Assume company A is a monopoly with a total cost function given as __C(q) = 50357 + 10q__, with q...
Question:
Assume company A is a monopoly with a total cost function given as C(q) = 50357 + 10q, with q representing quantity. Market inverse demand is given as P = 2450 - 2q.
Solve for marginal revenue, marginal cost, and average cost curves.
Marginal Revenue and Marginal Cost:
The marginal revenue is the additional revenue that accrues when one more unit of a good or service is sold. The marginal cost of production is the incremental cost incurred when one more unit of a good or service is produced.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answerTotal Revenue Function:
{eq}TR = P \times Q \\ TR = (2450 - 2q) \times q \\ TR = 2450q - 2q^{2} {/eq}
The marginal revenue function is derived...
See full answer below.
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
Marginal Revenue: Definition & Equation
from
Chapter 2 / Lesson 13
6.4K
Learn about marginal revenue and understand how to use the marginal revenue formula. See how to calculate marginal revenue and the impact of price and marginal cost.
Related to this Question
- Assume company A is a monopoly with a total cost function given as __C(q) = 50357 + 10q__, with q representing quantity. Market inverse demand is given as __P = 2450 - 2q__. Solve for P and Q at profit maximization and monopoly profit.
- Consider a monopoly whose total cost function is TC = 20 + 10Q + 0.3Q2 and whose marginal cost function is MC = 10 + 0.6Q. The demand function for the firms good is P = 120 - 0.2Q. The firm optimizes
- Consider a monopoly whose total cost function is TC = 10 + 5Q + 2.5Q2 and whose marginal cost function is MC = 5 + 5Q. The demand function for the firms good is P = 115 - 0.25Q. The firm optimizes by
- A monopoly produces widgets at a marginal cost of $10 per unit and zero fixed costs. It faces an inverse demand function given by P = 50 - 3Q. Which of the following is the marginal revenue function for the firm? A) MR = 100 - Q B) MR = 50 - 2Q C) MR = 60
- Monopoly A single monopoly firm faces the market demand of P = 90 - 2Q. Its cost function is characterized as C = Q2 + 100. a. Characterize the marginal revenue function. Plot the demand, marginal r
- 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
- The inverse demand curve that a monopoly faces is p = 78 - 4Q. The firm's cost curve is C(Q) = 228 + 2Q(squared) + 6Q, so that MC = 4Q + 6. a. Derive the marginal revenue for the monopolist. b. What i
- Consider a monopoly whose total cost function is TC = 40 + 4Q + Q^{2} and whose marginal cost function is MC = 4 + 2Q. The demand function for the firms good is P = 160 - 0.5Q. The firm optimizes by p
- Assume that a monopoly has the following inverse demand curve: P=80-5Q. The firm's total cost function is TC=20+10Q. At what output is the firm's total revenue maximized?
- Assume a monopolist firm has the cost function C = 10800 +1/4Q^2 And faces the demand function p = 5000-4/3Q a. Find the equation for marginal cost b. Find the equation for marginal revenue c. De
- Suppose the (inverse) demand function for a single-price monopoly is P = 520 - 2Q. This means that the marginal revenue function for the monopolist is MR = 520 - 4Q. Assume the marginal cost function is given by MC = 4Q. Find the price that the monopolist
- 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 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
- A monopolist faces a demand curve Q = 70 - P and has total costs TC(Q) = 0.25Q2 - 5Q + 300. a. Calculate the inverse demand curve P(Q) by solving the demand curve for P in terms of Q. b. Express the firm's total revenue as a function of quantity by multip
- 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 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
- Suppose the (inverse) demand function for a single-price monopoly is P=280-2Q. This means that the marginal revenue function for the monopolist is MR=280-4Q. Assume the marginal cost function is given by MC=3Q. Find the price that the monopolist will char
- 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
- 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
- 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:
- The demand for a monopoly is P = 60 - 0.3QD, where P is price and QD is quantity demanded. a) Plot the demand and marginal revenue curves. b) What is the equation for the firm's marginal revenue? c) At what output level would the monopoly maximize total r
- A monopolist faces demand given by: P = 100 - 0.4Qd, and has marginal costs given by: MC = 10 + 0.2Q a. Draw demand, marginal revenue and marginal cost curves. Calculate and show how much this firm
