A monopolist faces the following demand: P = 1,418 - 15Q The monopolist's cost function is: C...
Question:
A monopolist faces the following demand:
{eq}P = 1,418 - 15Q {/eq}
The monopolist's cost function is:
{eq}C = 10Q2 + 667Q + 326 {/eq}
Find the equilibrium price, P, if this market was perfectly competitive. Round your answer to one decimal.
Perfectly Competitive Market:
A perfectly competitive market is a market that has many buyers and many sellers in the market. The sellers sell goods that are homogeneous and sell at the same market price. Each firm in the market faces a perfectly elastic demand curve, which means that firms in a competitive market are price takers.
Answer and Explanation: 1
Firms in a perfectly competitive market maximize their profits at the point where the market price is equal to their marginal cost of production. That is:
{eq}P = MC {/eq}
The firm has an inverse demand curve given by:
{eq}P = 1,418 - 15Q {/eq}
And the total cost curve given as:
{eq}C = 10Q2 + 667Q + 326 {/eq}
The marginal cost function for this firm is:
{eq}MC = \frac{\Delta C}{\Delta Q}= 20Q + 667 {/eq}
Equating the marginal cost to the inverse demand curve and solving for Q:
{eq}1,418 - 15Q= 20Q + 667 {/eq}
{eq}35Q= 751 {/eq}
Solving for Q:
{eq}Q^*= \frac{751}{35} = 21.5 {/eq} units.
To get the price charged by the firm, we will substitute the profit maximizing level of output into the inverse demand curve.
{eq}P = 1,418 - 15Q {/eq}
{eq}P^* = 1,418 - 15(21.5) = $1,095.5 {/eq}
Ask a question
Our experts can answer your tough homework and study questions.
Ask a question Ask a questionSearch Answers
Learn more about this topic:
Get access to this video and our entire Q&A library
Perfectly Competitive Market: Definition, Characteristics & Examples
from
Chapter 3 / Lesson 63
43K
Learn the definition of perfect competition and understand how a perfectly competitive market works. Study the characteristics of a perfectly competitive market with examples.
Related to this Question
- A monopolist faces the following demand: P = 1,890 - 16Q The monopolist's cost function is: C = 15Q^2 + 581Q + 505 Find the equilibrium price, P, if this market was perfectly competitive. Round y
- A monopolist has the following cost function. C = 4.9 Q^2 + 144Q + 1,531 Market demand is given by: P = 1,770 - 47Q Find the market price, P, if this market was perfectly competitive. Round your ans
- A monopolist faces the following demand curve: P= 12- .3Q with marginal costs of $3. What is the monopolistic price? a. P=$5.50 b. P=$6.50 c. P=$7.50 d. P=$8.50 e. P=$9.50
- A monopolist has the following cost and inverse demand functions: C = 400 - 20Q + Q^2 P = 100 - 4Q What would have been the competitive price in this market? If this competitive price is imposed as a price cap on the non-discriminating monopolist, w
- A monopolist faces the following demand: Q = 592 - 0.4P The monopolist's cost function is: C = 0.69Q^3 - 6Q^2 + 105Q + 1,716 Find the price that maximizes the monopolist's profit. Round your answe
- Suppose that there is a monopolist that faces the following linear demand in the market: Q_D = 100 - (1/4)P and has the following cost function: C(Q) = 16Q^2 + 10 What quantity will the monopolist
- A monopolist faces the following demand curve: P = 140 - 0.3Q , its total cost is given by: TC = 300 + 0.2Q^2 and its marginal cost is given by: MC = 0.4Q. (a) If it is a single-price monopolist, what is its profit-maximizing price and quantity? Show
- A monopolist has the following cost and inverse demand functions: C = 400 - 20Q + Q^2 P = 100 - 4Q Determine output, profit and consumer surplus in the case where the monopolist can perfectly price discriminate.
