# Consider a monopolist facing linear demand P(Q) = 16 - Q. Find the monopolist's profit-maximizing...

## Question:

Consider a monopolist facing linear demand P(Q) = 16 - Q. Find the monopolist's profit-maximizing choice of price and quantity if C(Q) = 8Q so that marginal cost is constant at 8.

## Monopoly's Profits

In economics, monopoly profits are determined by subtracting the total revenue from the total cost at the point where the marginal revenue is equal to the marginal cost. The profit at this point is maximum.

## Answer and Explanation: 1

Become a Study.com member to unlock this answer! Create your account

View this answer

The demand function for the monopolist is given as:

{eq}P=16-Q {/eq}

The total revenue is equal to:

{eq}TR=PQ\\[0.3cm] TR=(16-Q)Q=16Q-Q^2 {/eq...

See full answer below.

#### Ask a question

Our experts can answer your tough homework and study questions.

Ask a question Ask a question#### Search Answers

#### Learn more about this topic:

from

Chapter 7 / Lesson 2Understand the meaning of a monopoly in economics and what it does. Also, know the characteristics of a monopoly and the different types of monopolies.

#### Related to this Question

- Consider a monopolist with a linear marginal cost which is decreasing for quantity 0 < or equal to 20 and at Q = 0, the marginal cost becomes 0. Assume a linear market demand so the marginal revenue i
- Consider a monopolist that produces a good at a constant marginal and average cost of 5$. The market demand is given by p = 53 - Q A) calculate the monopolists' profit at the profit-maximizing equilibrium
- Suppose the demand curve for a monopolist is P = 200 - QD. The monopolist has a constant marginal and average total cost of $50 per unit. a. Find the monopolist's profit-maximizing output and price.
- 1. Consider a monopolist in a market with linear inverse demand p(q) = 4-4/2. The monopolist's cost function is c(q) = 2q. Write down the monopolist's profit function. Compute the profit-maximizing qu
- Consider a monopolist with a demand equation P = 60 - 2Q with a constant marginal cost of $20 which is equal to the average total cost. a. Assume the monopolist charges a single price to all its customers. Identify the price and quantity with the aid of a
- Suppose a monopolist has a demand curve that can be expressed as P = 60 - Q. The monopolist's marginal revenue curve can be expressed as MR = 60 - 2Q. The monopolist has constant marginal costs of $20. The profit-maximizing monopolist will have a deadweig
- 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
- Consider a monopolist with a cost function pf c(Q)=4+2Q. Suppose the market demand function is QD=24-2P. a) Under uniform pricing (basic monopoly problem), find the monopolist's optimal price and quan
- Suppose a monopolist knows the own price elasticity of demand for its product is -5.4 and that its marginal cost of production is constant MC(Q) = 40. To maximize its profit, the monopoly price is:
- Suppose that a monopolist faces linear demand given by Q(p) = 1000 - 5p. The monopolist also pays a marginal cost of $10 for each unit produced. 1. What is the optimal quantity that the monopolist will charge to maximize its profits? a. 450 b. 475 c. 500
- Suppose that a monopolist faces linear demand given by Q(p) = 100 - 2p. The monopolist also pays a marginal cost of $1 for each unit produced. 1. What is the optimal quantity that the monopolist will charge to maximize its profits? A. 99 B. 49 C. 100 D. 5
- Suppose that a monopolist faces a linear demand given by Q(p) = 100 - 2p. The monopolist also pays a marginal cost of $1 for each unit produced. What is the optimal quantity that the monopolist will charge to maximize its profits?
- Suppose the demand curve for a monopolist is QD= 47,000 - 50 P, and the marginal revenue function is MR=940 - 0.04Q. The monopolist's Marginal Cost = 40+ 0.02Q and its Total Cost = 250,000+ 40Q+ 0.01Q^2. a. Find the monopolist's profit-maximizing output
- Suppose that a monopolist's market demand is given by P = 100 - 2Q and that marginal cost is given by MC = Q/2. a) Calculate the profit-maximizing monopoly price and quantity. b) Calculate the pri
- Suppose a monopolist's marginal costs are constant at $20 per unit, and it faces a demand curve of Q = 300 - p. a. If it cannot price discriminate, what are the profit-maximizing price and quantity?
- Suppose a monopolist has a demand curve that can be expressed as P = 90 - Q. The monopolist's marginal revenue curve can be expressed as MR = 90 - 2Q. The monopolist has constant marginal costs and average total costs of $10. The profit-maximizing monopol