- 1. Suppose you are a monopolist and the downward-sloping demand curve you face takes the form: P=30-3Q: Quantity Price Total Revenue Marginal Revenue Total Cost Marginal Cost Profit 0 1 2
- A monopoly has an inverse demand function given by p = 120 - Q and a constant marginal cost of $10. (a) Graph the demand, marginal revenue, and marginal cost curves. (b) What is the profit-maximizing quantity and price for this monopolist? (Assume uniform
- Assume a monopolist faces a market demand curve of 50 = Q - frac{1}{2}P and has a short run total cost function C = 640 + 20Q. A. What is the profit-maximizing level of output? What are the profits? Graph the marginal revenue, marginal cost, and demand cu
- 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
- Consider a monopoly faces a market demand function q(p)=200-p, where p is the price that the monopoly charges, q is the amount demanded by the consumer. The monopoly has marginal cost function MC(q)=q
- Suppose that a monopoly faces the inverse demand function: P = 70 - 2Q and its marginal cost function is MC = 40 - Q a. What should be the monopoly's profit-maximizing output? b. What is the monopoly'
- A monopoly will set price: (a) at the highest price along its demand curve. (b) equal to the value at which marginal cost intersects the demand curve. (c) so that it can sell the quantity at which marginal revenue is equal to marginal cost. (d) so that it
- 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
- Consider a monopoly faces a market demand function q(p) = 200 - p, where p is the price that the monopoly charges, q is the amount demanded by the consumer. The monopoly has marginal cost function MC(
- Suppose there is a monopoly in the industry. Derive an equation for the marginal revenue of the monopolist. Graph the demand and marginal revenue curves.
- Assume a monopoly's (inverse) demand function is as follows: P=250-10Q. The firm's total cost function is: TC=80+10Q a) What is the profit maximizing output for this firm? b) What will be the firm's
- Suppose that a monopolist faces market demand of Q = 200 - 0.5P and a cost function of C = Q^2 + 40Q + 50. On a well-labelled graph, show the marginal cost, and marginal revenue in this market. What is the profit-maximizing price and quantity for the mon
- A monopolist faces demand given by: P=100- .4Qd and has marginal costs given by: MC=10+.2Q a. Draw the demand, marginal revenue and marginal cost curves. Calculate and show how much this firm will se
- Assume a firm's inverse demand for its product is P = 150 - Q and total cost is TC = 500 + 50Q for a monopolistically competitive firm: a) Find marginal revenue (MR) and marginal cost (MC). b) Calcu
- Suppose a monopolist has zero marginal cost and faces the following demand curve D(p) = 10 - 2p (a) Graph the demand curve, the marginal revenue curve, and the firm's marginal cost curve. Calculate t
- Suppose that a single price monopolist faces a market demand curve P = 200 - 4Q. The costs are equal to C(Q) = 40Q^2 A. Give a function for revenue as a function of Q. What is the firm's profits as a function of Q. B. What price will the firm choose? What
- Consider a monopolist whose total cost function is TC = 20 + 10Q + 0.3Q2 and whose marginal cost function is MC = 10 + 0.6Q. The demand function for the firm's good is P = 120 - 0.2Q. The firm optimiz
- If a monopoly's inverse demand curve is P = 13 - Q and its total cost function is TC = 25 + Q + 0.5Q^2, A. what Q* maximizes the monopoly's profit (or minimizes its loss)? At Q^*, what are the price and the profit? Should the monopolist operate or shut do
- A monopolist faces demand given by: P = 100 - 0.4QD, and has marginal costs given by: MC = 10 + 0.2Q. (A) Draw the demand, marginal revenue and marginal cost curves. Calculate and show how much this firm will sell and what they will charge. (B) Calculate
- 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
- Suppose that a company has market power. The demand curve that it faces is Q=10-0.4P, and its marginal cost curve is MC=1+Q. a. Determine the marginal revenue function. b. Determine the company's prof
- A monopoly has the following demand, marginal revenue, total cost, and marginal cost curves: Demand P=1000-10Q MR= 1000-20Q TC= 100Q+5Q^2 MC=100+10Q a. Find the price and quantity that maximizes the monopoly's profits, b. How many profits does the monopo
- The inverse demand function a monopoly faces is p = 90 - Q. The firm's cost curve is C(Q) = 5 + 2Q. a) What are the profit-maximizing price and quantity? What is the firm's profit? b) How do the answers change if C(Q) = 1 + 4Q?
