Question

3) Suppose a firm’s cost function is C(q) = 3q2 (2 squared) + 15.

a. Find variable cost, fixed cost, average cost, average variable cost, and average fixed cost.(Hint: Marginal cost is given by MC = 6q.)

b. Find the output that minimizes average cost.

:4) Suppose that a firm’s production function is q = x0.5 in the short run, where there are fixed costs of $1,000, and x is the variable input whose cost is $1,000 per unit. What is the total cost of producing a level of output q? In other words, identify the total cost function C(q). Answer:

Answer 1

3.

A.

C(q) = 3*q^2 + 15

Variable cost = 3*q^2

Fixed cost = 15

Average cost = (1/q)*(3*q^2 + 15)

Average cost = 3*q + 15/q

Average variable cost = 3*q^2/q

Average variable cost = 3*q

Average Fixed cost = 15/q

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B.

AC = 3*q + 15/q

Differentiation of above equation with respect to x and setting it equal to zero.

3 - 15/q^2 = 0

3 = 15/q^2

q^2 = 15/3 = 5

q = 5^.5

q = 2.2360

So, at output level of q = 2.2360, average cost minimizes.

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4.

Fixed cost = $1000

Variable cost = $1000 per unit

So,

Total cost or C(q) = 1000 + 1000*q