Question

Symbolic and numerical tax incidence: Consider a market described by the following equations: ?? =?+1−?? ?? = ? Here A is a fixed parameter. Answer the following questions.

a. Solve for the equilibrium price and quantity.

b. Now suppose a specific tax, ? > 0, is imposed on this market that has to be paid to the government by suppliers. Using ?∗ and ?, give the new price paid by buyers and the new price received by sellers. Solve for the price paid by buyers, the price received by sellers, and the after tax equilibrium quantity.

c. Determine the marginal effect of an increase in the tax rate ? on the price paid by the buyer and the quantity sold in the market.

d. How does the tax incidence on the buyer vary with A? In no more than two sentences, provide an economic explanation in terms of elasticity of demand.

e. Now suppose the same tax from part (b) is changed so that it must be paid to the government by buyers. Using ?∗ and ?, give the new price paid by buyers and the new price received by sellers. Solve for the price paid by buyers, the price received by sellers, and the after tax equilibrium quantity. ?

f. Compare your answers to parts (b) and (e). Provide a brief explanation (no more than 3 sentences) for your results. Note your answer will be related to the logic of problem 2 part (d), you might want to work through that problem before you answer this.

Answer 1

Hi, Welcome to Chegg.

(a) Equilibrium exists where Qd=Qs

hence equilibrium price is,

Put this into Qs to get the equilibrium amount of Quantity,

(b) When a tax t is imposed that has to be paid by suppliers. (Let t = tau i.e. rate of tax)

The new Qs equation is

New Equilibrium price, when new Qs and Qd equates

(1)

Above given price represents price paid by buyer, price received by seller is given by

Hence the optimal quantity is given by

(2)

Which is lesser than the quantity in previous part.

(c) Differentiating (1) and (2) w.r.t t to get the marginal effect of an increase in t on optimal P and Q respectively.

(d) If A is high, it means that the elasticity of demand is high, i.e. a price increase may lead to relatively higher decrease in quantity demanded and vice versa in case the value of A is lower. Similarly, the tax incidence on buyer varies directly with A.