- A monopolist faces demand given by P = 100 - 0.4QD and has marginal costs given by MC = 10 + 0.2Q. a. Draw the demand, marginal revenue, and marginal cost curves. Calculate and show how much this firm will sell and what they will charge. b. Calculate the
- Suppose that a monopoly faces inverse market demand function as P = 70 - 2 Q and its marginal cost function is MC = 40 - Q. Answer the following two questions. a. What should be the monopoly's profit-maximizing output? b. What is the monopoly's profit?
- Suppose that a monopolist's inverse demand curve can be expressed as: P=20000-Q(2) The monopolist's total cost curve is: TC=8000Q a). Determine the monopolist's marginal revenue curve. b). Determin
- Assume a natural monopoly with total costs C=500+20Q. Market demand is Q=100-P. If price is set at marginal cost, what is the monopolist's profit?
- Given the inverse demand function: P = 15 - 0.025X, where X is the total quantity demanded: There are two firms in the market, each with a constant marginal cost of RM7.50. Find the outcome for: a) C
- Suppose a monopoly's inverse demand curve is P = 100 - 2Q, it produces a product with a constant marginal cost of 20, and it has no fixed costs. Compared to the consumer surplus if the market were per
- Assume a natural monopoly with total costs C = 500 + 20Q. Market demand is Q = 100 - P. a) If a price is set at marginal cost, what is the monopolist's output and profit? Compute consumer surplus. b)
- 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
- The inverse demand function for a monopoly is p = 350 - 3.5Q. a) What is its marginal revenue function? b) Draw the demand and marginal revenue curves. Label the quantities where the demand and marginal revenue hit the quantity axis.
- 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
- Consider a single monopoly that faces a market demand curve for a good given by the equation P = 100 - .1Q and the total cost function given as TC = 1000 + 20Q - .4Q^2. What is the total fixed cost for this monopoly?
- 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
- Assume a monopolist's marginal cost and marginal revenue curves intersect and the demand curve passes above its average total cost curve. The firm will: a. lower the price. b. make an economic profit. c. stay in operation in the short run but shut down in
- Suppose a single-price monopolist with TC = 20Q faces an inverse demand curve P = 120 - Q and marginal revenue curve MR = 120 - 2Q, where Q is output per period. a. What is the marginal cost (MC) for the firm? What is the average cost (AC) for the firm? I
- 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
- Assume that a monopolist has a demand curve given by P=1500-4Q, and TC=100+5Q(squared) with MC=10Q. A) Graph the Demand, marginal revenue, marginal cost, and average total cost curves B) what are the
- 1. Consider a monopoly where the inverse demand for its product is given by P = 50-2Q. Total costs for this monopolist are estimated to be C(Q) = 100 + 2Q + Q^2. At the Profit-maximizing combination of output and price, consumer surplus is? 2. You are th
- You are the manager of a monopoly that faces an inverse demand curve described by P = 63 - 5Q. Your total costs are C = 10 + 3Q. and your marginal cost are MC = 3. The profit-maximizing output for your firm is: a. 3. b. 4. c. 5. d. 6.
- If the inverse demand curve a monopoly faces is p = 55 - 4Q, and it has a constant marginal cost of 17, then what is the profit maximizing quantity?
- 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
- Assume a monopolist faces a market demand curve p = 100 - 2Q and MC = 20. a. What is the profit-maximizing level of output and price? b. Graph the marginal revenue, marginal cost, and demand curves,
- A monopoly has total cost and marginal cost given by: TC = Q^{2} + 5Q + 100 MC = 2Q + 5 The market demand curve is given by: P = 65 - 2Q A. Use the twice-as-steep rule to find the equation of the m
- If the demand curve of a company is P = $36 - $2Q and fixed cost is $10, the variable cost is 5Q + 0.5Q2. 1) What would be the quantity for revenue maximization and profit maximization? 2) What would be the quantity for break-even?
