# Assume a firm's inverse demand for its product is P = 150 - Q and total cost is TC = 500 + 50Q...

## Question:

Assume a firm's inverse demand for its product is {eq}P = 150 - Q {/eq} and total cost is {eq}TC = 500 + 50Q {/eq} for a monopolistically competitive firm:

a) Find marginal revenue (MR) and marginal cost (MC).

b) Calculate the profit-maximizing price and quantity in the short-run.

c) Calculate the firm's profit in the short-run.

d) Explain what happens in the market in response to short-run profitability.

## Monopolistic Competition:

Monopolistic competition is a market structure characterized by a large number of firms selling differentiated products and for which there are weak barriers to entry into the market. Firms may differentiate their goods and services on the basis of physical attributes, quality and the location where they operate. Monopolistically competitive firms will earn normal profits in the long-run as competition and weak barriers to entry in the market will drive the profits to zero.

## Answer and Explanation: 1

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

View this answer**a) Find marginal revenue (MR) and marginal cost (MC).**

The marginal revenue is the change in the total revenue with respect to output. Likewise,...

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 3 / Lesson 56Learn the monopolistic competition definition with examples. Study monopolistic competition vs. perfect competition and other market types to learn the differences.

#### Related to this Question

- 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
- 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
- Suppose the demand for a product is given by Q = 200 - 5P. a) Calculate the Price Elasticity of Demand when the price of the good is P = 8. b) What is the Marginal Revenue of the firm when P = $8? c) If the firm wants to increase its total revenue, shoul
- 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) f
- 1. A monopolist has total cost TC = .1Q(squared) - 2Q + 100. Market demand is Q = 86 - P, implying that the firm's marginal revenue is MR = 86 - 2Q. Its profit-maximizing output is: a. 92 b. 46 c.
- 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?
- Consider an N firm symmetric Cournot model where aggregate inverse demand is P = 100 -2Q where Q is total output. Suppose that marginal costs are 10. What are the profits per firm when there are 5 fi
- A demand equation is given by P = 800 - .5Q. The firm's marginal cost is MC = 40 and TC = 40Q. Determine its price (P), output (Q), and total profits.
- A monopolist has total cost TC = 200 + .5 Q2. Marginal cost is Q and the market demand is Q = 100 - P/2. 1) What is marginal revenue? 2) What quantity maximizes profits? 3) What is the price in th
- Assume that the demand for a product is equal to Q = 200p^2. Assume that the marginal cost of production is a constant $80. Calculate the price that a monopolist would charge for the product. Assume t
- 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.
- 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
- 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
- Consider a firm with the following total revenue, marginal revenue, total cost, and marginal cost functions. TR = PQ = 20Q - 2Q^2, MR = 20 - 4Q, TC = 4 + 2Q^2, MC = 4Q A. What is the demand curve for the above firm (P = a - bQ)? B. What are the profit-max
- 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
- Assume that a monopolist faces a demand curve for its product given by: p = 120 - q. Further assume that the firm's cost function is: TC = 580 + 11q. How much output should the firm produce at an optimal price?
- Firm B is a monopolist that faces market demand of Q = 200 - 2P. Firm B's total cost is given by TC(Q) = 2Q^2 + 20Q + 200. What. Firm B's profit maximizing output level (Q') (Hint: inverse demand is
- A firm is considering entering a market where demand for its product is Q = 100 - P. This demand function implies that the firm's marginal revenue function is MR = 100 - 2Q. The firm's total cost of producing the product for that market is TC = 1000 + 20
- A profit maximizing monopolist faces the demand curve P = 90 - Q and has total cost of 30Q. If the monopolist charges only one price, what is Q, P, producer surplus, consumer surplus, and total revenue?
- 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
- 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
- The demand function (inverse) and the marginal cost function of a manufacturing-supply firm are as follows: P = -4.7Q + 240 MC = 2.6Q (a) Write the total revenue function from the inverse demand fun
- 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?
- Assume the inverse demand function for a Bertrand oligopoly is P = 300 - Q/4, and that the firm's total cost function is TC = 200 + 100Q. What is the firm's profit-maximizing output? a. 400 b. 800 c. 1,200 d. 1,600
- Suppose a firm faces the inverse demand curve P = 600Q^-0.5. The firm has the total cost curve TC = 1000+0.5Q^1.5. Find the firm's profit maximizing output, price and profit.
- 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
- A firm's total cost and marginal cost functions are TC = 20Q^2 + 6Q - 10 ; MC = 40Q + 6. Assuming that the market price is 166 and that the marginal revenue (MR) is also 166 (it is constant at al
- The demand curve that a monopolist faces is given by P = 75 - 0.5 Q, so their marginal revenue is MR = 75 - Q, and the marginal cost function is given by MC = 2 Q. Assume also that ATC at the profit-maximizing level of production is equal to $12.50. The d
- 2. A monopolist has inverse demand P = 12 ? Q and cost of production C(Q) = Q2. Find its profit maximizing output, resulting pric2. A monopolist has inverse demand P = 12 - Q and cost of production C(
