Given a firm's demand function, P = 24 - 0.5Q and the average cost function, AC = Q2 8Q + 36 +...
Question:
Given a firm s demand function, P = 24 - 0.5Q and the average cost function, AC = Q2 8Q + 36 + 3/Q, calculate the level of output Q which
a. Maximizes total revenue
b. Maximizes profits
Profit Maximization:
Profit is maximized when the marginal revenue of producing an additional unit of production equals the marginal cost of production that extra unit.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answera. Maximizes total revenue
- {eq}R = PQ = 24Q - 0.5 Q^2 \\ R'=MR=24-Q=0 → Q^*=24 {/eq}
b. Profit is maximized when MR = MC
- {eq}AC = Q^2 - 8Q +...
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
Profit Maximization: Definition, Equation & Theory
from
Chapter 24 / Lesson 6
42K
Learn the profit maximization definition, its importance, and explore the profit maximization theory. See how to calculate profit maximization with examples.
Related to this Question
- 2. Given a firm s demand function, P = 24 - 0.5Q and the average cost function, AC = Q2 8Q + 36 + 3/Q, calculate the level of output Q which a) maximizes total revenue b) maximizes profits
- Given a firm demand function, P 24 0.5 Q and the average cost function, AC Q2 8Q 36 3 Q. Calculate the level of output Q which: a maximizes total revenue b maximizes profits
- Given a firms demand function, P 24 0.5Q and the average cost function, AC Q2 8Q + 36 + 3 Q, Calculate the level of output Q which a maximizes total revenue b maximizes profits.
- 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's demand function is Q = 16 - P and its total cost function is defined as TC = 3 + Q + 0.25Q2. Use these two functions to form the firm's profit function and then determine the level of output
- Cost function: TC = 680 + 4Q + .01Q2, P = 12 - Q/500 (inv. demand function) Determine: a) total revenue function b) production level Q* that maximizes total profit c) selling price P* and total pro
- A producer has a total cost function TC = Q^2 + 2Q + 66 and a demand function Q = 10 - 0.2P. A. Determine the average revenue (AR), marginal revenue (MR), and marginal cost (MC) functions. B. What are the outputs and prices that maximize profits? C. What
- A firm has a demand function P = 200 - Q and cost function: AC=MC=20 and a potential entrant has a cost function: AC=MC=30. a. Determine the optimal price, quantity and economic profit for the firm
- The demand for product Q is given by Q = 385 - P and the total cost of Q by: STC = 3000 + 40Q -5Q^2 + 1/3Q^2 a. Find the price function and then the TR function, b. Write the MR and MC functions, c. What positive value of Q will maximize total profit?
- 67. A firm has a demand function P = 200 - Q and cost function: AC=MC=20 and a potential entrant has a cost function: AC=MC=30. D. Determine the optimal price, quantity and economic profit for the fi
- 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?
- 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 firm's demand function is Q=16-P and its total cost functions is defined as TC=3+Q+0.25Q^2. Use these two functions to form the firm's profit function and then determine the level of output that yields the profit maximum. What is the level of profit at
- The Bramwell Corporation has estimated its demand function and total cost function to be as follows: Q = 25 - 0.05P TC = 700 + 200Q Find the price and quantity if Bramwell wants to: a. maximize profits b. maximize revenue c. maximize revenue but require t
- A firm faces the following demand and total cost functions: Q = 28 - 0.5P TC = 56.25 + 2Q + 0.25 (a) Calculate Q that minimizes Average Cost. (b) Calculate the Revenue-maximizing price. (c) Calculate
- A firm has an inverse demand function given by P(q) = 100 - 3q and its cost function is C(q) = 100 +10q a. What is the profit-maximizing level of output? b. What is the maximum profit the firm can e
- Given demand curve of the monopolist Q 30 0.3P and given the cost function C 2 Q 2 20 Q 10 a Find the profit maximizing level of output and price b Determine the max possible profit. c Check for the 2
- A firm faces the following demand and total cost functions: Q = 28 - 0.5P TC = 56.25 + 2Q + 0.25Q^{2} a) Calculate Q that minimizes average cost. b) Calculate the revenue-maximizing price. c) Calculat
- Given the cost function: C o s t 0.2 q 3 6 q 2 80 q F, and marginal cost: 0.6 q 2 12 q 80 where q output, and F fixed costs $100. The demand equation is: p 90 2 q .Determine the profit maximizing pric
- 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.