- A monopoly has total cost and marginal cost given by:TC = Q^2 + 5Q + 100, MC = 2Q + 5. The market demand curve is given by:P = 65 - 2QA. Use the twice-as-steep rule to find the equation of the margina
- A monopoly faces a market demand curve given by: Q = 60 - P, and a marginal revenue curve given by: MR = 60 - 2Q. If MC = AC = 10; A) Calculate profit-maximizing price and quantity for the monopoly. B
- Suppose a single price monopolist with TC=20Q faces an inverse demand curve P=120-Q and marginal revenue curve MR=120-2Q, where Q is output per period. a) What is the marginal cost (MC) for the firm?
- 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
- 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 t
- A monopoly has an inverse demand curve given by P = 16 - Q and a constant marginal cost of $2. Calculate deadweight loss if the monopoly charges the profit-maximizing price. (Give your response rounded to two decimal places.)
- 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.
- 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
- Firm total cost function: C = 100 + 2Q2 Firm marginal cost function: MC = 4Q Industry demand curve: P = 90 - 2Q Industry marginal revenue curve: MR = 90 - 4Q a. If there is only one firm in the industry, find the monopoly price, quantity, and level of pro
- Suppose two firms compete in an industry with an inverse demand function given by P = 200 - 2Q. Each firm has a marginal cost of $40. A) Solve for the monopoly profits, quantity, and price. B) Solve for the Cournot Nash Equilibrium. State the quantities a
- 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
- 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
- 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
- A monopolist has demand and cost curves given by: Q = 200 - P, TC = 50 + 25Q + 0.1Q^2. Show work for all parts: a. Find the equation for the inverse demand curve (P as a function of Q). b. Show total revenue as a function of Q. c. Show marginal revenue as
- 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 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
- Consider the information below for a monopoly firm. Assume the Q equals the level of output and all costs are economic costs. Total Revenue = 220Q - 0.5Q^2 Marginal Revenue = 220 - Q Total Cost = 1,000 + 20Q + 0.5Q^2 Marginal Cost = 20 + Q Under these c
- 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
- 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 monopoly's inverse demand curve is given by P = 200 - 5Q. The marginal cost of producing the product is $50. What is the profit maximizing price and output for the product? a. P = $150, Q = 10 b. P = $125, Q = 15 c. P = $50, Q =10 d. P = $50, Q = 30
- Let the inverse demand curve be p(q)=a-bq. Suppose there are two firms, with constant marginal cost equal to C. Now suppose that the two firm engage in price competition (set p) instead of quantity co
- 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.
- Suppose a monopoly firm faces a market demand of P = 500 - Q. The firm has a marginal cost of $40. What would we expect to be the consumer surplus in the market?
- Suppose that a monopolist faces the demand curve P) 2 Q, and has total cost curve TC(Q) = Q^2. (a) If the firm is unable to price discriminate, find the firm's 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
- Consider a monopoly whose total cost function is TC = 10 + 5Q + 2.5Q^2 and whose marginal cost function is MC = 5 + 5Q. The demand function for the firm's goods is P = 115 - 0.25Q. The firm optimizes by producing the level of output that maximizes profit
- 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
- Assume that a monopolist faces a demand curve for its product given by: \\ p = 100 - 1q \\ Further assume that the firm's cost function is: TC=550+9q \\ Using calculus and formulas (but no tables or spreadsheets) to find a solution, how much output
- 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 that you are a monopolist who produces gizmos, Z, with the total cost function C(Z) = F + 50Z, where F represents the firm's fixed cost. Your marginal cost is MC = 50. Suppose also that there
- 3. Suppose that an incumbent dominant firm produces with a cost function given by C = 100 + 1.5qi2 so that marginal cost is given by MC = 3qi Inverse demand is P = 200? Q where Q is total output of al
Explore our homework questions and answers library
Browse
by subject