- How does the monopolist determine the profit-maximizing price? A. Find where marginal cost and demand intersect, and then use the demand curve to determine the price. B. Find where marginal cost and marginal revenue cross, and then use the demand curve to
- Suppose the demand curve for a monopolist is Q_D = 47,000 - 50P and the marginal revenue function is MR = 940 - 0.04Q. The monopolist's marginal cost is MC = 40 + 0.02Q and his total cost is TC = 250,000 + 40Q + 0.01Q^2. A.. Find the monopolist's profit-m
- Suppose the demand curve for a monopolist is Q_D = 47,000 - 50P and the marginal revenue function is MR = 940 - 0.04Q. The monopolist's marginal cost is MC = 40 + 0.02Q and its total cost is TC = 250,000 + 40Q + 0.01Q^2. A. Find the monopolist's profit-ma
- Assume this monopolist's marginal cost is constant at $48. What quantity of output (Q) will it produce and what price (P) will it charge?
- 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?
- Consider a monopolist that produces a good at a constant marginal and average cost of $5. The market demand is given by p = 53 - Q. Suppose now that the demand for the monopolist is q = 100/p and marg
- Assume that a monopolist sells a product with a total cost function TC = 2,150+ 0.3Q^2 and a corresponding marginal cost function MC = Q. The market demand curve is given by the equation P= 240 - Q. a) Find the profit-maximizing output and price for this
- Assume that a monopolist sells a product with a total cost function TC = 1,200+ 0.5Q^2 and a corresponding marginal cost function MC = Q. The market demand curve is given by the equation P= 300 - Q. a) Find the profit-maximizing output and price for this
- Suppose a monopolist has no fixed costs and constant marginal cost of c. Demand is given by the equation P=alpha-beta q 1. Derive the profit maximizing price and quantity. 2. Calculate the monopolist'
- 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
- 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
- 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
- A monopolist faces a demand curve given by P=10-Q and has constant marginal (and average cost) of 2. What is the economic profit made by this profit-maximizing monopolist? a. 0 b. 12 c. 14 d. 16 e. None of the above
- If marginal costs are constant at $6, what is the profit-maximizing monopolist price?
- Suppose the demand curve for the product of a monopoly seller is reliably estimated as Qd = 300 - 15P (P is measured in dollars). If the marginal cost for the monopolist is constant at $5 per unit of output, the monopolist would maximize revenue by settin
- Assume that the market demand curve is Q = 60 - 2P. a. Write the equation for the monopolist's marginal revenue curve. b. Assume that the monopolist has constant marginal costs equal to 10. Calculat
- A monopolist has cost c(q) = q^2 and the inverse demand for its product is P = 15 - Q. What is its marginal revenue curve? Derive its marginal cost. Derive the firm's profit maximizing output, total
- 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 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 is selling in a market with the following demand curve: P = 300 - 0.5 Q The marginal revenue is MR = 300 - Q. The firm has constant marginal costs of $50 per unit. What is the monopolist's profit-maximizing quantity and profit-maximizing pric
- A monopolist can produce at a constant average (and marginal) cost of AC= MC= $5. It faces a market demand curve given by Q=53-P. a. Calculate the profit-maximizing price and quantity for this monopolist. Also, calculate its profits. b. Suppose a second
- Consider a monopolist who is faced with the market demand curve P = 10 - Q. Its total cost is given by 2Q. (a) If the monopolist has to use one price, what would be profit maximizing price? (b) If th
- 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
- 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 = 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
- The demand for a monopolist's output is q = 6,000/((p+7)^2) , where p is its price. It has constant marginal costs equal to $5 per unit. What price will it charge to maximize its profits? The answer i
- Suppose a monopolist has constant average marginal cost of (AC = MC = 8) and faces demand such that QD = 100 - P. The firm's profit maximizing revenue will be: a) 736 b) 368 c) 2484 d) 3680
