Answers to Homework #5
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1. Consider a monopolist where the market demand curve for the produce is given by P = 520 – 2Q. This monopolist has marginal costs that can be expressed as MC = 100 + 2Q and total costs that can be expressed as TC = 100Q + Q2 + 50.
a. Given the above information, what is this monopolist’s profit maximizing price and output if it charges a single price?
MR = 520 – 4Q
MC = 100 + 2Q
520 – 4Q = 100 + 2Q
Q = 70 units of output
P = 520 – 2Q = 520 – 2(70) = $380 per unit of output
b. Given the above information, calculate this single price monopolist’s profit.
Profit = TR – TC
TR = P*Q = ($380 per unit)(70 units) = $26,600
TC = 100Q + Q2 + 50 = 100(70) + (70)(70) + 50 = $11,950
Profit = $14650
c. At the profit maximizing quantity, what is this monopolist’s average total cost of production (ATC)?
To answer this question we first need to write an expression for ATC.
ATC = TC/Q = 100 + Q + (50/Q)
Then replace Q with 70 to find the average total cost of producing 70 units of output.
ATC= 100 + 70 + (50/70) = $170.71 per unit
d. At the profit maximizing quantity, what is the profit per