- Suppose a monopolist faces the following demand curve: P = 200 - 6Q The marginal cost of production is constant and equal to $20, and there are no fixed costs. (a) How much consumer surplus would there be if this market was perfectly competitive? (b) What
- A monopolist faces market demand given by Q_D = 65 - P and cost of production given by C = 0.5Q^2 + 5Q + 300. A. Calculate the monopolist's profit-maximizing output and price. B. Graph the monopolist's demand, marginal revenue, and marginal cost curves. S
- Suppose a monopolist faces the following demand curve: P = 440 - 7Q. The long-run marginal cost of production is constant and equal to $20, and there are no fixed costs. a) What is the monopolist's profit-maximizing level of output? b) What price will
- A monopolist faces a demand curve P = 50 - 5Q where P is the product price and Q is the output. The monopolists cost function is C(Q) = 10Q. What are the monopolist's profit maximizing price, output, and profit? What are the consumer surplus and dead-weig
- Suppose a monopolist faces the following demand curve: P = 100 - 3Q. Marginal cost of production is constant and equal to $10, and there are no fixed costs. What price will the profit maximizing monopolist charge? a. $100 b. $55 c. $45 d. $15 e. $10 f. No
- Suppose a monopolist faces the following demand curve: P = 88 - 3Q. The long-run marginal cost of production is constant and equal to $4, and there are no fixed costs. A) What is the monopolist's prof
- A monopolist faces a demand curve D(p)=100-2p and has a cost function c(y)=2y. What is the monopolist's optimal level of output and price?
- A monopolist faces the following demand curve: Price Quantity demanded $10 5 $9 10 $8 16 $7 23 $6 31 $5 49 $4 52 $3 60 The monopolist has total fixed costs of $40 and a constant marginal cost of $5. At the profit-maximizing level of output, the monopolist
- A monopolist has the following cost and inverse demand functions: C = 400 - 20Q + Q^2 P = 100 - 4Q Compute the DWL from monopoly power and in the case where the monopolist can perfectly price discriminate.
- Suppose a monopolist faces the following demand curve: P = 100 - 3Q. Marginal cost of production is constant and equal to $10, and there are no fixed costs. What is the value of consumer surplus? a. $300 b. $100 c. $412.50 d. $337.50 e. $750 f. None of t
- A monopolist faces a market demand curve given by Demand: Q = 70 - P. The monopolist faces the following cost structure: C = 0.25 Q^2 - 5 Q + 200. a. What output level will the monopolist choose in order to maximize profits? b. What is the price at this o
- A monopolist faces the following demand: P = 2265 - 17Q. The monopolist's cost function is: C = 2Q^3 - 13 Q^2 + 134Q + 1509. How much profit does the monopolist earn when it produces the quantity, Q,
- A monopolist faces the following demand: Q = 207 - 0.3P The monopolist's cost function is: C = 0.4 Q 3 ? 11 Q 2 + 238 Q + 1 , 949 How much profit does this monopolist earn when it
- Consider a monopolist that faces the following demand curve: P=150-Q. The total cost curve for this monopolist is given by the following: TC=100+10Q+Q2. Which of the following is true? a. The monopolist will set price equal to 115 and sell 35 units. b. Th
- Question One: A monopolist faces the following markets with the following demands functions: X1=100- P1 and X2=100- 2P2 Assume that the monopolist marginal cost is constant at KES 20. a) Find the pr
- Suppose a monopolist faces the following demand curve: P = 100 - 3Q. Marginal cost of production is constant and equal to $10, and there are no fixed costs. What is the monopolist's profit maximizing level of output? a. 10 b. 15 c. 16 d. 30 e. 33 f. None
- A monopolist faces demand P = 10 - Q. It has costs C(Q) = 2Q. It can perfectly price discriminate. a. What is its marginal revenue curve? Graph the demand curve. b. Derive the profit maximizing outpu
- A one-price monopolist faces a demand of P = 107 - 0.015Q and has a total cost function C(Q) = 5000ln(Q) + 30Q. Calculate the profit of the monopolist.
