Question

The demand is given by P = 20 – 0.1Q, where P is the price and Q is the quantity demanded. The monopolist’s total cost is C = 120 + 2Q + 0.05Q2. Find
a. Profit-maximizing price and quantity;
b. Monopolist’s profits
c. Consumer surplus
d. Deadweight loss

Answer 1

Answer to Question #91111, Economics / Microeconomics

Demand: $P = 20 - 0.1Q$

$$TC = 120 + 2Q + 0.05Q^2$$

c) Let maximum quantity and price be Qm and Pm respectively

At (Qm,Pm), MR=MC

$$TR = P * Q = 20Q - 0.1Q^2$$ $$MR = (TR)' = 20 - 0.2Q$$ $$MC = (TC)' = 2 + 0.1Q$$ $$Qm = 60, Pm = 20 - 0.1(60) = \$14$$

b) Profit = $TR - TC$

$$TR = Pm * Qm = \$840$$ $$TC(Qm) = \$420$$ $$Profit = 840 - 420 = \$420$$

c) Vertical intercept = 20

$$Cs = 0.5(20 - 14)(60) = \$180$$

d) DWL=0.5 * (P2 - P1) * (Q1 - Q2)

$$P = MC$$ $$20 - 0.1Q = 2 + 0.1Q$$ $$Q = 90, P = 11$$ $$DWL = 0.5(14 - 11)(90 - 60) = \$45$$

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