Answer in Microeconomics for Bornface Kandunda #181014
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]
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 = -0.0089times 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 = 0.0128times 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.
