Question

4. Consider a firm with total cost: TC = 200 +2q + 4q2, where q is output. (Decimals OK!)

a.[1] Is this a Short Run or a Long Run Total Cost function? Explain how you know.

b.[3] Find the equations for Marginal Cost, Average Total Cost and Average Variable Cost.

c.[2] What is the minimum efficient scale of production for this firm?

d.[1] Over what quantities does this firm exhibit diseconomies of scale?

e.[4] If this represents the cost curve for a firm in a perfectly competitive industry, what is the shutdown price for this firm?

f.[6] What is the firm’s short run supply curve, q(P)?

5. In a perfectly competitive market. The industry is made up of 20 firms, each of which has short run supply curve of , where q is the output of a typical firm.

a.[3] What is the total supply of the 20 firms, as a function of price, Q(P)?

b.[6] If the industry faces a market demand curve is given by QD = 200 – P, what is the optimal price in this market? How much will be produced by the market as a whole? How much will each firm produce?

6. A perfectly competitive industry consists of many identical firms, each with a long-run total cost of . The industry's demand curve is QD = 40,000 – 70P.

a.[3] In long-run equilibrium, how much will each firm produce?

b.[3] What is the long-run equilibrium price?

c.[3] How many units do consumers buy in long-run equilibrium?

d.[3] How many firms are in the industry?

Answer 1

(4)

(a) Since a fixed cost (= 200) exists in total cost function, this is a short run cost curve since in long run all costs are variable and no fixed costs exist.

(b) TC = 200 + 2q + 4q²

MC = dTC/dq = 2 + 8q

ATC = TC/q = (200/q) + 2 + 4q

Since TVC = 2q + 4q²,

AVC = TVC/q = 2 + 4q

(c) At minimum efficient scale of production, ATC is minimized, which holds true when dATC/dq = 0.

dTAC/dq = -(200/q²) + 4 = 0

200/q² = 4

q² = 50

Taking square root,

q = 7.07

(d) Diseconomies of scale occur when ATC is increasing with increase in output. Since at minimum efficient scale ATC is minimized, ATC curve reaches its lowest point at q = 7.07, and starts rising beyond this output. So diseconomies of scale exists after q = 7.07 units.

(e) Shut-down price is the minimum point of AVC curve.

AVC = 2 + 4q

AVC is minimized when q = 0, therefore

Shutdown price = (Minimum AVC)_q=0 = 2

(f) Firm's short run supply curve its its MC curve, therefore

p = MC = 2 + 8q

8q = p - 2

q = 0.125p - 0.25

NOTE: As per Answering Policy, 1st question is answered.