- 1. Your firm's cost function is: C = 2.5Q3 - 29Q2 + 545Q + 3,001 Your firm faces the following demand: P = 3,682 - 32Q Suppose your firm is a monopoly. Find the price that maximizes the monopolist'
- Suppose a monopolist faces the following demand curve: P = 314 - 7Q. The long-run marginal cost of production is constant and equal to $20. a. What is the monopolist's profit-maximizing level of output? b. What price will the profit-maximizing monopolist
- A monopolist sells a product with the following total cost function: TC = 1200 + 0.5Q^2 And the market demand curve is given by: P = 300 - Q (a) Find the profit-maximizing output and price for this monopolist. (b) Calculate the price elasticity of demand
- The monopolist faces a demand curve given by D(p) = 100 - 2p. Its cost function is c(y) = 2y. a. What is its optimal level of output and price? b. If the demand curve facing the monopolist has a constant elasticity of 2, then what will be the monopolist's
- Suppose that a monopolist faces market demand of Q = 200 - 0.5P and a cost function of C= Q^2 + 40Q + 50. What is the profit-maximizing price and quantity for the monopolist?
- A monopolist faces a demand function approximated by Qd = 125 - p. The monopolist total cost is C(Q) = 10Q. Which of the following statements is true? A. The optimal price for this monopolist is p* = $130. B. The optimal quantity is for this monopolist
- Consider a monopolist that faces the following demand curve: P = 150 - Q. The total cost curve for this monopolist is given by the following: TC = 100 + 10Q + Q^2. Which of the following is true? A) The monopolist will set the price equal to 115 and sell
- A monopolist faces the following demand and marginal cost data over the relevant range of output. {Price}&{Quantity Demanded}&{Marginal Cost} $7250&2&$450 $5000&3&$500 $3875&4&$575 $3200&5&$675 $2750&
- A monopolist faces the demand curve P = 100 - 2Q, where P is the price and Q is the quantity demanded. If the monopolist has a total cost of C = 50 + 20Q, determine its profit-maximizing price and output.
- Suppose the monopolist faces the demand P=100-3Q, which means MR(Q)=100-6Q, and marginal cost is given by MC(Q)=4Q. What price will the monopolist charge the consumers in equilibrium? a. $10 b. $20 c. $30 d. $70
- Suppose a monopolist faces a demand equation given by P = 20 - Q, and MC = AVC = ATC = $6. What is the profit maximizing price for the monopolist?
- A monopolist's cost function is C(y) = y(y/50 - 2) + y. It faces a demand function y = 100 - 25p. Solve for monopolist's output, price, profit and consumer surplus when the price is unregulated.
- Suppose a monopolist faces the following demand curve: P = 180 - 4Q. The marginal cost of production is constant and equal to $20, and there are no fixed costs. What price will the profit-maximizing monopolist charge? A. P = $100 B. P = $20 C. P = $60 D.
- Firm D faces the following demand: 40-P from male consumers and 30-3P from female consumers. The firm's cost function is C(Q)=25+5Q. a) Determine the profit of the monopolist if it can price discriminate between both demand functions. Monopoly pricing. b)
- A monopolist faces a market demand curve given by Q = 53 - P. Its cost function is given by C = 5Q + 50, i.e. its MC = $5. a. Calculate the profit-maximizing price and quantity for this monopolist. Also, calculate its optimal profit. b. Suppose a second
- Question 8 A monopolist faces the following demand: P = 2,141 - 13Q The monopolist's cost function is: C = 1Q3 - 12Q2 + 180Q + 1,308 How much profit does this monopolist earn when it produces the
- Suppose that, each period, a monopolist faces market demand P = 100 - 10Q and has constant marginal cost MC= 20 (with no fixed costs). A) If the monopolist can perfectly discriminate, how much d
- Tinysoft is a monopolist that faces demand curve D(p) = 7p^-3, has constant marginal costs MC = 30 and no fixed cost. What price should the monopolist charge? (a) p = 45 (b) p = 22.5 (c) p = 0.77
- The monopolist faces a demand curve given by D(p)=100-2p. Its cost function is c(y)=2y. What is its optimal level of output and price? If the demand curve facing the monopolist has a constant elastici