- Given an aggregate demand function Q (p) = 100 - 2 p and a cost function for each firm of C (q) = 5 q^2 + 2. Suppose there are 80 firms. Solve for the price, quantity, and profits for each individual firm, given that the number of firms is fixed.
- A firm has a demand function P = 200 - 5 Q and cost function: AC = MC = 20 and a potential entrant has a cost function: AC = MC = 40. a. Determine the optimal price, quantity and economic profit for the firm if it is a pure monopolist. b. If the firm want
- 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
- Using the demand function Q = 300 - 10P, determine the equation of the total revenue (TR), average revenue (AR) and marginal revenue (MR).
- 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 firm faces the following average revenue (demand) curve: P = 100 - 0.01 Q where Q is weekly production and P is price, measured in cents per unit. The firm's cost function is given by C = 5 0Q + 30,000. Assuming the firm maximizes profits, what are the
- A firm has a demand function P = 200 - 5Q and a cost function: AC=MC=10 a. What price, quantity, and corresponding profit occur if this a purely competitive market? b. Determine the optimal price, q
- A firm faces the following demand and total cost functions: Q = 28 - 0.5P, \; TC = 56.25 + 2Q + 0.25Q^2. Calculate the revenue-maximizing price.
- 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
- Given a firm has a demand function of: P = 45 - 4Q and an average cost function of: AC= 1.5Q + 25 + 26/Q. Calculate the values of the following when profit is maximized: i) TR and total cost ii) Aver
- Demand function of a monopolist is given as Q = 50 - 0.5p while the cost function is given as C = 50 + 40q. Calculate equilibrium quantity and profit-maximizing output.
- A firm faces the following demand curve P= 200 - 0.2 Q where Q is output and P is price. the firm's total cost function is given by TC=20,000 + 20 Q a. What is the level of production? b. What is t
- A firm faces the following demand and total cost functions: \\ Q = 28 -0.5P\\ TC = 56.25 + 2Q + 0.25Q^2 \\ A. Calculate Q that minimizes average cost. B. Calculate the revenue-maximizing price. C. Calculate the profit-maximizing price and quantity.
- Given the following demand and cost functions, determine the output and sales level that maximize profit. Demand function: Q = 25 - P, Cost function: TC = 100 + 5Q + Q^2.
- The revenue function for a company can be defined as TR = Price (P)' Quantity Demanded (Q). If the ordinary demand function for your firm is Q = 60 - 0.4P: a. What is the total revenue function for this firm in terms of Q? b. What is the average revenue f
- If TR=33Q-4Q^2, and the total cost function is TC=Q^3-9Q^2+36Q+6, find the output Q that maximizes profit.
- 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.
- The demand and cost curves for a monopoly firm are as follows: Q = 750 - 5P; TC = 2000 + 70Q (a) At what output and price will the firm maximize total revenue? (b) At what output and price will the firm maximize total profit? (c) Compare the maximum profi
- The demand function is Q = 100 - .5P. The cost function is TC = C = 100 + 60(Q) + (Q) 2. a. Find MR and MC. b. Demonstrate that profit is maximized at the quantity where MR = MC. c. Derive the relat
- Given a firm's revenue and cost functions: R(Q) = -0.0016Q2 + 44Q and C(Q) = 0.0004Q2 + 8Q + 64,000 construct a profit function, determine the level of Q that maximizes profits, and prove that it is a
- A firm faces the following demand and total cost functions: Q = 28 - 0.5P, \; TC = 56.25 + 2Q + 0.25Q^2. Calculate the profit-maximizing price and quantity.
- The demand function for a product is p = 220 - 0.5q. (a) Write the expression for the total revenue function. (b) Find the output quantity q* at which the total revenue function attains it s maximum. (c) Write the expression for the own price elasticit
- 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
- Consider a total cost function of TC = 0.5Q^2 +10Q + 20 and the market demand equation Q = 70 - P. What is the profit-maximizing output and price for the perfect competition? Calculate its profit.
- Suppose a firm's demand curve is P = 50 - Q and its total cost curve is TC = 10 + 10Q so that its MC = 10. A. Find its optimal (profit-maximizing) quantity of output. B. Find its optimal (profit-maximizing) price. C. Find its maximized profits.
