Question

Consider the following supply and demand equations: Supply: p = 10 + q Demand: p = 100 − 2q Show your work as your respond to the following questions.

(a) What is the market equilibrium price and quantity?

(b) What is the Total Surplus at equilibrium?

(c) The government enacts a price ceiling at ¯p = 50. What is the Total Surplus?

(d) Calculate the Consumer Surplus under a price ceiling of ¯p = 20.

(e) What is the Deadweight Loss under a price ceiling of ¯p = 10?

Answer 1

Given demand curve is : p=100-2q. When p=0,q=50 and when q=0,p=100. Thus, the demand curve has a vertical intercept of 100 and a horizontal intercept of 50.

Again, supply curve is : p=10+q. When q=0,p=10 and when q=50,p=60. Thus, the supply curve is a straight line that passes through the points (0,10) and (50,60).

In the diagram below, we have plotted the demand and supply curves as :

a) Equilibrium is attained at the point where Demand = Supply

or, 100-2q = 10+q

or, 3q = 90

or, q = 30 units is the equilibrium quantity

and p = 100-(2*30) = $40 is the equilibrium price

b) Total surplus = consumer surplus Area (A+B+C) + producer surplus Area (D+E+F+G)

or, Total surplus = {1/2*(100-40)*30} + {1/2*(40-10)*30}

or, Total surplus = (1/2*60*30) + (1/2*30*30)

or, Total surplus = 900+450

or, Total surplus = $1,350

c) When there is a price ceiling at p=50, quantity demanded q = 25 units.

Then, consumer surplus Area (A) = 1/2*(100-50)*25 = $625

and producer surplus Area (B+D+F+G) = 1/2*(40+15)*25 = $687.50

Then, total surplus = $1,312.50

d) Under price ceiling of p=20, quantity supplied = 10 units

Then, consumer surplus = Area (A+H+B+D+F)

or, consumer surplus = 1/2*(60+80)*10

or, consumer surplus = $700

e) Under a price ceiling of p=10, quantity supplied = 0

Thus, total surplus = 0

Then, dead-weight loss = total surplus in equilibrium condition (in b) = $1,350