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Posted: February 26th, 2022
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Problem Set 1
For graphs, it is often best to use Excel or draw your graph and print the picture
Total 15 points.
1. (5 points) Made the right way duck a l’orange is the most delicious thing ever. Your friend Beyoncé has abandoned her music career to open an Tab Cat Bistro, which specializes in French cuisine. She has done some market research and finds that your neighbors value duck according to the following schedule:
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serving
MU Duck
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1
$45.00
2
$42.75
3
$40.61
4
$38.58
5
$36.65
6
$34.82
7
$33.08
8
$31.43
9
$29.85
10
$28.36
Image result for Beyoncé cooking
https://www.phaidon.com/resource/duck-a-lorange.jpg
a. (2 points) Graph the demand curve for duck. Does the demand curve have a positive or negative slope? Why?
b. (2 points) How many servings will Beyoncé sell at $38.58? How many at $40.61? At $29.85?
c. (1 point) What will happen to the demand curve if a new study comes out showing duck increases the risk of heart disease? What will happen to the demand curve if instead a study comes out showing they reduce the risk of dementia?
2. (5 points) Production. Beyoncé uses equipment that she rents for $1000 and ingredients that cost $9.95 a serving for the first 6 servings; for additional servings, she can buy the ingredients at a discount for $8.95. (She does any discount on the first five servings!) (Note that she signed a lease and pays the rent regardless of how many dinners she serves; note that regardless of how much ingredients she buys for additional servings, she pays $9.95 for the ingredients for the first 6.) She hires workers at $13 each and finds that they produce servings according to the following schedule:
A picture containing food Description automatically generated
Servings
Total Worker Hours
1
0.75
2
1.58
3
2.48
4
3.48
5
4.58
6
5.79
7
7.12
8
8.58
9
10.18
10
11.95
a. (1 point) Calculate and graph the additional worker hours needed for each serving. (Use a spreadsheet!) What is happening to the marginal productivity of labor as more is produced and more workers are hired?
b. (2 points) Calculate and and graph the marginal cost of each serving. (Use a spreadsheet and show your calculations!) Why does the MC curve have the slope (up, down, or flat) that it does? What happens to the slope of the MC curve as Beyonce produces more and more servings? Why?
c. (2 points) Calculate and graph the marginal cost of each serving if workers get a raise to $16.25/hour, with the old productivity. What happens if they also become more productive so each serving can be made with only 80% as much labor. Show your calculations! Compare the results of high wages and high productivity with the initial situation. Which would you prefer as an employer? Which would you prefer as worker? Which is better for society?
3. (5 points) Perfect competition and equilibrium.
a. (1 point) Put the demand and supply curves together (at the original productivity and wages). Beyoncé is a musician and never took Economics so she naively assumes that she is in a perfectly competitive market. How many servings will she sell? At what price?
b. (2 points) Draw the graph again and shade in the entire area of consumer surplus. Shade in the entire area of producer surplus.
c. (2 points) Calculate consumer surplus as the sum of the difference between the marginal utility and the price for each serving up to the last sold. Calculate producer surplus as the sum of the difference between price and marginal cost for each serving. What is the dollar value of consumer surplus? What is the dollar value of the producer surplus? What is the dollar value of the total social surplus?
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