Question

Suppose that the demand and supply functions for good X are: Qd = 298 - 8P...

Suppose that the demand and supply functions for good X are:

Qd = 298 - 8P and

Qs = - 32 + 4p

A. Find the equilibrium price and quantity.

B. Sketch this market. [HINT: Be sure to draw the two curves carefully, using inverse demand and supply functions to calculate the quantity- and price-axes intercept points.]

C. Use the demand function to calculate consumer surplus.

D. Use the supply function to calculate producer surplus.

E. What is the total welfare to society?

Homework Answers

Answer #1

Answer:

A]

Qd = 298 - 8P

Qs = - 32 + 4p


The market is in equilibrium at Qd = Qs
equating both
298 - 8p = -32 + 4p
12p = 330
p = 330/12
p = 27.5
Q = -32 + 4*27.5
Q = 78

The equilibrium quantity is 78 units and price is 27.5

B]

C]

Consumer Surplus is the area ABO
CS = ½ * (37.25 - 27.5) * 78
Consumer Surplus = 380.25

D]

Producer Surplus is area CBO

PS = ½ * (27.5 - 8) * 78

Producer Surplus = 760.5

E]

Total welfare is the sum of CS and PS
TW = 380.25 + 760.5 = 1140.75

Total welfare = 1140.75

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