Duane breeds parrots for a living. He has discovered that the production function for parrot chicks (Q) is:
Q = K^1/2L^1/2
where K is capital (for example nest boxes, cages and the like) and L is parrot food. The marginal products of capital and labor are as follows:
MP_K = .5K^-1/2L^1/2 MP_L = .5K^1/2L^-1/2
The price of K is $8 and the price of L is $2.
a. What type of production function is this?
b. Does this production function exhibit constant, increasing or decreasing returns to scale? Explain.
c. What is the average product of capital?
d. Does capital obey the "law of diminishing returns?" Explain.
e. Suppose that Duane wants 144 parrot chicks, how much K and L should be employed to minimize costs, and what is the cost of producing 144 parrot chicks?
f. Suppose that Duane is faced with the same problem as in (f) except that he has a fixed amount of K. In fact, K = 16. How much L should be employed to minimize costs, and what is the total cost?

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The Answer of Duane breeds parrots for a living. He has discovered that the production function for parrot chicks (Q) is: Q = K^1/2L^1/2 where K is capital (for example nest boxes, cages and the like) and L is parrot food. The marginal products of capital and labor are as follows: MP_K = .5K^-1/2L^1/2 MP_L = .5K^1/2L^-1/2 The price of K is $8 and the price of L is $2. a. What type of production function is this? b. Does this production function exhibit constant, increasing or decreasing returns to scale? Explain. c. What is the average product of capital? d. Does capital obey the "law of diminishing returns?" Explain. e. Suppose that Duane wants 144 parrot chicks, how much K and L should be employed to minimize costs, and what is the cost of producing 144 parrot chicks? f. Suppose that Duane is faced with the same problem as in (f) except that he has a fixed amount of K. In fact, K = 16. How much L should be employed to minimize costs, and what is the total cost?

Duane Breeds Parrots for a Living