Question

In: Economics

A monopolist has the following total cost function: C = 50 + 10Q + 0.5Q2 They...

A monopolist has the following total cost function:

C = 50 + 10Q + 0.5Q2

They face the market demand:

P = 210 – 2Q

a. What is the profit-maximizing price and quantity set by this monopoly? What is this monopolist’s profit?  

b. Calculate the producer surplus, consumer surplus, and deadweight loss.  

c. If the price elasticity of demand (ԑ) faced by this monopolist at the equilibrium is –1.625, what is the Lerner Index?  

d. If the price elasticity of demand (ԑ) faced by this monopolist at the equilibrium is – 4, what is the Lerner Index?  

e. Is the price markup charged by the monopolist higher in the part c scenario or in the part d scenario? Why?  

Solutions

Expert Solution


Related Solutions

Consider a monopolist who has a total cost function C(q) = 1000 + 10q The demand...
Consider a monopolist who has a total cost function C(q) = 1000 + 10q The demand function for the market is D(p) = 600 - 12.5p Answer each part below:(a) Use the inverse demand equation to derive the monopolist's marginal revenue equation, MR(q). (1 points) (b) What is the marginal cost, MC(q)? (0.5 points) (c) Solve for the profit-maximizing quantity and price. Note: Explain or show your work! (2 points) (d) Compute the price elasticity of demand at the profit-maximizing...
A monopolist firm has the following cost function: C(q)=0.5q^2 +10q+2 The (inverse) demand function for the...
A monopolist firm has the following cost function: C(q)=0.5q^2 +10q+2 The (inverse) demand function for the monopolist’s output is as follows: P(q) = 100 - q a. Assume that the monopolist must charge the same price for all units of output (i.e. the monopolist cannot price discriminate). How many units of output will the monopolist produce to maximize profits? At what price will this output be sold? Illustrate this outcome in a graph. b. How much profit does this monopolist...
A monopolist has total cost TC = Q2 + 10Q + 100 and marginalcost MC...
A monopolist has total cost TC = Q2 + 10Q + 100 and marginal cost MC = 2Q + 10. It faces demand Q = 130 - P (so its marginal revenue is MR = 130 - 2Q). Its profit-maximizing price is$50$75$100
Suppose that there is “dominant” firm with total cost function of c(q) = 100 + 10q...
Suppose that there is “dominant” firm with total cost function of c(q) = 100 + 10q + 0.25q2. It faces a market demand function (inverse) of p = 100 − 0.5Q, where Q indicates total market supply. This dominant firm has to deal with 10 fringe firms, each of whom behaves perfectly competitively. Each fringe firm has a marginal cost function dc(q)/dq = 20q + 25 a) Calculate the supply function of the fringe firms b) Using this, calculate the...
The market demand function for a monopolist is p=58-2Q and its cost is C(Q)=10Q. a) Determine...
The market demand function for a monopolist is p=58-2Q and its cost is C(Q)=10Q. a) Determine the monopolist’s price and quantity in equilibrium. b)  Suppose now that a competition authority forces the monopolist to employ marginal cost pricing. Determine the price and the quantity with this new pricing scheme. c)   Compute and compare the consumer surplus, the firm’s profit, and the social welfare under unrestricted monopoly and under marginal cost pricing. What is the deadweight loss due to unrestricted monopoly pricing?
. A natural monopolist has the total cost function C(Q) = 500 + 5Q and faces...
. A natural monopolist has the total cost function C(Q) = 500 + 5Q and faces the inverse demand curve P = 100 – Q a) Find the monopolist’s price, quantity, profits, consumer surplus and deadweight loss if the monopolist is not constrained by a regulator (you probably want to draw a picture to help you answer CS and DWL) P = _________ Q = _________ π = _________ CS = ¬_________ DWL = _________ b) A regulator constrains the...
A company in perfect competition has the total cost function: C(q) = 50 + 0.5 q...
A company in perfect competition has the total cost function: C(q) = 50 + 0.5 q + 0.08 q2 a. Determine what is the long-run equilibrium price level and the corresponding output of the firm.. b. If the company experiences a technological improvement that reduces its costs by 25%, what is the equilibrium quantity of the company in the short term if the market price is the one found in point a.
. A monopolist has a cost function given by c(y) = 0.5y 2 and faces a...
. A monopolist has a cost function given by c(y) = 0.5y 2 and faces a demand curve given by P(y) = 120 − y. What is its profit-maximizing level of output? What price will the monopolist charge? • If you put a lump sum tax of $100 on this monopolist, what would its output be? • If you wanted to choose a price ceiling for this monopolist so as to maximize consumer plus producer surplus, what price ceiling should...
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).
A monopolist has the following cost function: C(q) = 800 + 8*q + 6*q2 It faces...
A monopolist has the following cost function: C(q) = 800 + 8*q + 6*q2 It faces the following demand from consumers: P= 200 – 2*Q. There is another firm, with the same cost function, that may consider entering the industry. If it does, equilibrium price will be determined according to Cournot competition. How much should the monopolist optimally produce in order to deter entry by the potential entrant? How much would the monopolist produce if there were no threat of...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT