Calculate profitmaximizing price quantity and profits assumi

Calculate profit-maximizing price, quantity, and profits, assuming that it is legal/possible to segregate the two groups of buyers. Consider a monopoly facing inverse demand function: p (y)- 16- y; and with total cost TC = 4y. Find optimal level of production and price. Illustrate optimal choice in the graph, depicting Consumer, Producer Surplus and DWL (Dead Weight Loss). Find the elasticity of the demand at the optimal point. Assume the market demand and supply for one commodity are y = 1000 -5p y = 4p-80 respectively, among which p refers to the price, and y refers to output level. the government imposes tax on such a commodity, $9 per unit. Solve for:

Solution

Solution :

18)

a) The optimal level of production is when marginal revenue = marginal cost

Revenue = Price X quantity demanded

P(y) = 16 - y

y = 16 - p

R = P X ( 16-P)

R =16p - p²

Marginal revenue = 16 - 2P

TC = 4y

marginal cost = 4

16 -2P = 4

12 = 2P

P = $ 6

Quantity produced = 16 - 6

Optimal quantity produced = 10 units

The optimal point = (10,6) i.e 10 units of output and price = $ 6

b) To find elasticity of demand

If price is changed from $ 6 to $ 7

% change in price = 16.66 %

The change in quantity demanded = 10%

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

Elasticity of demand = 10/16.66

Elasticity of demand = 0.6002

It is inelastic demand .