- Assume that for a perfectly competitive firm marginal revenue equals rising marginal cost at 100 units of output. At this output level, the firm's total fixed cost is $600 and its total variable cost is $400. If the price of the product is $10 per unit, t
- An imperfectly competitive firm has the following demand curve: Q = 100 - 2P. What is marginal revenue equal to when P = 30? A) 5 B) 10 C) 15 D) 20 E) None of the above Explain.
- 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
- 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
- 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
- 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 a monopolistically competitive firm's demand is given by P = 4,000 - 2Q and its cost function is given by TC = 5 + 40Q. A) Find the profit maximizing quantity, price, and total profit level. B) If the firm is regulated to charge Price = Marginal C
- Suppose a perfectly competitive firm has a cost function described by TC = 200 Q + Q^2 + 225 Each firm's marginal revenue is $240. a. Find the profit maximizing level of output. b. Is this a short-run or long-run situation? c. Assuming that this firm's to
- Suppose that each firm in a competitive industry has the following costs: Total Cost: TC = 50 + \frac{1}{2}q^2 Marginal Cost: MC = q where q is an individual firm's quantity produced. The market demand curve for this product is: Q_D = 120 - P where P is t
- Consider a monopolist where the market demand curve for the produce is given by P = 520 - 2 Q . This monopolist has marginal costs that can be expressed as M C = 100 + 2 Q and total costs that can be expressed as T C = 100 Q + Q 2 + 50. a. What is th
- Suppose a monopolistically competitive firm s demand is given by P = 100 2Q And its cost function is given by TC = 5 + 2Q a. Find the profit maximizing quantity, price, and total profit level. b. Is
- Consider a homogeneous-good duopoly in which inverse demand is given by P(Q) = 2 in Q, where Q denotes the total output in the market. Firm 1's marginal cost is c1 = 1 while
- 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
- Given a firm has a demand function of: P = 45 - 4Q and average cost function of: AC = 1.5Q + 25 + 26/Q a. Find the level of output (Q) which: i. Maximizes total revenue (TR) ii. Makes marginal cost
- A firm faces an inverse demand of P(Q) = 30 - Q and total cost function of TC(Q) = 1/2Q2 + 6Q + 7, where P is price, Q is quantity, and TC is total cost. What is the output that maximizes profit?
- 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
- Suppose (inverse) market demand for a monopolist's product is given by P=90-Q and the monopolist's marginal cost is given by MC=Q (i.e. the marginal cost of the first unit (Q=1) is 1; the marginal cos
- 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 the firm in monopolistic market faces the following demand function: Q = 5,000 - 125P; and total cost function TC = 50 + 0.008Q2. a. Write the equation for the inverse demand function. b. Find the marginal revenue function. c. How much output shou
- 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
- Two firms are engaged in Cournot competition. They face an inverse demand function given by P = 57 - Q, where Q is the amount of total output produced by the two firms. Each firm has a constant marginal cost c = 3. There are no fixed costs. Find the pric
- Consider a perfectly competitive firm with a total cost function given by c(q) = 100 + q2, where q is the firm's output. The corresponding marginal cost function is given by MC(q) = 2q. Answer the que
- You are the economist of a firm with market power. The inverse demand for your product is given by P= 200 -10Q and your marginal cost is 5 + Q. a. What is the profit-maximizing level of output? b.
- Two firms are engaged in Cournot competition. They face an inverse demand function given by P = 57 - Q, where Q is the amount of total output produced by the two firms. Each firm has a constant marginal cost c = 3. There are no fixed costs. Find the reac
- A monopolist has the total cost function c (q) = 750 + 5 q. The inverse demand function is 140 - 7 q, where prices and costs are measured in dollars. If the firm is required by law to meet demand at a price equal to its marginal costs, a. the firm will ma
- 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?
- 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
- We are given the following: Demand: P=900-5Q Marginal Revenue: MR=900-10Q Total Cost: TC=6000+10Q^{2} Marginal Cost: MC=20Q Compute the firm's profit maximizing output, the price it charges and firm's
- 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
- Suppose that each firm in a competitive industry has the following costs: Total Cost: TC=50 + 1/2 q^2 Marginal Cost: MC=q Where q is an individual firm's quantity produced. The market demand curve for
- Suppose a profit-maximizing monopolist can engage in perfect price discrimination and faces a demand curve for its products given Q = 20 - 5P. This monopolist has a cost function of TC = 24 + 4Q. How much will monopolists profits be?
- 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
- You are the manager of a monopoly firm with (inverse) demand given by P = 50 - 0.5Q. Your firm's cost function is C = 40 + 5Q2. What is your firm's marginal revenue?
- 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
- A single-price monopolist faces the demand curve P = 500 - 50Q, and has the total cost curve TC = 1000 + 100Q, where P is in $/unit and Q is in units. If the firm is a profit-maximizer, what output should it plan for?
- 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
