Question

1 A firm has fixed costs of $4,000. Its short-run production function is y = 4 x 2, where x is the amount of variable factor it uses. The price of the variable factor is $4,000 per unit. Where y is the amount of output, the short-run total cost function is a. 4,000 + 250 y². b. 8,000 y. c. 4,000+0.25 y² d. 4,000+4,000 y. e. 4,000 y + 4,000

Answer 1

The correct answer is option (c).

The short-run total cost function can be calculated as the sum of fixed costs and variable costs. In this case, the fixed costs are $4,000, and the variable cost per unit of the variable factor is $4,000.

So, the short-run total cost function (TC) is:

TC = Fixed Costs + (Variable Cost per Unit * Amount of Variable Factor)

TC = $4,000 + ($4,000 * x)

Now, we can use the production function y = 4x^2 to express x in terms of y:

x = sqrt(y/4)

Substitute this expression for x into the total cost function:

TC = $4,000 + ($4,000 * sqrt(y/4))

Simplify further:

TC = $4,000 + ($1,000 * sqrt(y))

So, the correct short-run total cost function is:

TC = $4,000 + $1,000 * sqrt(y)

This matches option (c):

c. 4,000 + 0.25y²