Question

Firms

All firms in a competitive industry have cost C = q2 + 16. Demand is D = 100 – 5p. a. Provide a pair of fully labelled diagrams showing “The Firm” and “The Industry” to illustrate and quantify the adjustments in prices, quantities, profits and the number of firms that would be caused by the introduction of a $9 lump-sum tax. Show all calculations. b. Revenue earned by the government from this industry will be _____________ dollars. c. TRUE or FALSE: “The amount earned by government (per firm) would be larger if this was an Decreasing Cost Industry.”

Answer 1

ATC is given by TC/q = q + 16/q. Minimum ATC is given by

1 + 16/q^2 = 0

q = 4

Long run price is ATC (q = 4) = 4 + 16/4 = $8

When a lumpsum tax is imposed, Cost becomes C = q^2 + 16 + 9 or C = q^2 + 25. ATC = C/q = q + 25/q

ATC is now minimized at 1 + 25/q^2 = 0

q = 5. ATC = 5 + 25/5 = $10

Before tax market quantity demanded = Qd = 100 - 5*8 = 60 units (there are 60/4 = 15 firms before tax).

After tax market quantity demanded = Qd = 100 - 5*10 = 50 units (there are 50/5 = 10 firms after tax).

Profits are zero in both conditions in the long run equilibrium. There are short run losses for firms (4*8 - 4^2 - 25) = -9

Government earns a revenue = tax * number of firms = $9*10 = $90.

False, because lump sum tax is fixed per firm whether it is any kind of industry.