- Two firms are producing identical goods in a market characterized by the inverse demand curve P = 60 - 2Q, where Q is the sum of Firm 1's and Firm 2's output, q1 + q2. Each firm's marginal cost is constant at $12, and fixed costs are zero. Answer the foll
- Two firms are producing identical goods in a market characterized by the inverse demand curve P = 60 - 2Q, where Q is the sum of Firm 1's and Firm 2's output, q_1 + q_2. Each firm's marginal cost is constant at $12, and fixed costs are zero. Answer the fo
- Suppose that the inverse demand curve for a good is P ( q ) = a - m q (assume m is greater than 0 and a is greater than 0). Prove that the marginal revenue curve for a monopolist is in this market
- Assume that the demand for a product equals Q = 40 - P and the marginal cost of production equals a constant $10. Assume that there are no fixed costs so that average total costs are also a constant $10. Rather than charge a single price, assume that the
- Suppose that market inverse demand for widgets is given by P = 200 - 0.5Q. Suppose a widget-producing firm's total cost function is given by TC = 10 + 5Q + 0.2Q^2. Write down the firms marginal cost (
- 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
- 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
- Suppose the demand function for a profit maximizing monopolists good is P = 120 - 0.2Q, its total cost function is TC = 40 + 4Q + Q2, and its marginal cost function is MC = 4 + 2Q. If the firm uses a
- A demand curve is given by P= -1/2Q + 100. A marginal cost curve is given by MC = 2Q + 10. An average cost curve is given by ATC = Q + 10. a. How many output will the firm produce? b. What is the total revenue? c. What is the total cost? d. What is the pr
- 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
- Suppose that the inverse demand equation for a firm's product is P = 420 - 10Q. The total cost is given by the equation TC = 500 + 20Q^2. A. What are the profit-maximizing price and quantity from a single-price strategy? B. Given your answer to part A, wh
- Suppose a firm's inverse demand curve is P = 100 - Q and its marginal cost is constant at $20. Show that the value of the Lerner index at the profit-maximizing quantity is 0.67. Find the corresponding price elasticity of demand.
- Suppose that a competitive firm's marginal cost of producing output q is given by MC(q) = 3 + 2q. Assume that the market price of the firm s product is $9. \\ a) What level of output will the firm produce to maximize profit? b) What is the firm's produc
- A firm's demand function is defined as Q = 30 - 2P. a) Use this demand function to calculate total revenue when the price is equal to 10 and when the price is equal to 11. b) What is marginal revenue equal to between P = 10 and P = 11?
- Suppose a firm's cost function is given by C (q) = 2 + 12 q + 3 q^2 and the demand for its product is given by p = 20 - q (the firm can affect the price of its product). What is the firm's maximized profit? (a) 5. (b) 2. (c) 15. (d) 4.
- 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 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
- Assume that a perfectly competitive firm has the following total and marginal cost functions: C (Q) = 2 Q^2 + 10 Q + 400 MC (Q) = 4 Q + 10 Assume that the fixed cost is evenly divided between sunk and avoidable fixed costs. A. State the firm's supply func
- Suppose that inverse demand is given by p(Q) = A - BQ, where Q is the total quantity supplied in the market. There are two firms in the market, each with a cost function of c(q) = cq, now assume that the first firm moves before the second firm. A) Compar
- (Assume rms compete over quantity) Two identical rms are serving a market in which the inverse demand function is given by P = 400-2Q (P = 400-2(q1+q2)). The marginal costs of each firm are $40 per un
- 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
- For a perfectly competitive firm, the marginal revenue is always A. below the firm's demand curve. B. equal to the market price. C. equal to marginal cost. D. declining.
- A monopolist has demand and cost curves given by: Q = 1,000 - 0.25P TC = 500 + 50Q + Q^2 Show work for all parts: a. Find the equation for the inverse demand curve (P as a function of Q). b. Show the total revenue function. c. Show the marginal revenue
- 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 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?
- Assume that a firm is maximizing profits. a. If the price is $10 and marginal revenue is $6, what is the price elasticity of demand? b. If the price is $10 and the price elasticity is five, what is marginal revenue? c. If marginal revenue is $8 and t
- 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 At the profit
- The demand and cost function for a company are estimated to be as follows: P = 100 - 8Q TC = 50 + 80Q - 10Q2 + .6 Q3 For Q = 1:15, calculate total cost, marginal cost, price, total revenue and marg
- Consider a market with inverse demand P(Q) = ab-Q. Assume there are two firms each with cost function C(q) = cq^2 . (a) Find the Cournot equilibrium output per firm, and the Cournot price. (b) Compu
- Consider a Cournot industry with 2 firms. The demand is given by P = 120 - 2 Q, where Q is the total quantity produced by all firms in the market. The marginal cost is c = 20. Which of the following is true? A) The reaction function of firm 1 is q_1 = 50
- Consider a situation where a monopolist faces the following inverse market demand curve \\ p = 100 - q \\ and the following cost function \\ TC = 4q + q^2 \\ A. Derive the marginal revenue and marginal cost functions. B. What are the equilibrium price a
- If the monopolist's demand is given by P = 100 - Q , find the expression for marginal revenue.