1. Consider the cost function:
C = 60 + 20Q + 30Q^2
with MC = 20 +60Q (here Q denotes output)
Part A) Write down the expression for the average cost.
Part B) What is the output elasticity of the total cost at output level of Q = 1 ?
Part C) At an output of 1, does the cost function exhibit economies of scale, diseconomies of scale or neither?
2. Duane breeds parrots for a living. He has discovered that the production function of parrot chicks, Q is:
Q = 0.4K^0.5*L^0.5 (where K is the amount of capital (cages, etc.) and L is the amount of parrot food). From this, Cobb-Douglas production function MP (of L) = 0.2K^0.5*L^-0.5 and MP (of K) = 0.2K^-0.5*L^0.5. The price of K is $8.00 and the price of L is $2.00.
Part A) Suppose Duane wants 144 parrot chicks, how much capital and food should be used to minimize cost and what is the cost of producing that amount of chicks?
Part B) Suppose that Duane is faced with the same problem as in Part (A) except that he has a fixed amount of capital, K = 16. How much food should be used to minimize cost and what is total cost?
Calculations provided for you.