point around the Edgeworth box. Each point in the box represents one way to divide the 200 units of good X and 300 units of good Y between Smith and Jones. ` ****** Problem 2 End ` ****** Problem 3 Start Screen 4 - Indifference Curves and Better Than Sets: Smith // 0: Title // Type of lab C // 1: Contract curve, First theorem, Second theorem // Slider scrollbar and slider label visibility L N L // 2: Smith utility, Jones utility, Endowments // Point visibility F T F // 3: Endowment point, mouse point Smith, mouse point Jones // Curve visibility F F F T F // 4: Contract curve, EndowSmith isoquant, EndowJones isoquant // MouseSmith isoquant, MouseJones isoquant // Better than set visibility F F T F // 5: Endowment base Smith, Endowment base Smith // Mouse base Smith, Mouse base Smith ` Text Start // 6: Text `RED`BLDObjective:`BLD Illustrate Smith's indifference curves and better than sets in the Edgeworth box.`BLK Some new items have appeared in the lab window: `0x2022 Smith's indifference curve. `0x2022 Smith's better than set. `0x2022 Smith's utility and marginal rate of substitution (MRS). Using your mouse's left button, drag Smith's red allocation point around the Edgeworth box. Observe Smith's indifference curve and better than sets. `BLDQuestions:`BLD When you drag the allocation point to the northeast, what happens to Smith's `0x2022 consumption of good X? `0x2022 consumption of good Y? `0x2022 utility? `BLDQuestions:`BLD When you drag the allocation point to the southwest, what happens to Smith's `0x2022 consumption of good X? `0x2022 consumption of good Y? `0x2022 utility? ` ****** Problem 3 End ` ****** Problem 4 Start Screen 5 - Indifference Curves and Better Than Sets: Jones // 0: Title // Type of lab C // 1: Contract curve, First theorem, Second theorem // Slider scrollbar and slider label visibility N L L // 2: Smith utility, Jones utility, Endowments // Point visibility F F T // 3: Endowment point, mouse point Smith, mouse point Jones // Curve visibility F F F F T // 4: Contract curve, EndowSmith isoquant, EndowJones isoquant // MouseSmith isoquant, MouseJones isoquant // Better than set visibility F F F T // 5: Endowment base Smith, Endowment base Smith // Mouse base Smith, Mouse base Smith ` Text Start // 6: Text `RED`BLDObjective:`BLD Illustrate Jones's indifference curves and better than sets in the Edgeworth box.`BLK Some new items have appeared in the lab window: `0x2022 Jones's indifference curve. `0x2022 Jones's better than set. `0x2022 Jones's utility and marginal rate of substitution (MRS). Note that Jones's origin is the upper right hand corner of the Edgeworth box rather than the lower left. Therefore, Jones's indifference curves are bowed in toward the upper right corner and the better than sets lie southwest of the indifference curve. Using your mouse's left button, drag Jones's blue allocation point around the Edgeworth box. Observe Jones's indifference curve and better than sets. `BLDQuestions:`BLD When you drag the allocation point to the southwest, what happens to Jones's `0x2022 consumption of good X? `0x2022 consumption of good Y? `0x2022 utility? `BLDQuestions:`BLD When you drag the allocation point to the northeast, what happens to Jones's `0x2022 consumption of good X? `0x2022 consumption of good Y? `0x2022 utility? ` ****** Problem 4 End ` ****** Problem 5 Start Screen 6 - Intersection of the Better Than Sets: Pareto Region // 0: Title // Type of lab C // 1: Contract curve, First theorem, Second theorem // Slider scrollbar and slider label visibility L L L // 2: Smith utility, Jones utility, Endowments // Point visibility T T T // 3: Endowment point, mouse point Smith, mouse point Jones // Curve visibility F T T T T // 4: Contract curve, EndowSmith isoquant, EndowJones isoquant // MouseSmith isoquant, MouseJones isoquant // Better than set visibility T T F F // 5: Endowment base Smith, Endowment base Smith // Mouse base Smith, Mouse base Smith ` Text Start // 6: Text `RED`BLDObjective:`BLD Show that the green Pareto region within the Edgeworth box represents Pareto moves, the allocations at which both Smith and Jones become better off.`BLK The green region, the intersection of the better than sets, illustrates all the possible Pareto moves. The allocations that would make both Smith and Jones better off. Drag the black endowment point into the green Pareto region. Note that the endowments of Smith and Jones are denoted by the gray endowment point. ` ****** Problem 5 End ` ****** Problem 6 Start Screen 7 - Contract Curve // 0: Title // Type of lab C // 1: Contract curve, First theorem, Second theorem // Slider scrollbar and slider label visibility L L L // 2: Smith utility, Jones utility, Endowments // Point visibility T T T // 3: Endowment point, mouse point Smith, mouse point Jones // Curve visibility T T T T T // 4: Contract curve, EndowSmith isoquant, EndowJones isoquant // MouseSmith isoquant, MouseJones isoquant // Better than set visibility F F T T // 5: Endowment base Smith, Endowment base Smith // Mouse base Smith, Mouse base Smith ` Text Start // 6: Text `RED`BLDObjective:`BLD Illustrate the relationship between the contract curve and the indifference curves of Smith and Jones.