Question

answer only part e

Problem 2 Bueller & Frye Auto sells cars. Their costs are described by the following total cost function, where q is the number of cars they sell: C(q) = 30° +100 (a) What are this firm's total fixed costs and total variable costs? (b) What are this firm's average total costs, average fixed costs, and average variable costs? (c) Use red ink to draw this firm's average fixed cost curve. Place quantity of cars on the horizontal axis. (d) What are this firm's marginal costs? Draw this firm's marginal cost curve in black ink. (e) Write this firm's unit cost function. Compare this to the firm's average total costs. Do you think this firm produces cars with constant returns to scale? (Hint: The firm's unit cost function is when the quantity is 1.)

Answer 1

(a) Given that Total Cost = C(q) = 3q2+100 so we know that Total cost = Variable cost + Fixed cost, so here Total Fixed cost is 100 and Total Variabe cost is 3q2.

(b) Average Total Cost(ATC) is Total cost divided by quantity so ATC = (3q2+100)/q = 3q + (100/q ) which includes Average Fixed Cost = (100/q) and Average Variable Cost = 3q.

(c) Graph of Average Fixed cost on Vertical axis show AFC and On Horizontal axis show quantity of cars

AFC 100 - AFC 20

(d) Marginal cost is first order condition of Total Cost Function so given that C(q) = 3q2+100 differentiate with respect to q. so we get Marginal cost = 6q

MC 30

Above graph on vertical axis show marginal cost and Horizontal axis show quantity of cars

(e) firm unit cost function is C(q) = 3q2+100 when quantity is 1 so C(q) = 103

Firm Average total cost at when quantity is 1 so ATC = 3q + (100/q ) = 103 so here ATC = Firm unit cost its show that firm produces car at constant return to scale.