A monopolist sells beer in two separate markets

A. Calculate the price and quantity if the monopolist maximized their profit and sells in both markets.

A. 1. Solving for the Canadian Market

qCanada = 1120 - 10pCanada

Total Cost = 10 + 2(qUSA + Canada)

Total Cost = 10 + 2qUSA + 2qCanada

Marginal Cost:

dTC/dqCanada = 2

MC = 2

Marginal Revenue

TR = PQ

TR = (112 - 1/10qCanada)qCanada

TR = 112qCanada - 1/10qCanada^2

MR = dTR/qCanada = 112 - 1/5qCanada = 2 = MC

qCanada = 550

pC = 112 - 1/10qCanada

pC = 112 - 1/10 (550)

pC = $57

A. 2. Solving for the USA Market

qUSA = 660 - 20pUSA

Total Cost = 10 + 2(qUSA + Canada)

Total Cost = 10 + 2qUSA + 2qCanada

Marginal Cost

dTC/dqUSA = 2

MC = 2

Marginal Revenue

TR = PQ

TR = (33 - 1/20qUSA)qUSA

TR = 33qUSA - 1/20qUSA^2

MR = dTR/qUSA = 33 - 1/10qUSA = 2 = MC

qUSA = 310

pUSA = 33 - 1/20qUSA

pUSA = 33 - 1/20 (310)

pUSA = $17.5

B. Calculate the profit if the monopolist maximized their profit and sells in both markets.

Profit = PQ - TC

Profit = (550)($57) + (310)($17.5) - (10 + 2(310) + 2(550))

Profit = 36,775 - 1,730

Profit = $35,045

C. In the absence of 3rd-degree price discrimination, and given the firm must sell at the same price in both markets, what is the price, quantity, and total profit?

The total demand curve is qTotal = qCanada + qUSA = 1780 - 30P

TR = PQ

TR = (178/3 - 1/30Q)Q

TR = 178/3Q - 1/30Q^2

Marginal Revenue = dTR/dQ = 178/3 - 1/15Q

Profit Maximization Rule

MR = MC

178/3 - 1/15Q = 2

Q = 860

Substituting Q for P,

P = 178/3 - 1/30Q

P = 92/3 = $30.67

Profit = TR - TC

Profit = 178/3Q - 1/30Q^2 - 10 + 2Q

Profit = 178/3 (860) - 1/30(860)^2 - 10 + 2(860)

Profit = $24,643.33