- Suppose that a monopolist faces a demand curve given by P = 100 - 2Q and cost function given by C = 500 + 10Q + 0.5Q^2. 9) What is the monopoly's profit-maximizing output level? A) 15 B) 18 C) 20 D) 3
- A monopolist faces a demand curve of Q = 400 - 2P and MR = 200 - Q. The monopolist has a constant MC and ATC of $30. a. Find the monopolist's profit-maximizing output and price. b. Calculate the monopolist's profit. c. What is the Lerner Index for this in
- A monopolist has the following cost function: C(q) = 800 + 8q + 6q^2. It faces the following demand from consumers: P = 200 - 2Q. There is another firm, with the same cost function, that may consider entering the industry. If it does, the equilibrium pric
- Suppose that a monopolist faces a demand curve: Q^ D = 3375P^{ -3} They have constant marginal costs: MC = 10. a) What is the price elasticity of demand? b) What is the monopoly price? c) What is the markup over marginal cost? How is this related to th
- Suppose a monopolist faces the following demand curve: P=200-6Q. Marginal cost of production is constant and equal to $20, and there are no fixed costs. A) What is the monopolist's profit-maximizing l
- Consider a monopolist with constant marginal cost c(c1) which faces the following demand function: Q(p,A)=1+\sqrt{A}-p, where A is the advertising expenditure and p is a relevant price. a) Derive the monopolist's optimal price and advertising expenditu
- A monopolist's cost function is TC(y) = y(\frac{y}{50} - 2)^2 +y. It faces a demand function y = 100 - 25p. Solve for monopolist's output, price, profit, and consumer surplus when the price is unregulated.
- Suppose a monopolist has costs to produce output of TC=1/6 Q^2+10 and faces the demand curve Q=3000-3P. Find equilibrium quantity, equilibrium price, and monopoly profit.
- A natural monopolist faces the following demand: P = 715 - 7Q The monopolist has the following cost function: C = 319Q + 736 How much output will this firm produce to maximize profit? Round our answe
- Suppose a monopolist faces the market demand function P = a - bQ. Its marginal cost is given by MC = c + eQ. Assume that a > c and 2b + e > 0. a) Derive an expression for the monopolist's optimal quantity and price in terms of a, b, c, and e. b) Show that
- A monopolist faces a market demand curve given by Q=53-P. Its cost function is given by Q=53-P, i.e. its MC=$5. a) Calculate the profit-maximizing price and quantity for this monopolist. Also calculate its optimal profit.
- Suppose a monopolist faces the following demand curve: P = 596-6Q. Marginal cost of production is constant and equal to $20, and there are no fixed costs. a) What is the monopolists profit maximizing level of output? b) What price will the profit maximi
- A monopolist faces a demand curve: P = 100 - Q for its product. The monopolist has fixed costs of 1000 and a constant marginal cost of 4 on all units. Find the profit maximizing price, quantity, and p
- Suppose a monopolist faces the following demand curve: P = 200 - 6Q The marginal cost of production is constant and equal to $20, and there are no fixed costs. (a) How much profit will the monopolist make if she maximizes her profit? (b) What would be t
- A natural monopolist faces the following demand: P = 8 - 0.01Q The monopolist has the following cost function: C = 0.018Q + 8 How much output will this firm produce to maximize profit if
- A natural monopolist faces the following demand: P = 19 - 0.024Q The monopolist has the following cost function: C = 0.039Q + 964 How much output will this firm produce to maximize profit?
- A monopolist faces the following demand curve P = 222 - 2Q. The monopolist's cost is given by C = 2Q. Calculate the profit-maximizing quantity and the corresponding price. What is the resulting profit/loss? Calculate the monopolist's markup.
- Suppose a monopolist faces the following demand curve: P = 180 - 4Q. Marginal cost of production is constant and equal to $20, and there are no fixed costs. What is the value of the deadweight loss created by this monopoly? A) 200 B) 400 C) 800 D) 512
- Suppose a monopolist faces the following demand curve: P = 100 - 3Q. Marginal cost of production is constant and equal to $10, and there are no fixed costs. What is the value of the deadweight loss created by this monopoly? a. $250 b. $675 c. $412.50 d.
