Question

A firm faces the following average revenue (demand) curve: P = 130 - 0.02 where Q is weekly production and P is price, measured in cents per unit. The firm's cost function is given by C = 50Q + 20,000. Assume that the firm maximizes profits. a. What is the level of production, price, and total profit per week? (Round all responses to two decimal places.) The equilibrium quantity is 2000 units, the price is 90 cents, and the total profit is $ 600 per week. b. If the government decides to levy a tax of 14 cents per unit on this product, what will be the new level of production, price, and profit? (Round all responses to two decimal places.) The equilibrium quantity is 1700 units, the price is 164 cents, and the total profit is $ 1737.88 per week.

Answer 1

Demand is P = 130 – 0.02Q and MR = 130 – 0.04Q

Marginal cost is MC = 50

MR = MC gives

130 – 0.04Q = 50

Q = 80/0.04 = 2000 units

P = 90 cents per unit

Profit = revenue – cost = 90*2000 – 20000 – 50*2000 = 60000 cents = $600 per week

After tax

Now cost is increased to C = 64Q + 20000 because of tax

Marginal cost is now MC = 64

MR = MC gives

130 – 0.04Q = 64

Q = 66/0.04 = 1650 units

P = 97 cents per unit

Profit = revenue – cost = 97*1650 – 20000 – 64*1650 = 34450 cents = $344.50 per week