Question

Consider a market described by the following equations:

1. Symbolic and numerical tax incidence: Consider a market described by the following equations: where Y denotes income and α, β, y, 4, and μ are parameters. Note that β must be less than zero and the other parameters are positive. Answer the following questions a. Solve for the equilibrium price and quantity b. Now suppose a specific tax, r > 0, is imposed on this market that has to be paid to the government by suppliers. How can you represent the new price paid by buyers and the new price paid by sellers? Solve for the price paid by buyers, the price paid by sellers, and the after tax equilibrium quantity. Now suppose the same tax from part (b) is changed so that it must be paid to the government by buyers. How can you represent the new price paid by buyers and the new price paid by sellers? Solve for the price paid by buyers, the price paid by sellers, and the after tax equilibrium quantity. Compare your answers to parts (b) and (c). Provide a brief explanation (no more than 3 sentences) for your results. Note your answer wil be related to the logic of problem 2 part (d), you might want to work c. d. through that problem before you answer this.

Where Y denotes income and

,

휑

, and

휇

are parameters.

Note that

훽

must be less than zero

and the

other parameters are positive

.

Answer the following questions.

a.

Solve

for the equilibrium price and

quantity.

b.

Now suppose a specific tax,

휏

>

0

, is imposed on this market that has to be paid to the government by

suppliers. How can you represent the

new

price

paid by buyers

and the

new

price paid by sellers? S

olve

for the price paid by

buyers, the price paid by sellers, and the after tax equilibrium quantity.

c.

Now

suppose the same tax from part (b) is changed so that it must be paid to the government by

buyers.

How can you represent the

new

price paid by buyers and the

new

price paid by sellers? Solve for

the price paid by buyers, the price paid by sellers, and the after ta

x equilibrium quantity.

d.

Compare your answers to parts (b)

and (c). 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

a) Qd=$\small \alpha +\beta P+\gamma Y$

Qs=$\small \phi +\mu P$

At the equilibrium, Qd=Qs

P=$\small \frac{\phi -\gamma Y-\alpha }{\beta -\mu }$

Q=$\small \frac{\beta \phi -\mu (\gamma Y+\alpha )}{\beta -\mu }$

b) Qs=$\small \phi +\mu (P-\tau)$

Qd=$\small \alpha +\beta P+\gamma Y$

Equating the two equations we get,

Q'= $\small \frac{\beta \phi -\mu (\gamma Y+\alpha+\mu \tau )}{\beta -\mu }$

Ps is the price seller's pay and Qs=$\small \phi +\mu (P-\tau)$

Then Ps=$\small \frac{Qs-\phi +\mu \tau }{\mu }$

And Pb is the price buyer's pay. Qd= $\small \alpha +\beta P+\gamma Y$

Then Pb= $\small \frac{Qd-\alpha -\gamma Y}{B}$

Pb=Ps= $\small \frac{\beta (\phi -\gamma Y-\alpha)-\mu ^{2}\tau }{\beta (\beta -\mu )}$

c) When the tax burden shifts to the buyers we get.

Qd= $\small \alpha +\beta(P-\tau )+\gamma Y$ which means Pb= $\small \frac{Qd-(\alpha +\gamma Y)+\beta \tau}{B}$

Similarly, Ps= $\small \frac{Qs-\phi }{\mu }$

The equilibrium quantity Q'= $\small \frac{\beta \phi -\mu (\gamma Y+\alpha+\mu \tau )}{\beta -\mu }$

d) No matter who bears the burden of the tax incidence, the equilibrium quantity and price will remain the same. The burden of the tax is borne more by the suppliers' if the supply is more inelastic as compared to the demand and vice versa.