# Problem set on Production and Cost

PROBLEM SET #2 (Due 10/29 at 2359hrs)

1. Production and Cost The following represents the output per worker for kite production. Assume fixed plant size (constant capital), with a fixed cost of \$20. A kite sells for \$10; unskilled workers earn \$5/hour and skilled workers earn \$15/hour. Assume for simplicity that workers work one hour.

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UNSKILLED WORKERS

Worker

Total Product (per hour)

1 5

2 8

3 10

4 11

5 12

6 12

SKILLED WORKERS

Worker Product (per hour)

Total Product (per hour)

1 8

2 14

3 19

4 22

5 24

6 25

a) Assuming there are only unskilled workers, how many workers will the firm hire to maximize profit? Why? What are the firm’s Total Cost, Total Revenue, and Profit?

b) Assume there are both unskilled and skilled workers, working in separate factories (each with the same fixed cost). How many workers of each kind will the firm hire to maximize profit? Why? What are the firm’s Total Cost, Total Revenue, and Profit?

c) Assume the government imposes a minimum wage of \$11/hr. How many unskilled workers and skilled workers, will the firm hire, in order to maximize profit? What are the firm’s Total Cost, Total Revenue, and Profit?

2. Revenue and Elasticity Amazon.com is trying to increase its total revenue. It explores a 10% discount on its products. Based on internal research, amazon knows that its customers can be divided into two distinct groups (Prime and Others). The following table shows how the two groups respond to the discount (amounts are sales/week). Assume that all products sold cost the same (production and price).

a) Calculate the price elasticity of demand for Prime Customers and for Others.

b) Explain how the discount will affect total revenue from each group.

c) In order to maximize revenue, should discounts be offered to Prime Customers only, to Others only, to neither, or to both? Why?

3. Price Discrimination A ski resort caters to both out-of-town skiers and local skiers. The demand for lift tickets for each market segment is independent of the other market segment. The marginal cost of servicing a skier of either type is \$40. The demand formulas for the two market segments are:

Out-of-towners: Qo=1000-5P Locals: QL=1000-10P

(a) Assume that the resort charges one price to all skiers. What is the total demand curve? What is the profit-maximizing price? How many tickets will be sold to each group? What are the total revenue, total cost, and profit from the two combined markets?

Amazon Prime Customers

Others

Volume of sales before the 10% discount

1.50 million 1.55 million

Volume of sales after the 10% discount

1.70 million 1.65 million

(b) Assume that the resort charges a different price to locals than it does to out-of-town skiers. What is the profit-maximizing price for each group of consumers? How many tickets will be sold to each group? What is the combined profit with price discrimination? Show all calculations.

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