- The profit-maximizing quantity for a monopolist is found where marginal revenue equals marginal cost. How does the monopolist find the profit-maximizing price? a. It is equal to the height of the supply curve at the profit-maximizing quantity. b. It is eq
- 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
- Consider a market which is served by a single-price monopolist with marginal cost given by MC = 2Q. The market demand is given by P = $800 - 3Q. Calculate the following: a) the firm's marginal revenue function b) its profit-maximizing quantity c) its prof
- Consider a monopolist with the cost function C(Q) = 10Q and a corresponding marginal cost of MC(Q) = 10. The market demand is Q = 40 - 2P, which gives a marginal revenue of MR(Q) = 20 - Q. a. Write out the firm's inverse demand curve. b. Draw the (inverse
- 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
- For the next 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 price will the profit-maximizing monopol
- 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. How much profit will the monopolist make if she maximizes her profit? A. Profit = $1,600 B. Pr
- Consider a monopolist facing an inverse demand function of p(q) = 15 - 3q, where 'q' denotes units of output. Assume that the cost of this firm is TC(q) = 5 + 4q. A) Find the monopolist's marginal rev
- 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.
- 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?
- 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 is characterized as follows: P = 1200-6Qdemand curve for the monopolist, C = 8600 +32Q + Q^2 total cost function for the monopolist, MC =32 + 2Q marginal cost function for the monopolist. a. To maximize its profit, the monopolist s
- 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. How much profit will the monopolist make if she maximizes her profit? a. $300 b. $327.50 c. $825 d
- A monopolist has a demand function of Q=1600-100P. Suppose that marginal cost is constant, MC=2 and C=2Q. a. What are the monopolist's choices of quantity and price? b. How large are consumer surplus, producer surplus, and deadweight loss?
- 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.
- 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
- Assume that a monopolist sells a product with a total cost function TC = 1,200 + 0.5Q^2. The market demand curve is given by the equation P = 300 - Q. a) Find the profit-maximizing output and price for this monopolist. Is the monopolist profitable? b) C
- 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
- The marginal cost for a monopolist is 5 and the price elasticity of demand (in absolute terms) is 4. What is the profit -maximising price? a. P = 8 b. P = 10 c. P = 12 d. P = 4 e. P = 16
- If a profit maximizing monopolist faces a linear demand curve and has zero marginal cost, it will produce at : A elasticity of demand equals 1. B the lowest point of marginal profit curve. C All of
- 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 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 a monopolist faces the demand function 12\times 0.1 - Q. The corresponding marginal revenue function is 12 \times 0.2 - Q. Further, suppose that marginal cost is constant at $5. a) What will be the profit maximizing quantity and the profit maximiz
- A monopolist faces a demand curve given by P = 10 - Q and has a constant marginal (and average) cost of $2. What is the economic profit made by this profit-maximizing monopolist? a. $0 b. $12 c. $14 d. $16 e. none of the above
- A monopolist faces a demand curve given by P = 10 - Q and has constant marginal and average cost of 2. What is the economic profit made by this profit-maximizing monopolist? A) 0 B) 12 C) 14 D) 16
- Suppose a monopolist knows the own price elasticity of demand for its product is -5.7 and that its marginal cost of production is constant MC(Q) = 47. To maximize its profit, the monopoly price is: R
- Consider a monopoly with the cost curve c(q) = 60 + 10q and the demand function p(q) = 45 - q - frac{q^2}{3}. What is the profit-maximizing solution for the monopoly? How large are its profits?
- Assume a profit-maximizing monopolist faces a market demand given by P = (12,000 ? 90Q)/100 and long run total and marginal cost given by LRTC = 5Q + Q2 + 40 LRMC = 5 +2Q a) Use the twice-as-steep ru
- Assume that a monopolist has a demand curve given by P = 1500 - 4Q, and T C = 100 + 5Q^2 with MC = 10Q 1. Graph the Demand, Marginal Revenue, Marginal Cost, and Average Total Cost curves. 2. What ar
