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 marks] b) What is the price elasticity of demand at equilibrium after tax and comment on the answer? [5 marks

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

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

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

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 poibt 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

(b) Price ELasticity of Demand

PeD= % change in quantity demanded divided by % change in price

Initial quantity And price:

$10-\frac{Q}{2}=\frac{Q}{0.5}-21$

$31=2.5Q$

Q=12.4

P=$10-\frac{12.4}{2}=3.8$

%change in quantity demanded =

$\frac{12.29-12.4}{12.4}×100=-0.89$%

%change in price=

$\frac{3.849-3.8}{3.8}×100=1.29$%

PeD=$\frac{-0.89}{1.29}=-0.69$

Tge negative sign in price elasticity is often ignored so PeD=0.69