Question

Use the following supply and demand equations.

Supply:p= 4 + 3q.

Demand:p= 2,132−q.

Use these equations to respond to the following questions.

(a) What is the market equilibrium?

(b) Under the market equilibrium, what is Total Surplus?

(c) Suppose the government enacts a price ceiling of ̄p= 2,000. What is ProducerSurplus, Consumer Surplus, Total Surplus, and Deadweight Loss?

(d) Instead, suppose that the government enacts a price ceiling of ̄p= 1,100. What is Producer Surplus, Consumer Surplus, Total Surplus, and Deadweight Loss?

(e) Under a price ceiling of ̄p= 2,000, what is the Shortage? What if ̄p= 1,100？

Answer 1

Supply is P = 4 + 3q and demand is P = 2132 - q

a) Market equilibrium has S = D

4 + 3q = 2132 - q

Quantity q = 2128/4 = 532 units

Price P = 1600

b) Total surplus = 0.5*(max price - min price)*qty

= 0.5*(2132 - 4)*532

= 566048

c) Price ceiling of 2000 has no effect on market outcome since it is above the market price.

Hence, we have PS = 0.5*(1600 - 4)*532 = 424536

CS = 0.5*(2132 - 1600)*532 = 141512

TS = CS + PS = 566048

DWL = 0

d) When price is set at 1100 it becomes binding.

Market quantity is (1100-4)/3 = 365.33 and price is 1100.

CS = 0.5*(2132 - 1766.67)*365.33 + (1766.67 - 1100)*365.33 = 310287.66

PS = 0.5*(1100 - 4)*365.33 = 200200.8

TS = 510488.4

DWL = 0.5*(1766.67 - 1100)*(532 - 365.33) = 55557

e) When P is 2000 there is no shortage.

When P is 1100 there is shortage of (532 - 365.33) = 166.67 units