3. A firm has the following total-cost and demand functions: C = }Q – 7Q? + 111Q+50 %3D Q = 100 P (a) Does the total-cost function satisfy the coefficient restrictions of (9.5)? (b) Write out the total-revenue function R in terms of Q. (c) Formulate the total-profit function 7 in terms of Q. (d) Find the profit-maximizing level of output Q*. (e) What is the maximum profit?
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- A firm's demand and total cost function are given by the expression: P = 20 - Q/2 (1) TC = 0.5Q2 + 36 (2) Where P is price per unit in £ TC = total cost in £ Q is quantity demanded and produced. Use equation (1) to find the total revenue (TR) function and determine the total revenue maximising output. Calculate the profit associated with this level of output.For a company with (inverse) demand function P = 4,510 - 55Q and cost function C = 88,000 + 660Q, let QR, QU, and QP denote, respectively, the quantities that maximize revenue, per-unit profit, and overall profit. Which of the following statements is true?A. QU > QP > QRB. QP > QU > QRC. QU > QR > QPD. QR > QU > QPConsider the following price-demand function: P = 80 − 4Q, {Q/0 ≤ Q ≤ 10} (i) Sketch the price-demand function(ii) Find the revenue function.(iii) Suppose C = 20 + 5Q , find the profit function(iv) Calculate the profit if Q=8(v) Find the break-even level of output You have to solve iv and v
- Suppose that the total revenue function of a firm is defined as TR= (P)(Q) where TR= f(Q). The usual notation applies. 1. . Find the total revenue function TR(Q) if the inverse demand function is given by P(Q) = 80-0.2Q2. What is the shape of the total revenue function if graphed? State your basis.2. ABC Manufacturing has provided you with their demand function Qd = 2000-2p and supply function Qs = 60+5p, please answer the following questions: a. What is the company’s marginal revenue function? b. At level of output is profits maximized? c. At what price is profits maximized? d. What is total revenue at the profit maximization level of output?The price-demand equation for the production of bluetooth speakers is: p = 250 - 1/20x, for 0 is less than or equal to x and x is less than or equal to 5000 where x speakers can be sold at $p per each speaker. The cost to produce x speakers is given as C(x) = 150,000 + 30x, where both C(x) and p are represented in dollars ($). - find the profit function and the marginal profit and interpret the quantity P'(4500) - find the marginal cost and interpret the quantity C'(3000) - find the revenue function and the marginal revenue and interpret the quantity R'(3000)
- Q=0, P=220; Q=2, P=200; Q=4, P=180; Q=6, P=160; Q-8, P=140; Q=10; P=120; Q=12, P=100. a) Based on the information in the table, what is the demand function for this market? b) Calculate total and marginal revenues for this market in the table c) if the total cost function for this market is TC = 500 + 10Q^(2), calculate the total and marginal costs for each of the quantities in the table d) What are the profit-maximizing quantity, price, and profit for this market? e) If there are two firms Atlas and Bowden in this market with the same earlier total cost function and they engage in Cournot competition, what is each firm's equilibrium quantity, price, and profit? f) Is this a long-run equilibrium? Why or why not?Q1. A firm faces the following average revenue (demand) curve: P = 100 - 0.01Q where Q is weekly production and P is price, measured in cents per unit. The firm’s cost function is given by C = 50Q + 30,000. Assuming the firm maximizes profits, a. What is the level of production?The Lumins Lamp Company, a producer of old-style oil lamps, estimated the following demand function for its product:Q = 120,000 - 10,00Pwhere Q is the quantity demanded per year and P is the price per lamp. The firm’s fixed costs are $12,000 and variable costs are $1.50 per lamp.a. Write an equation for the total revenue (TR) function in terms of Q.b. Specify the marginal revenue function.c. Write an equation for the total cost (TC) function in terms of Q.d. Specify the marginal cost function.e. Write an equation for total profits (π) in terms of Q. At what level of output (Q) are total profitsmaximized?What price will be charged? What are total profits at this output level?f. Check your answers in Part (e) by equating the marginal revenue and marginal cost functions, determined in Parts (b) and (d), and solving for Q.g. What model of market pricing behavior has been assumed in this problem?
- A firm produces two goods in pure competition and has the following total revenue and total cost functions: TR = P1Q1 + P2Q2 and TC = 2Q12 + Q1Q2 +2Q22 Where, P1 = 12 and P2 = 18. a)Form the profit function and identity the critical value Q1* & Q2*. b)Construct the Hessian matrix and calculate the value of |H1| & value of |H2|. c)Based on the values of Hessian, what can you say about the profit?For the following total-revenue and total-cost functions of a firm: TR=22Q - 0.5Q2 TC= (1/3)Q3 - 8.5Q2 + 50Q + 90 Determine the level of output at which the firm maximizes its total profit. Determine the maximum profit that the firm could earn.1. Teddy J is a manufacturer of dish washing liquid . If his monthly demand function for 750ml size is: q = 4000 − 250p and his total cost function is: C(q) = 500 + 0.2q (i) Derive an expression, R(q) for Teddy J′s total revenue curve.(ii) Derive an expression, Π(q) for Teddy J's profit function.(iii) Determine whether Teddy J′s profit is increasing or decreasing when he produces 5 hundred, 750ml bottles of dish washing liquid.