Question

5. 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 #91082, Economics / Microeconomics

Demand: $P = 20 - 0.1Q$

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

a) $R = PQ = 20Q - 0.1Q^2$

MR=20-0.2Q

MC=2+0.1Q

At Qm and Pm, MR=MC

Qm=60, Pm=20-0.1(60)=$14

b) $ATC = \frac{120}{Q} + 2 + 0.05Q$

$$Profit = TR - TC$$ $$TR = Pm * Qm = \$840$$ $$TC = (ATC \text{ at } Qm)Qm = \$420$$ $$Profit = \$420$$

c) P with 0Q=20

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

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

At DWL P=MC

20-0.1Q=2+0.1Q

Q=90, P=11

DWL=0.5(14-11)(90-60)=$45

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