Exercise 1. Monopoly with Linear Costs facing a Linear Demand A monopoly has the cost function...

Exercise 1. Monopoly with Linear Costs facing a Linear Demand

A monopoly has the cost function c(y)=10y+100, and is facing a market demand D(p)=100-2p.

a) What is the inverse demand function, p(y)? Having profits be π = p(y)∙y – c(y), what is the profit maximizing output level? What is the corresponding market price?

b) Calculate the monopolist’s profit and producer surplus. What is the consumer surplus? What is the deadweight loss?

c) The government imposes a production tax, tP=10, so that the new cost function is c(y)=(10+tP)y+100. What happens to y and p? What happens to the firm’s profit and producer surplus? What happens to consumer surplus and the deadweight loss? How much is tax revenue?

d) The government imposes instead a lump sum tax, T=300, so that the new cost function is c(y)=10y+100+T. What happens to y and p? What happens to the firm’s profit and producer surplus? What happens to consumer surplus and the deadweight loss?

e) The government imposes instead a sales tax, tS=25%, so that the new demand function is D(p)=100-2p(1+tS). What happens to y and p? What happens to the firm’s profit and producer surplus? What happens to consumer surplus and the deadweight loss? How much is tax revenue?

f) The government imposes instead a profit tax, τ=40%, so that the new profit function is π=(1- τ)[p(y)∙y–c(y)]. What happens to y and p? What happens to the firm’s profit and producer surplus? What happens to consumer surplus and the deadweight loss? How much is tax revenue?

Expert Solution

Rahul Sunny answered 6 months ago

Consider a monopoly facing inverse demand function ?(?) = 12 − ?, where ? = ?1...

Consider a monopoly facing inverse demand function ?(?) = 12 − ?, where ? = ?1 + ?2 denotes the monopolist’s production across two plants, 1 and 2. Assume that total cost in plant 1 is given by ??1 (?1 ) = (5 + 4?1)?1, while that of plant 2 is ??2 (?2 ) = [5 + (4 + ?)?2]?2, where parameter ? ≥ 0 represents plant 2’s inefficiency to plant 1. When ? = 0, the total (and marginal)...

Monopoly with linear inverse demand. Consider a monopolist facing a linear inverse demand curve p(q)= a-...

Monopoly with linear inverse demand. Consider a monopolist facing a linear inverse demand curve p(q)= a- bq, and cost function C(q)= F + cq, where F denotes its fixed costs and c represents the monopolist's (constant) magical cost a>c 1. Graph demand, marginal revenue and marginal cost. Label your graph carefully, including intercepts 2. Solve the profit maximizing output q^m. To do this, first write down the expression for MR=MC and solve for the optimal quantity. Next find the price...

Is a monopoly with the following cost curve facing the following demand curve a natural monopoly?...

Is a monopoly with the following cost curve facing the following demand curve a natural monopoly? P(Q)=100-5Q C(Q) = 8,000 + 10 Q2 A.Yes B. No C. Cannot be determined from the information provided

A monopoly has the cost function c(y)=10y+100, and is facing a market demand D(p)=100-2p. What is...

A monopoly has the cost function c(y)=10y+100, and is facing a market demand D(p)=100-2p. What is the inverse demand function, p(y)? Having profits be π = p(y)∙y – c(y), what is the profit maximizing output level? What is the corresponding market price? Calculate the monopolist’s profit and producer surplus. What is the consumer surplus? What is the deadweight loss? The government imposes a production tax, tP=10, so that the new cost function is c(y)=(10+tP)y+100. What happens to y and p?...

A monopoly has the cost function c(y) = y^2 + 2500 and is facing a market...

A monopoly has the cost function c(y) = y^2 + 2500 and is facing a market demand D( R) = 300-2p. a) What is the inverse demand function p(y)? Having profits be π = p(y) * y - c(y), what is the profit maximising output level? What is the corresponding market price? b) Calculate the monopolist's profit and producer surplus. What is the consumer surplus? What is the deadweight loss? c) Ideally, what is the price and quantity that would...

A monopolist facing a market demand Q = 240 – 2p has the total cost function...

A monopolist facing a market demand Q = 240 – 2p has the total cost function TC(q) = q2. 1. What is the monopolist’s profit maximizing quantity and price? How many units are produced in each plant? Now the government notices that the monopolist is actually composed of two production plants, the first plant has a total cost function TC1(q) = 2q^2+ 16q 2. Derive the marginal cost of the second plant, MC2(q).

14. Consider a monopoly facing the following demand, marginal revenue, total cost, and marginal cost curves:...

14. Consider a monopoly facing the following demand, marginal revenue, total cost, and marginal cost curves: Demand curve: P = 12 – 0.002 Q Marginal revenue curve: MR = 12 – 0.004 Q Total cost curve: TC = 3Q +0.0005Q2 Marginal cost curve: MC = 3 + 0.001 Q a. Calculate the profit maximizing output of this monopoly. Briefly explain your answer. b. What is the socially efficient output level? Briefly explain your answer. c. Suppose the government wants to...

1.Using a linear demand function and constant marginal cost function as illustration, explain the Cournot model...

1.Using a linear demand function and constant marginal cost function as illustration, explain the Cournot model with product differentiation. Derive the sufficient condition that all firms have no incentive to cheat. 2.In the context of a static duopoly model explain why the joint profit maximizing solution is unstable. Discuss some factors that may engender collusion. 3.Using a quadratic net birth function, and linear total cost and catch functions as illustration, derive the supply function of fishery. Why this supply function...

Monopoly pricing: Consider a simple linear demand function that intersects the quantity 0 point at $110...

Monopoly pricing: Consider a simple linear demand function that intersects the quantity 0 point at $110 and the $0 axis at 1,200 units. The marginal cost is linear and starts at $10 at 0 quantity and reaches $110 at 500 units. What is the elasticity of demand? Is it constant? Why or why not? What is the competitive market clearing price? What is the competitive consumer surplus? What is the competitive producer profit (surplus)? What is the profit-maximizing monopoly price...

1. The research department of Cardinal Novelties has estimated the demand function facing the firm for...

1. The research department of Cardinal Novelties has estimated the demand function facing the firm for price increases and price declines from the prevailing price are, respectively: Q = 220 -10P and Q’ = 145-5P The marginal and average total cost functions of the firm were also estimated to be, respectively: MC =2.5 + .05Q and ATC = 2.5 + .025Q Determine the best level of output of the firm, the price at which the firm sells its output, as...

Question