1.Suppose the production function of the fishing industry is q = 60L 0.4 K 0.7 F

Question

1.Suppose the production function of the fishing industry is q = 60L0.4 K0.7
Find the marginal product of capital. Show how capital is subject to the law of
diminishing marginal returns.

2.Suppose the market for lemonade is a competitive market.The prevailing
market price is $10. A typical seller in the market has a cost function of:
C = q3 - 6q2 + l0q + 100
a.   Find its profit-maximizing output level. Calculate her profit.

b.   What is the lowest price a typical seller is willing to accept in the short
run? Explain with calculation.

c.   Given the result in (a), what will happen to the market price in the long
run? Explain briefly in words.   

3. Some economists believe that world market for some raw materials(like cotton) comes close to a perfectly competitive market.

With reference to the world market for cotton,briefly explain THERE reasons why the world market for cotton comes close a perfectly competitive market.

Explanation / Answer

q = 60L0.4 K0.7

For marginal productivity of capital take derivative of q with respect to K

MPk = dq/dK= 0.7*60L0.4 * K-0.3 = 0.7*60L0.4 / K0.3

For K=1 q= 0.7*60L0.4 / 10.3                                                      (1)

For K=2 q= 0.7*60L0.4 / 20.3                                            (2)

For K=2 q= 0.7*60L0.4 / 30.3                                            (3)

Ratio (1) / (2)

= 0.7*60L0.4 / 10.3 / 0.7*60L0.4 / 20.3

=20.3 / 10.3

This means that output for K=1 is greater than output for K=2, this shows that additional unit of capital gives diminishing returns to the firm.

In similar way we can go on with substituting values for K=1,2,3,4,…..

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