- Call Us demand function is Q 410 P and MC 10+5Q. Given that TFC $0 a Derive an equation for TC b Calculate the profit maximizing level
- A firm faces the following demand: Q=244-0.23P The firm's cost function is: C=5Q^2+120Q+1,907 How much profit does this firm earn when it produces the quantity, Q, that maximizes profit? Round your an
- A firm faces the following demand and total cost functions: P = 50 - 0.5Q, \; TC = 0.25Q^2 + 35Q + 25. Show that the Q, which minimizes average cost, also maximizes profits.
- A firm faces the following demand and total cost functions: P = 50 - 0.5Q TC = 0.25 Q2 + 35Q + 25 Show that the Q, which minimizes Average Cost, also maximizes 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
- Suppose a monopolist faces the market demand Q ( p ) = 800 - 4p and has a cost function C ( q ) = 50q. What is the amount that maximizes its profits (q)? a) 400 b) 300 c) 600 d) 100 e) 200
- 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
- Derive the profit level at this profit maximizing levels of p and q (p = 55) and q = 50. Where the demand curve for a monopoly is p=105-q. Its cost function is C= 100+5q?
- 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
- 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
- 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
- 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
- The Bramwell Corporation has estimated its demand function and total cost function to be as follows: Q = 25 - 0.05P TC = 780 + 200Q a. What will the price and quantity be if Bramwell wants to maximize profits? b. What will the price and quantity be if Bra
- A firm faces the following demand and total cost functions: Q = 28 - 0.5P, \; TC = 56.25 + 2Q + 0.25Q^2. Calculate Q that minimizes average cost.
- A firm faces the following demand: Q = 259 - 0.46P The firm's cost function is: C = 5Q^2 + 23Q + 1,764 How much profit does this firm earn when it produces the quantity, Q, that maximizes profit?
- The demand function for a monopolist's product is given by P = 100 - 2Q, and the cost is given by C(Q) = 10 + 2Q. a. Determine the profit-maximizing price and quantity. b. What is the maximum profit? c. What is total revenue and total cost at profit maxim
- The demand for a good produced by a firm has been reliably measured by P = 100 - 5 Q, output Q is measured in thousands of units. If the total cost function is given by C = 10Q, what is the optimal level of output produced by the monopolist?
- 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
- Assume that the demand function is Q 22 P 5 and T C 100 10 Q Q 2. a. Find the optimum profit b. Find the maximum profit
- The demand and cost function for a company are estimated to be as follows: P = 100 - 8Q TC = 50 + 80Q - 10Q^2 + 0.6Q^3 a. What price should the firm charge if it wants to maximize its profit in the
- 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 monopolist can produce quantity Q of product at total cost of C(Q) = (10,020)Q + Q^2. The demand schedule for the product is Q = 1/3(140P) where P is the price charged for the product. Find the profit maximizing output (Q) and the maximum profit.
- A profit-maximizing competitive firm uses just one input, x. Its production function is q = 4x^{1/2}. The price of output is $28 and the factor price is $7. The amount of the factor that the firm demands is A. 8. B. 16. C. 64. D. 60. E. None of the above.
- A profit-maximizing competitive firm uses just one input, x. Its production function is q = 4x^{1/2}. The price of output is $28 and the factor price is $7. What is the amount of the factor that the firm demands?
- A firm has an inverse demand function given by P(q)=100-3q and its cost function is C(q)=100+10q. a. What is the profit-maximizing level of output? b. What is the maximum profit the firm can earn? c.
- Suppose a firm faces a downward sloping demand curve given by the equation 1 100 1 3P. The firm's cost function is given by the equation C 30 1 4 Q 2. Find the profit maximizing level of output.
- 1. A firm has a demand function P = 100 - 5Q and a cost function: AC=MC=20 a. What price, quantity, and profit occur if this a purely competitive market? b. Determine the optimal price, quantity, and economic profit for the firm if it is a pure monopol
- Assume a profit-maximizing firm's short-run cost is TC = 1200 + 7Q^2. If it's demand curve is P = 60 - Q, what is the profit-maximizing quantity? a. 15 b. 14 c. 4 d. 1200
- 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
- The following are equations for a firm: Demand: P = 50 - 2Q Total Cost: TC = 60 + 10Q + Q^2 A. Use calculus to find the quantity (Q*) that maximizes profit. B. At the Q* derived in part (A), how much is the profit? C. Now, "prove" that you've maximized pr
- 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?
