Question

Suppose that the Market for Cigarette is facing the Demand function Q = 20 – 2P and Supply function Q =

10.5 + 0.5P:

a) What is the effect on the Equilibrium Price and Quantity when Government imposes a 7% of tax as

percent of equilibrium price on each unit of Cigarette produced? [5

Answer 1

(a) Given Q=20-2P

Q=10.5+0.5P

Making P the subject of the two functions, we have:

2P=20-Q

$P=10-\frac{Q}{2}$

And for the supply function:

Q-10.5=0.5P

$P=\frac{Q}{0.5}-21$

The new supply function after taxation will be:

$P=\frac{Q}{0.5}-21+0.07P$ ,

$P-0.07P=\frac{Q}{0.5}-21$

$P=\frac{Q}{0.465}-\frac{21}{0.93}$

Market equilibrium is found at the point of intersection of demand curve and supply curve. Thus, to find equilibrium quantity and price, we equate the two functions:

$10-\frac{Q}{2}=\frac{Q}{0.465}-\frac{21}{0.93}$

32.581=2.651Q

$Q=12.29 units$

To get the price, we substitute Q in the new supply function:

$P=\frac{12.29}{0.465}-\frac{21}{0.93}$

$P=3.848$

Hence the new equilibrium quantity is 12.29 units and the new equilibrium price is 3.849.

When 7% tax is imposed, it will increase the cost of production hence less will be supplied.