Problem Set 5
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PROBLEM SET 5 QUESTION 1 A firm has Cobb-Douglas production function Q = 10L ½ K ½ . How much of inputs K* and L* will the firm demand to maximise output, if the total cost of production is 100 where the price of labour, w, is 4 and the price of capital, r, is 10? QUESTION 2 A firms production function is given as q=16L 1/2 K 1/2 and w=16 and r=1 a) In what ratio will the firm use L and K? b) What are the input demand functions (K* and L*) c) What is the cost function? QUESTION 3 Suppose the production function is Q = min{L, K}, the market wage w = 1, and the rental rate of capital is r = 1. 1. What type of production technology is this? 2. What is the cost minimizing input bundle for producing Q = 10 units? 3. What is the minimum cost? QUESTION 4 Suppose variable cost is Q 3 and that fixed cost is 10. Solve for the following: 1. Total Cost 2. Average Total Cost 3. Average Variable Cost 4. Average Fixed Cost 5. Marginal Cost 6. The firms profit if the market price for output is equal to p. 7. The firms supply function if the market price for output is equal to p.
description
microeconomics
Transcript of Problem Set 5
PROBLEM SET 5
QUESTION 1 A firm has Cobb-Douglas production function Q = 10L½ K½ . How much of inputs K* and L* will the firm demand to maximise output, if the total cost of production is 100 where the price of labour, w, is 4 and the price of capital, r, is 10? QUESTION 2 A firms production function is given as q=16L1/2K1/2 and w=16 and r=1
a) In what ratio will the firm use L and K? b) What are the input demand functions (K* and L*) c) What is the cost function?
QUESTION 3 Suppose the production function is Q = min{L, K}, the market wage w = 1, and the rental rate of capital is r = 1.
1. What type of production technology is this? 2. What is the cost minimizing input bundle for producing Q = 10 units? 3. What is the minimum cost?
QUESTION 4
Suppose variable cost is Q3 and that fixed cost is 10. Solve for the following:
1. Total Cost 2. Average Total Cost 3. Average Variable Cost 4. Average Fixed Cost 5. Marginal Cost 6. The firms profit if the market price for output is equal to p. 7. The firms supply function if the market price for output is equal to p.