- 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
- 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?
- What is the profit-maximizing quantity for the monopolist when marginal revenue is MR = 100 - 5Q, demand is P = 100 - \frac {1}{2}5, variable cost is 60 + \frac{1}{2} 8 Q^2 , and marginal cost is MC = 8Q ?
- 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
- 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-
- Consider a monopolist who produces good X using a total cost function 10+10X. The demand for good X is X=100-0.5P, where P is the market price. a. Find the profit maximizing output level for the firm,
- Suppose a monopoly with a cost function of C(Q) = 4Q2 - 6Q + 200 faces a market demand of QD = 2,388 - 2P. A) Calculate the firm's total revenue, marginal revenue, and marginal cost. B) Calculate the profit-maximizing output and price. C) Over what ran
- Suppose a monopolist has costs to produce output of TC = 4.5Q(squared) and faces the demand curve Q = 2000 - 2P. Find the equilibrium quantity, equilibrium price, and monopoly profit.
- Suppose a monopolist has costs to produce output of TC = 4.5Q^2 and faces the demand curve Q = 2000 - 2P. Find the equilibrium quantity, equilibrium price, and monopoly profit?
- Suppose the demand function for a monopolist's product is given by Q = 50 - 0.5P, and the cost function is given by C = 10 + 2Q. Calculate the MC. Calculate the MR. Determine the profit-maximizing price. Determine the profit-maximizing quantity. How much
- A monopolist faces a demand curve MB = 300 - 10Q and has declining marginal costs equal to MC = 150 = 5Q. A. Compute the optimal quantity Q* and the optimal price P*. B. Write down the equation for the monopolists' marginal revenue curve MR. C. How much w
- 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 has costs C(Q)=5Q. It has one consumer whose inverse demand is P=35-Q. a. Derive the monopolist's marginal cost and average cost. Graph the demand and marginal cost curve. b. Derive the p
- Consider a situation where a monopolist faces the following inverse demand curve, p = 350 - q and constant marginal costs of MC = 50. What are the equilibrium price and quantity for this monopolist?
- Assume that a monopolist's marginal cost is $10 and the elasticity of demand is -2. We can conclude that the firm's profit maximizing price is approximately a. $20 b. $5. c. $10. d. The answer cannot be determined without additional information.
- Consider a monopolist who faces a market demand curve given by QD = 200 - p and produces at a constant marginal cost of MC = 2.
- 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
- For the next 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. How much profit will the monopolist make if she m
- A monopolist has demand and cost curves given by: Q_D = 1000 - 2P \\ TC = 5,000 + 50Q a. The monopolist's profit-maximizing quantity is [{Blank}] units and the price is $[{Blank}], b. The monopolist's profit is $ [{Blank}].
- Consider a monopolistic market with market demand function q = 8 - 2p. Also suppose marginal cost of production is constant and equal to 2. We examine the fact that profit maximization should yield th
- Consider a monopolist with a marginal cost equal to $5 selling to two market segments with inverse demands given by pH = 20 - qH and pL = 15 - qL. There are no fixed costs. Calculate the amount of profit the monopolist could theoretically make if he could
- For a pure monopolist, marginal revenue is less than price because a.the monopolist's demand curve is perfectly elastic. b.the monopolist's demand curve is perfectly inelastic. c.when a monopolist
- Suppose a monopolist faces a market demand curve given by P = 50 - Q, and a marginal revenue curve given by MR = 50 - 2Q. Suppose marginal cost is initially equal to zero and constant. a. Calculate t
- A single price monopolist faces a demand curve given by Q = 200 - 2p and has constant marginal (and average total cost) of 20. What is the economic profit made by this profit-maximizing monopolist? A. 0 B. 800 C. 3200 D. 6400 E. None of the above
- Assume that a monopolist sells a product with a total cost function TC=1200+1/2Q2. The market demand is given by the equation P=200-Q. a) Find the profit-maximizing output and price for this monopolis
- 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 the demand curve for a monopolist is QD = 500 - P, and the marginal revenue function is MR = 500 - 2Q. The monopolist has a constant marginal and average total cost of $50 per unit. a. Find th