Question

• (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 not get 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:

Servings	Total Workers
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

• (1 point) Calculate and graph the additional workers 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?
• (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?

• (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?

• (5 points) Perfect competition and equilibrium.
  • (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?
  • (2 points) Draw the graph again and shade in the entire area of consumer surplus. Shade in the entire area of producer surplus.

• (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?

  serving	MU Duck
  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

    

Answer 1

ANSWER:

Summarized the information and data provided in the question; Beyoncé uses equipment that she rents for $1000 and ingredients that cost $9.95 a serving for the first 6 servings- - - - - - -

1) Marginal Productivity of Labor is going down as more and more workers are added as is depicted by the graph attached. Clearly, more additional workers are required to produce more serving as the production increases.

3 st Servings Total Workers Additional Worker needed 1 0.75 2 1.58 0.83 3 2.48 0.9 4 3.48 1 5 4.58 1.1 6 5.79 1.21 7 7.12 1.33 8 8.58 1.46 9 10.18 1.6 10 11.95 1.77 7 00 Additional Worker needed N 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 O 0 N 4 6 CO 10 12

2)Marginal Cost curve has a upward slope as Marginal Productivity of Labor(MPL) is lower as production increases. Hence, more additonal cost incurred as more servings are produced. As long as MPL decreases with increase in production, the MC curve will have slope upwards, as is evident from the data provided. Ideally, if the production is expanded beyond the data provided (10 servings), the MC curve should flatten and then slope downwards as the production achieves economies of scale.

Servings Additional Cost Additional Labor Cost Marginal Cost 1 9.95 2 9.95 10.79 20.74 3 9.95 11.7 21.65 4 9.95 13 22.95 9.95 14.3 24.25 6 9.95 15.73 25.68 7 8.95 17.29 26.24 8.95 18.98 27.93 9 8.95 20.8 29.75 10 8.95 23.01 31.96 UT 6 00 Marginal Cost 35 30 25 20 15 10 5 0 0 2 st 6 8 10 12

3) As an employer, We want higher labor producitivty(lower costs) and higher profits, so the second scenario is preferred. As an employee, Higher wages is demanded, so the second scenario is preferred. As a society (the social welfare), it is the result of benefits gained by the employer and employee as a whole, and aims to increase the efficiency of the inputs used to produce outputs. So the second scenario one with higher productivity is preferred.

2 Servings Total Workers Additional Worker needed 1 0.6 2 1.264 0.664 3 1.984 0.72 4 2.784 0.8 5 3.664 0.88 6 4.632 0.968 7 5.696 1.064 6.864 1.168 9 8.144 1.28 10 9.56 1.416 5 00 Additional Worker needed (higher wage and higher productivity) 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 N 4 6 8 10 12

Servings Additional Cost Additional Labor Cost Marginal Cost 1 9.95 2 9.95 10.79 20.74 3 9.95 11.7 21.65 4 9.95 13 22.95 5 9.95 14.3 24.25 6 9.95 15.73 25.68 7 8.95 17.29 26.24 8 8.95 18.98 27.93 9 8.95 20.8 29.75 10 8.95 23.01 31.96 LC 8 Marginal Cost (higher wage and higher productivity) 35 30 25 20 15 10 5 0 0 N 4 6 8 10 12

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