Question

Given the following Cost Function: C(q) = 100 + 50q – 10q + q^3. Find the equations for Total Variable Costs, Average Variable costs, and Marginal Costs.

Suppose the Value of the firm is given by 14t1+rt , where the expected profit is 100, the interest rate is 3 percent. Derive the value of the firm.

Answer 1

Question 1

Total cost function is as follows -

TC = 100 + 50q - 10q² + q³

The constant part of total cost function represents total fixed cost and the variable part represents total variable cost.

The constant part is 100.

The variable part is 50q - 10q² + q³.

So,

The equation for total variable cost is as follows -

TVC = 50q - 10q² + q³

Thus,

The equation for total variable cost is TVC = 50q - 10q² + q³

Calculate the equation for average variable cost -

AVC = TVC/q

AVC = [50q - 10q² + q³]/q

AVC = 50 - 10q + q²

Thus,

The equation for the average variable cost is AVC = 50 - 10q + q².

Calculate the equation for marginal cost -

MC = dTC/dq

MC = [100 + 50q - 10q² + q³]/dq

MC = 50 - 20q + 3q²

Thus,

The equation for marginal cost is MC = 50 - 20q + 3q².