Question

The profit-maximizing monopolist Alga has the cost function C (y) = 16y and meets an (inverse) demand function: p (y) = 80 - y What is the maximum profit? Draw a picture and enter the welfare loss in the figure. Explain the concept of welfare loss. Assume finally that the introduction of a tax of SEK 4 per unit, which then becomes Algas profit-maximizing price?

Answer 1

Solution:- Total cost (TC)=16Y ,MC=d(TC)/dy = 16 ( Y is Quantity)

Demand function, P= 80—Y , Total revenue (TR)=P ×Y = 80Y—Y² , or MR=d(TR)/dY= 80—2Y  

At the equilibrium ( profit maximization); MR=MC or, 80—2Y= 16 or, 2Y = 64 or, Y= 32 ( equilibrium quantity) , Putting the value of equilibrium quantity in the demand function; P =80—32= 48 ( equilibrium price)

Here profit =TR —TC = 80Y—Y²—16Y = (80×32)—(32)²—(16×32)= 2560—1024—512= $1024

B) Concept of welfare loss — Monopoly market is not efficient as it creates deadweight loss (welfare loss) because it is not competitive. Welfare loss means loss of potential gain which could have been enjoyed by buyers or sellers. So a deadweight loss is a loss to society from a market not being efficient.

Diagram of welfare loss from a monopoly market.....

C) Now when a unit tax of SEK 4 is introduced so the new total cost = 16Y+4Y = 20Y , and Marginal cost =20

So at the new equilibrium: MR= new MC or, 80—2Y= 20   or, Y= 60/2 = 30 ( new equilibrium quantity) and P= 80—30=50 ( new equilibrium price)

So, new profit maximizing price =SEK 50