Question

A firm has the following production function Y=K^0.25L^0.25. Total cost (TC) is given by TC=w_LL+w_KK+ZC, where w_L and w_K are prices of the two inputs L and K, and ZC are costs that the firm has to pay regardless of production volume as long as it is operative.

1. Derive total cost as a function of output C(Y). Derive marginal cost MC and average cost AC.
   
2. Assume that the firm is one of many identical ones operating on a perfectly competitive market that is in long run equilibrium. ZC is 1800 and w_L and w_K are both equal to 1. What are the price of the product and how much does each of the firms produce?
   
3. The same economy is inhabited by two different types of consumers. Type A consumers have the utility function U_A=yx, and Type B consumers U_B=[4ln⁡(yx)]³. y denotes how much the individual consumes of the good produced by the firms in a) and b) above and x represents consumption of another good. Both two types of consumers have an Income of I. State the demand function for good y for the two types of consumers.
   
4. If there are 20.000 units of Y sold in equilibrium, the consumers earn an income of 1200 each, and the price of good x is 60, how many consumers are there in total if
   1. There are only type A consumers in the economy
   2. There are only type B consumers in the economy
   3. 50% of the consumers are of type A and 50 % of type B.

Answer 1

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