Question

1. Assume you are given the following equation (Y = 80-20X). The Y value represents Price while X value represents Quantity demanded for books.
   1. In the space below, neatly calculate the values of X when Y are 15, 10, 5, and 0. Work must be shown.
2. 2. Next, with the four data points calculated, neatly construct a graph below by drawing and labeling both axes (Price and Quantity Demanded). Now plot the four coordinates you have calculated from questions 2.a. to draw a line.
3. 2. With the same equation, what is the value of the slope and explain what does this number mean in terms of price and quantity demanded. Explain thoroughly. You must use the value to (slope value) to precisely explain.

Answer 1

a) Y = 80 - 20X

Putting Y = 15, 15 = 80 - 20X

20X = 80 - 15

X = 65/20 = 3.25 is the answer.

Putting Y = 10, 10 = 80 - 20X

20X = 80 - 10

X = 70/20 = 3.5 is the answer.  

Putting Y = 5, 5 = 80 - 20X

20X = 80 - 5

X = 75/20 = 3.75 is the answer.

Putting Y = 0, 0 = 80 - 20X

20X = 80

X = 4 is the answer.

c) Rewriting the above equation, X = (80 - Y) / 20

X = 4 - Y/20

X = 4 - 0.05Y

The slope of this function is calculated by differentiating the demand function with respect to price. So, differentiating X with respect to Y, slope = -0.05 is the answer. This means that if price of the commodity increases by 1 unit, its quantity demanded will decrease by 0.05 units.

b)