Homework Questions -
Show ALL work related to your calculations and graphs.
Q1. Cherry pie and Coffee budget constraint
a. Imagine you are one individual looking to purchase some of the only two goods in your economy, cherry pies and coffee. Your income is $90. You hear that the pies in town are the best in the country, so you buy one pie for the absorbitant price of $30. You have invited your entire class over for pie and coffee, so you stop by a café on your way home and purchase as many coffee cups as you can afford. They cost $3 per cup. How many coffee cups do you purchase?
b. Draw (by hand is fine) the budget constraint that corresponds to the situation in a graph with quantity of coffee on the vertical axis and quantity of pies on the horizontal axis.
c. The price of pies falls to $27 per pie. Since your income and the price of coffee remain the same, you purchase 12 cups of coffee. How many pies will you purchase? Draw a graph of this new budget constraint. How does the change in price and quanity of pies help illustrate your demand for pies?
Q2. Cherry pie demand
a. Your friend Helen B. Carter has left school to open a bakery. She has done some market research and finds that you and your neighbors value pies according to the following schedule:
|
Cherry Pie
|
P
|
|
1
|
$30.00
|
|
2
|
$27.00
|
|
3
|
$24.30
|
|
4
|
$21.87
|
|
5
|
$19.68
|
|
6
|
$17.71
|
|
7
|
$15.94
|
|
8
|
$14.35
|
|
9
|
$12.91
|
|
10
|
$11.62
|
|
11
|
$10.46
|
|
12
|
$9.41
|
|
13
|
$8.47
|
|
14
|
$7.63
|
Graph (carefully by hand or in excel) the demand curve for cherry pie. Does the demand curve have a positive or negative slope? Why?
b. How many pies will Helen sell at $19.68? How many at $10.46?
c. What will happen if a new doctor comes to town and tells everyone to lose weight? What will happen if people learn that Helen makes really delicious pies?
Q3. Cherry Pie Production
Helen makes pies using equipment that she rents for $500 and cherries and other ingredients that cost $2.66 a pie. She hires workers and finds that they produce pies according to the following schedule:
|
Pies
|
Workers
|
|
1
|
0.15
|
|
2
|
0.35
|
|
3
|
0.61
|
|
4
|
0.97
|
|
5
|
1.44
|
|
6
|
2.06
|
|
7
|
2.89
|
|
8
|
4.00
|
|
9
|
5.46
|
|
10
|
7.42
|
|
11
|
10.02
|
|
12
|
13.47
|
|
13
|
18.07
|
|
14
|
24.18
|
Workers are paid $16/hour.
a. Calculate and graph (by hand of in excel) the marginal cost of each pie. Why does the MC curve have the slope (up, down, or flat) that it does?
b. Calculate and graph the marginal cost of each pie if workers become 25% more productive, that is to say, if each pie can be made with only 75% as much labor. Calculate and graph marginal cost if workers get a raise to $18/hour, with the old productivity.
c. Put the demand and supply curves together (at the original productivity and wages). Helen assumes that she is in a perfectly competitive market. How many pies will she sell? At what price?
d. Draw the area of consumer surplus on your graph. Draw the area of producer surplus.
e. Calculate consumer surplus as the sum of the difference between the price and the marginal utility for each pie. Calculate producer surplus as the sum of the difference between price and marginal cost for each pie.