Question

6.

a. The market for coats is perfectly competitive with market supply given by QS= 2500 + 40P and market demand given by QD given by QD= 7500 – 10P. Solve for the equilibrium values of price and quantity. Calculate the values of elasticity of demand and elasticity of supply at the equilibrium.

b. With reference to question 6a, the government imposes a tax of 20% on coats. Calculate the new equilibrium prices and quantity and explain how the burden of the tax is shared between consumers and producers. How much tax revenue is collected?

c. With reference to your answer for part b, suppose that the government had imposed on the producers a license fee (a one time fixed payment) that generated the same revenue for the government as did the tax. What is the new equilibrium value of price and quantity. Explain the difference between the two answers.

Answer 1

a)Here in the question, the demand function and supply function is given. It is asked to find the equilibrium price. For this, we have to equate both demand and supply equations.

Qd = 7500 - 10P

Qs=2500+40P

Qd=Qs

7500 - 10P = 2500+40 P

50 P = 5000

P = 5000/50 = 100

Equilibrium quantity is obtained by solving either of the 2 equations, both should be same.

Qs = 2500+40 P

Substituting (P=100)

Qs = 2500+4000 = 6500

Similarly, Qd= 7500-10 P = 7500-1000 = 6500

Therefore the equilibrium quantiy = 6500 and equilibrium price = 100

Now, we have to find the elasticity of demand and elasticity of supply.

Demand Elasticity(Ed) = percentage change in quantity demanded/percentage in change in price

Ed = 1/slope . P/Qd               

In the given demand equation is of the form Q=a-bP i.e, Qd = 7500-10 P(given) slope = 10

Ed = 1/10*100/6500 = 0.1538

Es = 1/slope . P/Qs = 1/40 *100/6500 = 0.038

b. When a tax of 20 percent is imposed on coat, then the price will increase 20 percent ,ie price will shift to 120.

Then the equilibrium quantity demanded = Qd = 7500 - 10 P = 7500 - 1200 = 6300

or elasticity of demand = -P/Q * Q/P

0.154 = 100/6500* Q/20

Q = 200

New qty demanded = 6500-200 = 6300

Here the demand elasticity exceeds the supply elasticity, tax burden will be on the producers than on the consumers.

Then the tax revenue collected by the government on imposing 20% tax = 20 i.e, 120-100 = 20

c. Now if the producer is charged a fee, then equilibriun quantity is

Supply elasticity = 0.038

We know, Es = +P/Q*Q/P = 100/6500 * Q/120

Q = 49

Therefore the new quantity supplied = 6500+49 = 6549

When a tax is imposed, the price increases and the quantity demanded will decrease by 200 units(elasticity 0.154) and it will become 6300 units of quantity and whwn a licence fee is imposed, the government revenue remains the same 20 and as the price increases the quantity supplied will increses by 49 units(sibce Es = .038) and the quantity supplied become 6549.