Question

Mark is a farmer that grows corn using fertilizer and a fixed input. The production process can be described by this relationship q(F,K) =5F^0.50K^0.25, where F is fertilizer and K is fixed at 81. The price of fertilizer is 4.0 per kg and the price of the fixed input is 4.0 per unit. Calculate the total cost of producing 30 units of output. Round your answer to one decimal place.

If Mark doubles his output, how will his total variable cost change? Explain your answer. (You may recalculate your total variable cost with the new output level, but I am not looking for calculations. I am looking for a general prediction that can be made without any calculations.)

Answer 1

Ans

a) Production function, q = 5F^0.5 * K^0.25

at K = 81 units,

q = 15*F^0.5

=> F = (q/15)^2

Thus, at cost of $4 per unit of capital and $4 per kg of fertilizer, the total cost is,

C = 4*(q/15)^2 + 4*81

Thus, when q = 30 units,

C = 4*(30/15)^2 + 4*81

C = 16 + 324

=> C = $340

When q is doubled, the variable cost will become four times because quantity of fertilizers depends on the square of the total output (q), thus the new variable cost will be = 4* 16 = $64

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