Question

1. Suppose the market for headphones in Brooklyn is described by the following supply curve

QS = -4 + 8P and demand curve QD= 20 – 4P, with prices measured in dollars. What is the value of net

social surplus at equilibrium?

A. $18

B. $27

C. $12

D. $9

E. $16

2. Consider a price taking firm in the umbrella market. Currently, an umbrella sells for a market price

of $10. The firm’s marginal cost curve is mc = 2q and its total costs are tc = 20 + q2 , where q is the

number of umbrellas produced by the firm. What are the firm’s maximum economic profits?

A. $15

B. $5

C. $0

D. -$5

E. -$15

Answer 1

1)

Q_s= -4 + 8P and Q_d = 20 - 4P

Solving the above two equation: -4 + 8P = 20 - 4P Therefore, P = 2 and Q_P=2 = 12

Therefore at equilibrium P=2 and Q=12

Net social surplus at equilibrium = Consumer Surplus + Producer Surplus

From the above diagram, Consumer surplus= Area of triangle ABC = 0.5*(5-2)*12 = 18

Producer Surplus = Area of triangle BCD = 0.5*(2-0.5)*12 = 9

Therefore, Net Social Surplus = 18+9 =$27

2)

Profit = Price*Quantity - Total Cost = P*Q - TC

= (10*Q) - (20+Q²) = 10Q - 20 - Q²

In order to maximize profit:
First order condition: d(Profit)/d(Q) = 0 => 10 - 2Q = 0 => Q=10/2 = 5
Second order Condition: For maximization condition d²(Profit)/d(Q)² < 0 at Q=5 =>   d²(Profit)/d(Q)² = -2 < 0
Therefore Profit is maximized at Q=5

Profit at Q=5 is (10*5) - (20+5*5) = 50 - 45 = $5