`BLK Note that a new curve has appeared in the Edgeworth box connecting Smith's origin with Jones's origin. As we will see, this is the contract curve. `BLDDefinition:`BLD Contract curve: All the allocations that are efficient. That is, all the allocations at which it is impossible to make one household better off without making the other worse off. Geometrically, the contract curve are all the allocations at which the indifference curves are tangent. Focus on the black allocation point and note that the indifference curves are not tangent. When the indifference curves are not tangent it is possible to make both consumers better off. Recall that the green Pareto region is the intersection of Smith's and Jones's better than sets, the allocations what make both Smith and Jones better off. Use your mouse to drag the black allocation point gradually into the green Pareto region, the intersection of Smith's and Jones's better than sets. When you do so, the utilities of both household increase. Therefore, when the indifference curves intersect, the allocation is not on the contract curve. `BLDQuestion:`BLD Why does the green Pareto region shrink as you drag the black allocation point into it? Continue to drag the black allocation point gradually into the shirking green region. What happens when you reach the contract curve? More specifically, when you reach the contract curve is it possible to make one household better off with making the other worse off? Explain. `BLDQuestions:`BLD When you reach the contract curve `0x2022 Are Smith's and Jones's indifference curves tangent or do they intersect? `0x2022 How are Smith's and Jones's marginal rates of substitution related? ` ****** Problem 6 End ` ****** Problem 7 Start Screen 8 - First Theorem of Welfare Economics // 0: Title // Type of lab F // 1: Contract curve, First theorem, Second theorem // Slider scrollbar and slider label visibility L L L // 2: Smith utility, Jones utility, Endowments // Point visibility T T T // 3: Endowment point, mouse point Smith, mouse point Jones // Curve visibility T T T T T // 4: Contract curve, EndowSmith isoquant, EndowJones isoquant // MouseSmith isoquant, MouseJones isoquant // Better than set visibility F F F F // 5: Endowment base Smith, Endowment base Smith // Mouse base Smith, Mouse base Smith ` Text Start // 6: Text `RED`BLDObjective:`BLD Illustrate the first theorem of welfare economics: A Walrasian equilibrium is Pareto optimal.`BLK Observe the changes in the lab window: a price ratio scrollbar and a new dark green line in the Edgeworth box. The dark green line represents the budget constraint of Smith and Jones based on the price ratio. The utility maximizing bundles of Smith and Jones appear as red and green points in the box. The excess demands for goods X and Y are reported immediately below the price ratio scrollbar. Check to be certain that the excess demands are being calculated correctly. The current price ratio is not an equilibrium since the excess demands are not 0. Adjust the price ratio scrollbar to find the equilibrium price ratio, the price ratio at which the excess demands of both goods equal 0. `BLDQuestions:`BLD `0x2022 Does the Walrasian equilibrium lie on the contract curve? `0x2022 Does this confirm the first theorem of welfare economics? Explain. ` ****** Problem 7 End ` ****** Problem 8 Start Screen 9 - Second Theorem of Welfare Economics // 0: Title // Type of lab S // 1: Contract curve, First theorem, Second theorem // Slider scrollbar and slider label visibility L L L // 2: Smith utility, Jones utility, Endowments // Point visibility F T T // 3: Endowment point, mouse point Smith, mouse point Jones // Curve visibility T F F T T // 4: Contract curve, EndowSmith isoquant, EndowJones isoquant // MouseSmith isoquant, MouseJones isoquant // Better than set visibility F F T T // 5: Endowment base Smith, Endowment base Smith // Mouse base Smith, Mouse base Smith ` Text Start // 6: Text `RED`BLDObjective:`BLD Confirm the second theorem of welfare economics: Any Pareto optimal allocation is a Walrasian equilibrium for an appropriate price ratio and set of endowments.`BLK We will now describe a two step procedure to find a price ratio and set of endowments that will produce a Walrasian equilibrium for a specified Pareto optimal allocation. Our example is the dark green allocation now appearing on the contract curve. Step 1: Assume the Pareto optimal allocation is also the endowment allocation. This is reflected in the reported endowments of Smith and Jones appearing in the lab window: `0x2022 Good X and Y endowment for Smith: 110 and 152. `0x2022 Good X and Y endowment for Jones: 190 and 48. The dark green budget line in the box represents the budget constraints of Smith and Jones for the current price ratio. Step 2: The current price ratio is not an equilibrium since the excess demands for good X and good Y are not 0. Adjust the price ratio scrollbar to find the equilibrium price ratio, the price ratio at which the excess demands of both goods equals 0.0. We have now found a Walrasian equilibrium. Note that the dark green budget line has turned black. This indicates that this price ratio is not only an equilibrium for the original dark green endowment allocation, but also for every endowment allocation lying on the black budget line. This confirms the second theorem of welfare economics. Confirm the theorem for a different Pareto optimal allocation by using your mouse's left button to drag the dark green Pareto optimal allocation to a different location on the contract curve. Again, adjust the price ratio scrollbar to confirm the second theorem. ` ****** Problem Screen 9 End """ }