Question

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?

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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