Question

# 1. Juan has just started a taco restaurant. In order to enter the business he had to pay a sunk cost of 2, that

is, the total value of the time he spent learning tacos recipes. In addition he needs to pay for labor and capital. The wage rate he has to pay is 14, and the rental rate of each unit of capital is 1. Juan knows that his production function is given by q=K1/3L1/3

In the short run the units of capital that Juan has are fixed and equal to 3. Find the short run total cost function. (Exclude the sunk costs from this function.) To verify that you have found the correct short-run total cost function, compute the short-run total cost of producing 30 tacos.

TC(30)=

2. Now, let's consider a time horizon long enough such that producers like Juan can adjust the level of capital, although they still have to pay the sunk cost of 2 in order to learn the recipes. Assuming that they face the same price for labor (w=14) and for the rental rate of capital (r=1), find the long run total cost production function in this market. (Exclude the sunk costs in this function.) To verify that you have found the correct long-run total cost function, compute the long-run total cost of producing 30 tacos

TC(30)=

3. You make very tasty hot dogs. You can do hot dog business in two potential monopoly markets: one inside Fenway Park, Boston's baseball stadium, and one inside TD Garden, the home arena for Boston's ice hockey team, the Bruins, and basketball team, the Celtics. The demand for hot dogs in each game in Fenway Park is QFenway=100−5p and the demand for hot dogs per game in TD Garden is QTD=50−5p. You need to pay 100 dollars per game for renting the space in each market. The cost of making a hot dog is 2 dollars. Assume that you can sell fractions of hot dogs

What will the price of hot dogs in each market be if you enter both markets?

a. pFenway=

b. pTD=

4.Now suppose that Fenway Park has space for another potential hot dog seller, who can make the same hot dogs with the same marginal cost as you and has to pay the same amount of rent. Customers will always buy from the cheaper seller, but when the price is the same, they are indifferent and buy randomly (that is, each seller gets half of the customers). In the questions that are part of this problem, assume hot dog sellers are competing over price (not quantity).

If you and the other hot dog seller agreed to charge the same price that maximizes each's profit, what would this price be?

a. p=

b. What would your (alone, not combined) profit be?

π=

(Express loss as a negative profit.)

c. How much will you charge?

(Assume that you can set the price down to cents (hundredths of a dollar)

d. What will your profit be?

(Round to the nearest cent.)

e. And what will the profit of the other seller be?

(Round to the nearest cent.)

5.Suppose both of you are operating in the market. Find the price of hot dogs such that if you and the other seller have no agreement on what price to charge, both of you acting in your own best interest charge the same price.

a. p=

b. What will the profit for each of you be?

π=

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