Question

1.Suppose a study found that the price elasticity of demand for cigarettes in Zambia is -0.4. If a pack of cigarettes currently costs K8 and the government wants to reduce smoking by 20 percent,
a.By how much should the government increase the price?
b.What will be the new price level?

2. Zambian Breweries sells its products in Zambia and three neighboring countries. Data collected from 2010 to 2018 shows that the company produced 300,000 barrels of beer annually. During this period, the average price per barrel of beer P (in Kwacha) was related to the quantity of beer sold Q (in thousands of barrels) by the demand function
P=-0.3224Q+245.4031
The total cost of producing Q thousand barrels of beer was
TCQ=101.1995Q+4699.3441
a. At what output level revenue be maximized?
b. Find the quantity and price levels that maximize profit.

Answer 1

1) Price elasticity of demand = -0.4

Cost of pack of cigarette = K8

Government wants to reduce smoking by 20%

a) Elasticity of demand = %change in quantity demanded / %change in price

-0.4 = 0.2 / %change in price

%change in price = 0.5 = 50%

It means that to reduce smoking by 20%, price must rise by 50%.

b) New price would be K8 * 1.5 = K12

2) P = -0.3224Q + 245.4031

TC = 101.1995Q + 4,699.3441

a) Total Revenue = P * Q

Total Revenue = -0.3224Q2 + 245.4031Q

Total Revenue will be maximized when marginal revenue which is first derivative of total revenue with respect to Q which is -0.6448Q + 245.4031 = 0

Q = 380.5879

b) Profit is maximized when marginal revenue = marginal cost

Marginal Cost is the first derivative of total cost which is 101.1995

-0.6448Q + 245.4031 = 101.1995

Q = 223.6408

At this Q, P = 173.3013

Profit is maximum when P = 173.3013 ans Q = 223.64