- The demand and cost equation is set to Q = 100 - 5P and TC = 100 +4Q. If fixed costs were underestimated by 30%, what price and quantity should the firm should charge and produce to maximize profits?
- 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
- Given the following linear demand function, identify the price and quantity that would maximize total revenue: Qx = 80 - 4P A. Q = 80; P = $10 B. Q = 40; P = $20 C. Q = 40; P = $10 D. Q = 20; P = $40
- 5. A firm's total revenue and total cost functions are, respectively, TR =45Q-0.5Q^2 TC = Q^3 - 8Q^2 +57Q+2 i) Find the value of Q which maximizes TR.
- 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.
- A market or industry demand curve is described by Q 50 0.5 P. The firm s cost function is TC 10 + 2 Q a. Find the profit maximizing quantity and price. b. If the industry is regulated in a way that re
- Suppose a price-taking firm has a cost function given by C (q) = q + 1 / 2 q^2. If the price of output is 2, what is the profit-maximizing choice of q? (a) 0. (b) 1. (c) 2. (d) None of the above.
- A firm has a total cost function SC(q)=3q^3-42q^2+200q+800. Find the profit maximizing quantity of output and profit in the short run for the firm if the price is 260.
- A monopolistic ally competitive firm faces the following demand: P 2 961 9 Q C 2Q3 12Q2 178Q 1,872 The firm's cost function is:Find the quantity, Q, that maximizes profit. Round your answer to one dec
- The demand function for a product sold by an oligopolist operating in the short run is given below: Q_D = 370 - P. The firm's marginal cost function is given below: MC = 10 + 4Q. Calculate the profit-maximizing price and quantity, if the firm operates in
- Let's say the cost function and the demand function of a monopolistic firm are as follows C=10+Q ^2 P=20 - Q (a)What is the price and output this monopolistic firm will produce? (h)What will he the
- The total cost of a firm as a function of its output q is given by: C(q)=2-2/2q+1 a. Find the firm's marginal cost, b. Find the elasticity of total cost with respect to output.
- 1. Your firm's cost function is: C = 2.1 Q 3 ? 14 Q 2 + 166 Q + 1 , 289 The demand for your product is: P = 1,022 - 20Q If the firm is a monopoly, how much profit does this firm ea
- 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
- You are the manager of a monopolistically competitive firm, and your demand and cost functions are given by Q = 36 - 4P and C(Q) = 4 + 4Q + Q^2. Calculate your firm s maximum profits.
- a) A firm is in a perfectly competitive industry and has total cost function: C (Q) = 10 Q^2 - 10 Q + 3 How much will the firm produce in the short if P = 50? If P = 70? b) Now say that the firm's cost function is: C (Q) = 10 Q^2 - 10 Q + X and P = 50. Wh
- Define Q to be the level of output produced and sold, and assume that the firm's cost function is given by the relationship TC = 20 + 5Q + Q2 Furthermore, assume that the demand for the output of the firm is a function of price P given by the relationship
- Suppose the demand function for a profit-maximizing monopolists good is P = 160 - 0.5Q, its total cost function is TC = 20 + 10Q + 0.3Q2, and its marginal cost function is MC = 10 + 0.6Q. If the firm uses a uniform pricing strategy, then rounded to the ne
- A perfectly competitive firm sells its product for $200/unit and has an average total cost of production given by: ATC(Q) = 1,500/Q + 40 + 5Q. A) What are this firm's fixed costs? B) Determine this firm's profit maximizing level of output. C) Calculate th
- 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
- The profit function is T(Q) = 24Q - Q2 - 5. a. Find the marginal profit. b. Find the value of Q* that maximizes profits.
- Suppose a demand function is given as Q = 50-0.5P and TC = 10+0.5Q2 Calculate: i) The profit maximizing level of output ii) The maximum profit iii) Proof that this is a maximum
- The demand function is Q= s/p, where Q is the total quantity demanded, s is a measure of the size of the market, and p is the price of the homogeneous good. Let F be a firm's fixed cost and m be its constant marginal cost.
- 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?
Explore our homework questions and answers library
Browse
by subject