Answer to Question #181014 in Microeconomics for Bornface Kandunda

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

Solution:

a.). At equilibrium: D = S

20 – 2P = 10.5P + 0.5P

20 – 10.5 = 0.5P + 2P

9.5 = 2.5P

P = 3.8

Equilibrium price = 3.8

Substitute for Q:

20 – 2P = 20 – 2(3.8) = 20 – 7.6 = 12.4

Q = 12.4 units

Equilibrium quantity = 12.4 units

If the government imposes a 7% of tax as a percent of equilibrium price on each unit of Cigarette produced, then the equilibrium price will increase and the equilibrium quantity will decrease.

Calculate the new equilibrium price and quantity:

D: Q = 20 – 2P

Make P the subject:

2P = 20 – Q

P = 10 – 0.5Q

S: Q = 10.5 + 0.5P

Q – 10.5 = 0.5P

P = 2Q – 21

New supply function after tax:

P = 2Q – 21 + 0.07P

P – 0.07P = 2Q – 21

0.93P = 2Q – 21

P = $\frac{2Q}{0.93}$ – 22.581

At equilibrium:

D = S

10 – 0.5Q = $\frac{2Q}{0.93}$ – 22.581

10 + 22.581 =$\frac{2Q}{0.93}$ + 0.5Q

32.581 = 2.151Q + 0.5Q

32.581 = 2.651Q

Q = $\frac{32.581}{2.651}$ = 12.29

Q = 12.29 units

New equilibrium quantity = 12.29 units

Substitute for Price:

P = $\frac{2Q}{0.93}$ – 22.581 = $\frac{2(12.29)}{0.93}$ – 22.581 = 26.43 – 22.581 = 3.849

P = 3.849

New equilibrium price = 3.849

 

b.).  Price elasticity of demand at equilibrium after-tax and comment on the answer?

Elasticity of demand (PED) = $\frac{\%\;change\; in\; quantity\; demanded}{\%\; change\; in\; price}$

% change in qty demanded = $\frac{Q_{2} -Q_{1}}{(Q_{2}+Q_{1})/2 } \times 100 = \frac{12.29 -12.4}{(12.29+12.4)/2 } \times 100$

$\frac{-0.11}{12.345} \times 100 = -0.0089\times 100 = -0.89\%$

% change in price =$\frac{P_{2} -P_{1}}{(P_{2}+P_{1})/2 } \times 100 = \frac{3.849 -3.8}{(3.849+3.8)/2 } \times 100$

$\frac{0.049}{3.8245} \times 100 = 0.0128\times 100 = 1.28\%$

Elasticity of demand (PED) = $\frac{-0.89\%}{1.28\%} = -0.695$

Elasticity of demand (PED) = 0.695 or 0.70

The elasticity of demand is less than 1, which means that the market for cigarettes is price inelastic and a normal good. Demand for the product does not change significantly after a price increase due to taxes.