- A monopolist faces the following demand: Q = 284 - 0.2P. The monopolist's cost function is: C = 0.5Q3 - 6Q2 + 235Q + 1,891. How much profit does this monopolist earn when it produces the quantity, Q,
- Suppose a monopolist faces the following demand curve: P = 200 - 6Q The marginal cost of production is constant and equal to $20, and there are no fixed costs. (a) What is the monopolist's profit-maximizing level of output? (b) What price will the profit-
- Suppose a monopolist faces the following demand curve: P = 180 - 4Q. The marginal cost of production is constant and equal to $20, and there are no fixed costs. What is the monopolist's profit-maximizing level of output? A. Q = 45 B. Q = 40 C. Q = 30 D. Q
- 1) A monopolist and competitive firm face the following demand: Q = 106 - 0.12P This firm's cost function is: C = 2Q^2 + 80Q + 1,375 Find the quantity, Q, that maximizes profit. Round your answer to
- 1. A natural monopolist faces the following demand: P = 12.6 - 0.03Q The natural monopolist has the following cost function: C = 0.039Q + 948 What price will this firm produce to maximize profit? (Rou
- For the following question, consider a monopolist. Suppose the monopolist faces the following demand curve: P = 100 - 3Q. Marginal cost of production is constant and equal to $10, and there are no fixed costs. What is the monopolist's profit maximizing l
- Suppose the monopolist faces the following demand curve: P = 180 - 4 q. Marginal cost of production is constant and equal to $20, and there are no fixed costs. What is the value of consumer surplus? a. 400.00. b. 150.00. c. 1600. d. 600. e. 512.5. f. None
- Suppose a monopolist faces the demand curve P = 164 - 1Q. The monopolist's marginal costs are a constant $22 and they have fixed costs equal to $132. Given this information, what will the profit-maximizing price be for this monopolist? Round answer to two
- Suppose a monopolist faces the following demand curve: P = 180 - 4Q. The marginal cost of production is constant and equal to $20, and there are no fixed costs. What is the value of consumer surplus? A. CS = $400 B. CS = $150 C. CS = $1,600 D. CS = $600 E
- A monopolist faces a demand curve given by P = 10 - Q and has constant marginal (and average cost) of 2. What is the output and the price that maximizes profit for this monopolist? (a) Q = 0, P = 10. (b) Q = 2, P = 8. (c) Q = 4, P = 6. (d) Q = 8, P = 2. (
- A monopolist faces a demand curve given by P = 10 - Q and has constant marginal (and average cost) of 2. What is the output and the price that maximizes profit for the monopolist? A) Q = 0, P = 10 B) Q = 2, P = 8 C) Q = 4, P = 6 D) Q = 8, P = 2 E) None of
- A monopolist faces the following demand curve: Price Quantity demanded $51 1 $47 2 $42 3 $36 4 $29 5 $21 6 $12 7 The monopolist has total fixed costs of $60 and has a constant marginal cost of $15. What is the profit-maximizing level of production? A) 5 u
- A natural monopolist faces the following demand P = 12.6 - 0.03 Q The natural monopolist has the following cost function: C = 0.039Q + 948 What price will this produce to maximize profit? Round your a
- Suppose a monopolist faces the demand curve P = 162 - 2Q. The monopolist's marginal costs are a constant $27 and they have fixed costs equal to $55. Given this information, what will the profit-maximizing price be for this monopolist?
- A monopolist faces the following market demand: Q=200-2P Suppose the firms total cost is given by: TC=50Q 1) Absent the ability to price disseminate, the monopolist, wanting to maximize profit, will
- A monopolist faces the following demand curve. Suppose the monopolist has total fixed costs equal to $5 and a variable cost equal to $4 per unit for all units produced. What is the total profit if she operates at her profit-maximizing price? A. $9 B. $7 C
- For the following question, consider a monopolist. Suppose the monopolist faces the following demand curve: P = 100 - 3Q. The marginal cost of production is constant and equal to $10, and there are no fixed costs. What is the value of consumer surplus?
