Question

The demand for peaches is QD = 24 – (1/10)P and the supply of peaches is QS = (1/2)P -6. Currently there is no tax on peaches.

a. Graph the demand and supply curves for the peach market below. Make sure to label all axes, intercepts and curves.

b. Now the government imposes a tax of "T per unit" on all suppliers of peaches. As a result of the tax, the quantity of peaches supplied falls by 3. How much is the tax per unit (T=?)?

Answer 1

(a) Qd = 24-(1/10)P

When Q= 0 , P= 240

When P=0 , Qd= 24

Qs = (1/2)P-6

when Q=0 , P=12

At equilibrium Qd=Qs, we get:

24-(1/10)P= (1/2)P-6

P= $ 50 (Equilibrium price)

Q= (1/2)(50)- 6= 19 units (Equilibrium quantity)

(b) Quantity of peaches supplied falls by 3 units because of tax . This means Qs after tax = (19-3)=16 units.

After tax, Qs= (1/2)(P-T) -6

16 = (1/2)(P-T)-6

(P-T)= 44   

At equilibrium after tax : Qs after tax =Qd

(1/2)(P-T)-6 = 24-(1/10)P

(1/2)(44)- 6 -24 = -(1/10)P

-8 = -(1/10)P

P= 80 (Equilibrium price after tax)

P-T = 44

This implies T= 80-44 = $ 36 (Tax per unit)