Question

Consider the following market. Demand is given by 5- P where Qo is the quantity demand and P is the price. Supply is given by Qs- where Qs is the quantity supplied. a. What is the market equilibrium quantity and price? b Calculate consumer, producer and total surplus Depict your answer in a graph. c. Suppose the government imposes a price floor of P - 4. Calculate the consumer surplus, producer surplus, and deadweight loss. Depict your answer in a graph.

Answer 1

Given, Q_D = 5 - P

Q_S = 0.5P

A. Market equilibrium will be at that point where Quantity Demanded is Equal to Quantity Supplied

5 - P = 0.5P

1.5P = 5

Equilibrium price, P* = $ 3.33 per unit

Equilibrium Quantity, Q* = 1.67 units

B. Consumer Surplus, CS = (1/2)*(5 - 3.33)*1.67 = $ 1.39

Producer surplus, PS = (1/2)*(3.33 -0 )*1.67 = $ 2.78

Total surplus = Consumer Surplus + Producer surplus

Total surplus = $ 1.39 + 2.78

TS = $ 4.17

C. When a price floor of $4 is introduced

Quantity Demanded = 1

Price = 4

When Q = 1,

Price of supply = $2

Consumer Surplus = (1/2)*(5-4)*1 = $ 0.5

Producer surplus = (4-2)*1 +(1/2)*(2-0)*1 = $3

Deadweight loss = (1/2)*(1.67-1)*(4-2) = $ 0.67

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