- Consider a monopolist who faces a market demand curve given by QD = 200 - p and produces at a constant marginal cost of MC = 2.
- Assume that a monopolist faces a demand curve given by Q = 10 p^-3. His cost function is c (y) = 2 y. a. What is the optimal level of output and price? b. What would be the optimal level and price if the firm behaved as a perfectly competitive industry?
- Consider a monopolist that faces a linear inverse demand of: P(q) = 304 - 4q. The firm has the cost function of: C(q) = 100 + 4q + 2q^2. What are the monopolist market price (p^M), quantity (q^M), and
- A monopolist with total cost function T C = 30Q + Q2 is facing a market demand given by P = 150 - Q. a) What is the optimal quantity and price the monopolist will set on this market? (Q=30, P=120) b
- A monopolist faces inverse demand P = 300 - 2Q. It has total cost TC = 60Q + 2Q2 and marginal cost MC = 60 + 4Q. What is the maximum profit the monopolist can earn in this market?
- Suppose a monopolist faces the demand curve P = 250 - 2Q. The marginal cost of production is constant and equal to $10, and there are no fixed costs. A. What is the monopolist's profit-maximizing level of output? B. What price will the profit-maximizing m
- Suppose a monopolist faces the demand curve P = 100 - 3Q. The marginal cost of production is constant and equal to $10, and there are no fixed costs. a. What is the monopolist's profit-maximizing level of output? b. What price will the profit-maximizing m
- A monopolist firm faces the following cost curve: C(Q) = Q^2 + 12, where 'Q' is the output produced. The demand for its product is given by P = 24 - Q. A) Derive the MR for this firm. B) Find the equi
- Suppose that monopolist's inverse demand on market 1 is given by P 1 = 100 - x 1 , and monopolist's inverse demand on market 2 is given by P 2 = 50 - 0.5x 2 . Monopolist's cost function is c(x 1 + x 2
- A monopolist faces the demand curve P = 11 - Q. The firm's cost function is C = 6Q. a. Draw the demand and marginal revenue curves, and the average and marginal cost curves. What are the monopolist's
- A monopolist faces a market demand curve given by P(y) = 100 - y. Its cost function is c(y) = y^2 + 20. a. Find its profit-maximizing output level y* and the market price p(y*). b. Calculate its total revenue, total cost, and profit at y*. c. Calculate th
- A monopolist with total cost function c(Q) = 4 + 3 Q + 1/2Q^2 faces a market demand function of QD(P) = 60-4P. a) Calculate the monopolist's profit-maximizing price and quantity sold, and the monopol
- 1. Consider a monopoly that faces a market demand curve given as Q=100-P. the marginal cost of production for the monopolist is MC=$10. The monopolist faces total cost given by the following equation:
- A monopolist is seeking to price discriminate by segregating the market. The demand in each market is given as follows: Market A: P = 111 - 4Q Market B: P = 156 - 1Q The monopolist faces a marginal cost of $17 and has no fixed costs. Given this informatio
- A monopolist faces a demand curve given by P=10-Q and has constant marginal (and average cost) of 2. What is the output and the price that maximizes profit for this monopolist? a. Q = 0, P = 10 b. Q = 2, P = 8 c. Q = 4, P = 6 d. Q = 8, P = 2 e. None of th
- A monopolist faces an inverse demand P = 300 - 2Q and has total cost TC = 60Q + 2Q2 and marginal cost MC = 60 + 4Q. What is the maximum profit the monopolist can earn in this market? A) 60 B) 240
- Suppose a monopolistic competitor in long-run equilibrium has a constant marginal cost of $4 and faces the demand curve given in the following table. ||Price ($)||Quantity |8|0 |7|1 |6|2 |5|3 |4|4 |3
- Suppose a monopolist faces consumer demand given by P = 400 - 2Q with a constant marginal cost of $80 per unit (where marginal cost equals average total cost. Assume the firm has no fixed costs). A. If the monopoly can only charge a single price, what wil
Explore our homework questions and answers library
Browse
by subject