Answer to Question #264810 in Microeconomics for QJJ

Question

A2-5. Suppose a firm operating in a perfectly competitive industry has costs in the short run given by:

SRTC = 8 + ½q2 and therefore MC = q.

(a) Derive expressions for fixed costs (FC), those that do not vary with output, variable costs (VC), those that do vary with output, average variable cost (AVC), and average total cost (ATC). [4]

(b) At what quantity is AVC at its minimum (at what AVC level)? At what quantity is ATC at its minimum (at what ATC level)? Calculate ATC at q = 2 and q = 8 and sketch MC, AVC and ATC between q = 0 and q = 8. [6]

(d) If the minimum point of the short-run ATC curve for all firms (existing and potential) is also the minimum point of the long-run average cost curve (LRAC), calculate the long-run equilibrium price, market quantity, and firm quantity. What is the long-run equilibrium number of firms in the industry? [4]

Answer 1

(a)

Fixed cost is found when $Q=0$

Given $TC=8+\frac{1}{2}Q^2$

$TC=8+\frac{1}{2}(0)^2=8$

Variable cost = Total Cost minus Fixed Cost.

$\therefore VC=8+\frac{1}{2}Q^2-8$

$VC=\frac{1}{2}Q^2$

Average Total Cost=$\frac{Total Cost}{Q}$

$ATC=\frac{8+\frac{1}{2}Q^2}{Q}$

(b)

AVC is at its minimum at the quantity where Marginal Revenue =Marginal Cost.

ATC at q=2: $\frac{8+\frac{1}{2}(2)^2}{2}=5$

ATC at q=8:$\frac{8+\frac{1}{2}(8)^2}{8}=5.$