Question

In: Economics

A monopolist can produce a constant average (and marginal) cost of AC=MC=$5. It faces a market...

A monopolist can produce a constant average (and marginal) cost of AC=MC=$5. It faces a market demand curve given by Q=53-P.

A)

Consider Problem 2 in the Homework 12 Supplement. Suppose a second firm enters the market. Let Q1 be the output of the first firm and Q2 be the output of the second. Market demand is now given by Q1+Q2 = 53-P. Assuming that this second firm has the same costs as the first, how much will each firm produce (Cornot equilibrium)?

B)

Consider Problem 2 in the Homework 12 Supplement. Suppose a second firm enters the market. Let Q1 be the output of the first firm and Q2 be the output of the second. Market demand is now given by Q1+Q2 = 53-P. Assuming that this second firm has the same costs as the first, what price will the equilibrium price be (Cornot equilibrium)?

Expert Solution

A) Now a second firm enters the market. So now the profit function of first firm ( firm 1) can be written as:

profit₍₁₎ = TR₍₁₎ - TC₍₁₎

= P*Q1 - AC₍₁₎*Q1

= (53- Q1 - Q2)*Q1 - 5Q1 [ as Q1+Q2 = 53-P implies

_Profit(1) = 48*Q1 - (Q1)²- Q1*Q2 P = 53-Q1-Q2]

Under the Cournot assumption, each firm treats the output of the other firm as a constant in its maximization calculations. Therefore, Firm 1 chooses Q1 to maximize its profit with Q2 being treated as a constant.

d(profit₍₁₎)/dQ1 = 48 - 2Q1 - Q2

Put it equal to 0, we get

Q1 = 24 - Q2/2

Similarly we can find ?₍₂₎

_Profit(2) = P*Q2 - 5Q2

= (53-Q1-Q2)*Q2 - 5*Q2

Profit₍₂₎ = 48*Q2 - (Q2)² - Q1*Q2

d(profit₍₂₎)/dQ2 = 48 - 2Q2 - Q1,

Put it equal to 0, we get

Q2 = 24 - Q1/2

Now solve Q1 and Q2 , by substitute Q2 in Q1 we get

Q1 = 24 - (1/2)*(24 - Q1/2)

Q1 = 16, similarly we get

Q2 = 16 .

B) Now for equilibrium price put Q1 and Q2 in demand curve we get,

P = 53 - 16 -16

P = $21 (cournot equilibrium price)

Rahul Sunny answered 2 years ago

4. A monopolist can produce at constant average and marginal costs of AC = MC =...

4. A monopolist can produce at constant average and marginal costs of AC = MC = 10. The firm faces a market demand curve given by P = 100 - Q. (a) Calculate the profit-maximizing level of output and price for the monopolist. Also calculate the monopolist's profit. (b) Assume this industry suddenly becomes perfectly competitive. Calculate the price and industry output if this industry is perfectly competitive. (c) Calculate the deadweight welfare loss that the monopoly in (a) imposes...

A monopolist can produce at a constant average and marginal cost of ATC = MC =...

A monopolist can produce at a constant average and marginal cost of ATC = MC = $5. It faces a market demand curve given by Q = 53 - P. 5. Suppose there are N firms in the industry, all with the same constant MC = $5. Find the Cournot equilibrium. How much will each firm produce, what will be the market price, and how much profit will each firm earn? Also show that as N becomes large, the market...

Suppose a monopolist has constant (average and marginal cost of AC = MC = 8) and...

Suppose a monopolist has constant (average and marginal cost of AC = MC = 8) and faces demand such that QD = 100 - P. Derive MR curve (hint: you can calculate TR with Demand curve, then you can drive MR from TR) Calculate a monopolist’s profit-maximizing Quantity and Price Calculate the equilibrium Price and Quantity in the perfectly competitive market Draw all curves (Demand, MR, and MC curves) Calculate Monopoly Profit and Dead Weight Loss (DWL). Comparing the profit-maximizing...

A monopolist in Ba can produce at constant marginal cost of MC = 10. The monopolist...

A monopolist in Ba can produce at constant marginal cost of MC = 10. The monopolist faces a market demand curve given by Q = 50 - P. You can assume that average cost is same as marginal cost. a) Calculate the profit-maximizing price-quantity combination for the monopolist. b) Compute the monopolist’s profits and consumer surplus. c) What output level would be produced by this industry under perfect competition? d) Calculate the consumer surplus obtained by consumers under perfect competition....

5. A monopolist faces inverse demand P= 30−4Q and has constant marginal cost MC= 6. Currently...

5. A monopolist faces inverse demand P= 30−4Q and has constant marginal cost MC= 6. Currently the government provides a per-unit subsidys to the firm. i. What is the quantity provided by the monopolist as a function of subsidys?What price does the monopolist charge? ii. What is the size of the per unit subsidys for which the monopolist will produce the socially efficient quantity? How much deadweight loss is saved by this subsidy? What is the total payment that the...

41. A monopolist has a constant marginal and average cost of $10 and faces a demand...

41. A monopolist has a constant marginal and average cost of $10 and faces a demand curve of QD = 1000 – 10P. Marginal revenue is given by MR = 100 – 1/5Q. a. Calculate the monopolist’s profit-maximizing quantity, price, and profit. b. Now suppose that the monopolist fears entry, but thinks that other firms could produce the product at a cost of $14 per unit (constant marginal and average cost) and that many firms could potentially enter. How could...

A monopolist with constant average and marginal cost equal to 8 faces demand Q = 100...

A monopolist with constant average and marginal cost equal to 8 faces demand Q = 100 - P, implying that its marginal revenue is MR = 100 - 2Q. (Wrong question Its profit maximizing quantity is ... should be deadwieght loss) the deadweight loss is Select one: a. 1058 b. 966 c. none of the answers. d. 3680

5. A monopolist faces a demand curve P = 64−2Q. His marginal cost is MC =...

5. A monopolist faces a demand curve P = 64−2Q. His marginal cost is MC = 16. (a) Draw a graph to illustrate and calculate the profit maximizing output and price. (b) Calculate the efficient level of output and the DWL. (c) Suppose the government gave the monopolist a subsidy of $4 per unit produced. Compute the profit maximizing output level and the deadweight loss associated with this new output. Explain intuitively why the DWL has changed.

A monopolist sells in two states and has constant marginal cost MC =10. Demand in market...

A monopolist sells in two states and has constant marginal cost MC =10. Demand in market 1 is Q1 = 50- p1. Market 2 demand is Q2 = 90-1.5p2. a) If the monopolist is unable to discriminate price, what would be the profit maximizing price and quantity? b) If the monopolist can discriminate price between two states, what would the price and quantity in each market? c) Calculate the demand elasticity of each market and explain the price strategy.

A monopolist with marginal cost of MC=Q faces a demand curve of QD = 20 -...

A monopolist with marginal cost of MC=Q faces a demand curve of QD = 20 - 2P. This implies that P = 10 - (1/2)Q and that the marginal revenue is MR = 10 - Q. a. Sketch demand, marginal revenue, and marginal cost curves. b. What quantity and price will the monopolist set? c. What quantity and price would the monopolist set if it produced at the efficient market outcome where P=MC? d. Identify the CS, PS and DWL...