// LabDemFunctAndCurveSpecs.txt. 2/1/2023.

import Foundation`RED`BLDObjective:`BLD

class LabDemFunctAndCurveSpecs {

let strDemFunctAndCurveSpecs :String = """

`` Lab Specs

// Slider specs
50 100 10 100		// 0: Demand function constant
-5.0 -1.0 1.0 -2.0	// 1: Demand function coefficient
5 45 5 10		// 2: Price

// Graph specs
0 0 115 50		// 3: Min-max points
Q P			// 4: Names

`` Prob Specs

` Problem 0 Start
Screen 1 - Plotting the Demand Curve and the Demand Function	// 0: Title

// Slider specs
L L B			// 1: Function constant, function slope, price

F F F			// 2: Draw entire demand curve, initial point, calculate slope

` Text Start    	// 3: Dialogue
`RED`BLDObjective:`BLD Illustrate how the demand function allows us to plot the demand curve.`BLK

The demand curve answers a long series of hypothetical questions:
`INDIf the price were _______, what would the quantity demanded equal?
`IND
The demand function allows us to calculate the answers to these questions. In this lab, we specify the following demand function:
	Q = 100 - 2.0P
where
	Q = Quantity
	P = Price
	-2.0 = Price coefficient

Initially, the price equals $10. The equations above the graph show the algebra used to determine that if the price were $10, the quantity demanded would equal 80 units. We have found one point on the demand curve, the point representing a price of $10.

`BLDQuestion:`BLD How can we find another point?
`BLDAnswer:`BLD Choose another price.

Increase the price to $15 using the vertical scrollbar to the left of the graph. The equations above the graph now show the algebra used to determine that if the price were $15, the quantity demanded would equal 70 units. We have now found a second point on the demand curve. Also, all the points between the prices of $10 and $15 have been filled in.

Continue to adjust the price scrollbar to trace out the entire demand curve.
` Prob End

` Problem 1 Start
Screen 2 -The Demand Curve's Slope and the Demand Function's Price Coefficient	// 0: Title

// Slider spes
L L B			// 1: Function constant, function slope, price

T T T			// 2: Draw entire demand curve, initial point, calculate slope

` Text Start    	// 3: Dialogue
`RED`BLDObjective:`BLD Show that the slope of the demand curve is the reciprocal of the demand function's price coefficient.`BLK

We begin by recalling the general form for a linear function:
	Y = a + bX
where
	Y = Dependent variable
	X = Independent variable
	b = Independent variable's coefficient
The dependent variable, Y, depends on the independent variable, X. 

When we graph the general form of a linear function, we place X on the horizontal axis and Y on the vertical axis. The slope, rise over run, equals the independent variable's coefficient, b:
	Slope = Rise/Run = X coefficient = b

Now, we turn our attention to the demand curve and the demand function: 
	Q = 100 - 2.0P
where
	Q = Dependent variable
	P = Independent variable
	-2.0 = Independent variable's coefficient

Now, calculate the slope of the demand curve:
`IND`BLDDefinition:`BLD Slope equals the rise over the run.
`INDIncrease the price from $10 to $20 using the price scrollbar.
`IND`BLDQuestions:`BLD What does the
	`0x2022 rise equal?
	`0x2022 run equal?
	`0x2022 the slope equal?
`IND
We have a puzzle here. The price coefficient, the independent variables coefficient, equals -2.0, but the slope of the demand curve does not equal -2.0. Instead the slope equals -1/2, the reciprocal of -2.0.

To resolve this puzzle, look at the graph to the right again. The independent variable, P, is on the vertical instead of the horizontal axis and the dependent variable, Q, is on the horizontal instead of the vertical axis. When we graph a demand curve we switch the axes of the independent and dependent variables.

It makes sense that the slope of the demand curve is -1/2 rather than -2.0 doesn't it? Since we have switched the axes, we have in some sense switched rise over run. The slope of the demand curve equals the reciprocal of the demand function's price coefficient.
` Prob End

"""

}