A monopolist faces a market A demand curve given by: QA = 70 – P and market B de
ID: 2494472 • Letter: A
Question
A monopolist faces a market A demand curve given by: QA = 70 – P and market B demand curve given by: QB = 50 – 0.5P. This monopolist pursues a separate monopoly pricing policy in each market. Assume arbitrage between the two markets can be prevented. If the monopolist can produce at constant average and marginal costs of AC = MC = 6, the monopolist’s total profits from both markets A and B are equal to what number? (NOTE: Write your first answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Use a period for the decimal separator and a comma to separate groups of thousands). Show all steps.
Explanation / Answer
Calculate profit in market A -
Demand function in market A -
QA = 70 - P
P = 70 - QA
Calculate Total Revenue, TR -
TR = P * QA = (70 - QA)*QA = 70QA - QA2
Calculate Marginal Revenue, MR -
MR = dTR/dQA = d(70QA - QA2)/dQA = 70 - 2QA
MC = 6
Profit-maximization condition -
MR = MC
70 - 2QA = 6
2QA = 64
QA = 32
Putting value of QA in demand equation to ascertain price -
P = 70 - QA = 70 - 32 = 38
TR = P * QA = 38 * 32 = $1,216
TC = AC * QA = 6 * 32 = $192
Profit = TR - TC = $1,216 - $192 = $1,024
The profit of monopolist in market A is $1,024.
Calculate profit in market B -
Demand function is as follows -
QB = 50 - 0.5P
0.5P = 50 - QB
P = 100 - 2QB
Calculate Total Revenue, TR -
TR = P * QB = (100 - 2QB) * QB = 100QB - 2QB2
Calculate Marginal Revenue, MR -
MR = dTR/dQB = d(100QB - 2QB2)/dQB = 100 - 4QB
MC = 6
Profit-maximization equation -
MR = MC
100 - 4QB = 6
4QB = 94
QB = 23.5
Putting value of QB in demand equation to ascertain price -
P = 100 - 2QB = 100 - (2*23.5) = 100 - 47 = $53
TR = P*QB = 53 * 23.5 = 1245.5
TC = AC * QB = 6 * 23.5 = 141
Profit = TR - TC = 1,245.5 - 141 = $1,104.5
The profit of monopolist in market B is $1,104.5
Calculate monopolist's total profits from both market A and market B -
Total profit = Profit from market A + Profit from market B
= $1,024 + $1,104.5
= $2,128.5
The monopolist's total profits from both market A and market B is $2,128.5