All firms in a competitive industry have cost C = q2 + 100. Market demand is D = 240 − 3p.

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 $20 per-unit tax. Show all calculations.

b. Revenue earned by the government will be _____________ dollars per firm.

c. TRUE or FALSE: "The amount earned by government (per firm) would be larger if this was an

Decreasing Cost Industry."

 

a) Price = $70 and quantity = 30

Step-by-step explanation

a) q = 240 - 3p

3p = 240 - q

p = 80 - q/3

Total revenue = p*q

Total revenue = 80q - q²/3

Marginal revenue = 80 - 2q/3

Total cost = q² + 100

Marginal cost = 2q

Putting marginal revenue equal to marginal cost

80 - 2q/3 = 2q

80 = 2q + 2q/3

80 = 8q/3

240/8 = q

q = 30

At q = 30, market price = p = 80 - 30/3

p = 70

With an imposition of $20 per unit tax, the supply curve will shift upwards by $20. Due to this price increase, many firms could leave the industry reducing the number of firms.

The new price will be $90 and quantity will decline.

In a competitive market, firms are price takers and thus the price of all the firms will increase by $20.

b) The revenue earned by the government will be $20 multiplied by the new quantity. Then this would be divided by the number of firms and gives the revenues earned by government from each firm.

c) In a decreasing cost industry, the burden of tax is fully on producers. The amount earned by the government depends on the demand schedule and elasticity of demand and supply. This statement is false as amount earned by the government can be larger, smaller or constant.

Please see the attached file for the complete solution