Pecan pie demand. Your friend Helen B. Carter

Pecan pie demand. Your friend Helen B. Carter has left school to open a bakery. She has done some market research and finds that your neighbors value pies according to the following schedule:

Pecan pie MU
1 $40.00
2 $36.00
3 $32.40
4 $29.16
5 $26.24
6 $23.62
7 $21.26
8 $19.13
9 $17.22
10 $15.50
11 $13.95
12 $12.55
13 $11.30
14 $10.17

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a. (2 points) Graph the demand curve for pecan pie. Does the demand curve have a positive or negative slope? Why?

b. (1 point) How many pies will Helen sell at $19.13? How many at $29.16?

c. (1 point) 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?

2. (4 points) Production. Helen makes pies using equipment that she rents for $20 and pecans and other ingredients that cost $4.66 a pie. She hires workers and finds that they produce pies according to the following schedule:

Pies Workers
1 0.25
2 0.58
3 1.02
4 1.61
5 2.40
6 3.44
7 4.82
8 6.66
9 9.11
10 12.36
11 16.69
12 22.45
13 30.11
14 40.30

Workers are paid $12/hour.

a. (2 points) Calculate and graph the marginal cost of each pie. Show your calculations! Why does the MC curve have the slope (up, down, or flat) that it does?
b. (2 points) Calculate and graph the marginal cost of each pie if workers become more productive, that is to say, if each pie can be made with only 80% as much labor. Show your calculations! Calculate and graph marginal cost if workers get a raise to $18/hour, with the old productivity.

3. (4 points) Perfect competition and equilibrium.
a. (1 point) 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?
b. (1 point) Draw the area of consumer surplus on your graph. Draw the area of producer surplus.
c. (2 points) 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.

4. (6 points) Monopoly and equilibrium
a. (2 points) Helen gets smart and realizes that she is the only pie shop around. Calculate the marginal revenue she gets for each additional sale as the change in total revenue (price times sales). Graph this and show the new quantity of sales and the new price.

b. (1 point) Draw the area of consumer surplus on your graph. Draw the area of producer surplus.
c. (2 points) 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.
d. (1 point) Compare the sum of consumer and producer surplus for the monopoly with the results for perfect competition. Which is better for consumers? Which is better for producers? Which is better for society?

5. (2 points) Moving Equilibrium. Show the effect of each on the monopoly market equilibrium; you don’t need to have exact answers but explain the direction of change in the demand and/or marginal cost curves.
a. (0.5 points) Pecan prices rise..
b. (0.5 points) Helen gets her oven for free.
c. (0.5 points) More people see Sweeney Todd and are scared of pie shops.
d. (0.5 points) More people see Sweeney Todd and more people are curious about Helen’s pies.