A company has cost function C(q) = 4000 + 2q dollars and revenue function R(q) = 10q dollars.

Question

 A company has cost function C(q) = 4000 + 2q dollars and revenue function R(q) = 10q dollars.

(a) What are the fixed costs for the company?

(b) What is the marginal cost?

(c) What price is the company charging for its product?

Answer 1

Given the information surrounding the costs and revenue function, the total cost is the fixed costs plus the cost per item multiplied by the number of items.

C(q) = 4000 + 2q

Fixed cost = 4000

The marginal cost is the cost per item (i.e the derivative of the total cost function). In this case the marginal cost is 2 (this is the cost per item produced)

The price for the item is the function multipling the item quantity in the revenue function. q is a measure of the quantity of items, therefore, the price charged is 10 (as seen in the revenue function).