Question

Demand for novels is given by D(p)=50.0−1.0p, and the supply function is S(p)=1.0p.

Give all answers to one decimal.

A) What is the equilibrium price for novels?    $   

B) What is the equilibrium quantity?      

C) Suppose a $1 per-unit tax is imposed on buyers of novels. Find the equilibrium price buyers pay, the price sellers receive, and the quantity with the tax.  

Buyers pay   $  .

Sellers receive   $  .

     novels are sold.

D) Would the answer to Part 2 be different if the tax were charged to sellers instead of buyers?

Choose one:

A. yes

B. no

C. not enough information to say

Answer 1

Ans) 1) At equilibrium, quantity demanded is equal to the quantity supplied.

Qd=Qs

50 - P = P

P= $25

Plug value of P in either demand or supply equation to get the equilibrium quantity.

Qd= 50-P = 50-25 = 25units

Or

Qs= P =25 units

2) When tax is imposed, on buyers, buyers pay more than the equilibrium price and sellers get less than the equilibrium price. Let price paid by buyers after tax be Pb and price received by sellers after tax be Ps.

Pb = Ps + t

New Qd = 50 - Pb , Qs = Ps

At equilibrium, Qd=Qs

50 - Pb = Ps

50 - (Ps + t) = Ps

50 - Ps - t = Ps

50 - Ps - 1 = Ps

49 = 2 Ps

Ps = $24.5 (sellers receive)

Pb = Ps + t = $24.5 + $1 = $25.5 (buyers pay)

Novels sold, Qs = Ps = 24.5 units

Or Qd = 50 - Pb = 50 - 25.5 = 24.5 units

3) No. It does not matter upon whom the tax is legally imposed, as tax depends upon the elasticity of demand and supply. Consequently, the less elastic side bears more burden of the tax.