A company has two products, and the following demand functions p1 = 100-2q1 + q2 p2 = 75 +2q1 -q2 %3D %3D the firms cost function is K = 1000 + 20q1 + 10q2 + 2q1q2 show that the profit function is I = -2Q?- Q + Q1Q2 + 80Q1 + 65Q2 – 1000. %3D |
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- Dari R es for Shipharah Zurbuchen x Math 148 weekend number 2.pdf x Course Home oweekend%20number%202.pdf 2 / 3 100% +| E O 13) Assume that the price, in dollars, of a sound system is given by 1000 + 1000 q² Where q represents the quantity demanded for the product a) Find the Revenue function R(q) and the marginal revenue function R'(q) b) Find an interpret (write a sentence explaining the meaning) of the marginal revenue when demand is 10 systems Suppose the cost of producing q sound systems is given by the equation C (q) = 0.4q² + 160q + 50 c) Find the profit function, P(q) and the marginal profit function P'(q) d) Find and interpret he marginal profit when the demand is 10 systems ar product are given .Suppose that the steel firm’s costs are shown below: Complete the table and determine the optimal output to be Price of steel is P175 per unit. Output (Q) TFC TVC TC MC TR MR Profit/Loss 0 500 0 1 500 50 2 500 90 3 500 140 4 500 200 5 500 270 6 500 350 7 500 450 8 500 600 9 500 800Question Four a) A fim, focusing on producing meat pie has a demand function 20 25-0.25P. If fixed cost is 145 and variable cost per urit function is 2Q- 40 + , where Q is number of meat pie produced and Pis the price per unit: i. 275 Determine the number of meat pies that maximizes the company's profit. ii. How much should the fimcharge per unit of the product? iii. Find the total profit at the profit mximizing level of output. iv. Using the own price edasticity of demand, comment on the fimis pricing policy optiors. b) The production function for Amzonbuưgers, producers of delicious burgers at Sao Tome, is given as: Q = K%L% If the wage rate is $15 per unit of labour, and cost of capital is $1,920 per unit and you have 1 unit of capital which carmot be changed, and the firmemploys 8 units of labour; i. Calculate the fimts total cost ii. Calculate the fim's average cost ii. Estimate the marginal product of labour
- Attempt all questions. Q1. a) A local Pepsi company has total costs of production given by the equation TC-500+10q+Sq2. This implies that the firm's marginal cost is given by the equation MC 10+10q. The market demand for cold drink is given by the equation QD-105 (1/2)*P. Write the equations showing the company's average total cost and average variable cost and average fixed cost, each as a function of q. Show the firm's MC, ATC and AVC on one graph. What is the breakeven price and breakeven quantity for this firm in the short run? What is the shutdown price and shutdown quantity for this firm in the short run? If the market price of the output is $50, how many units will this firm produce? iv) Assuming the cold drink industry is perfectly competitive, what output would be produced by the firm in long-run equilibrium? What would be the long-run equilibrium price? i) ii)The chart below gives a firm's total cost of producing different levels of output. The profit maximizing level of output for this firm is Output 0123456 02 0 3 04 O 5 Total Cost $13 20 25 28 32 43 60 O Cannot be determined from the information givenGiven the following profit function: T=-2Q^2+260Q-4500, Answer the following questions.
- 1- iro % What quantity of output will this profit-maximizing firm choose to sell? units) (Round your response to the nearest whole number) Dellars per Unit 1927 176- 160- 120 112 00 BO 04 10 32 Output MR MC ATC 80 od5- A manufacturer of doors, windows, and cabinets writes her yearly profit (in thousands of dollars) for each category in 248 a vector as: P= 319 632 40 30 Her fixed costs of production can be described by the vector:C- 60 What would her incomebif increasing it threefold would cause her profit to be fice times as arger 513,02 421; 623 427 72 907: 03 542 513,02 007;23 542 542: 3 007 421: 23 513Break-Even The total revenue function for Frenchdoor refrigerators is given by R = 550x dollars, andthe total cost function for this same product is givenby C = 10,000 + 30x + x2, where C is measured indollars. For both functions, the input x is the numberof refrigerators produced and sold.a. Form the profit function for the refrigerators fromthe two given functions. b. What is the profit when 18 refrigerators areproduced and sold?c. What is the profit when 32 refrigerators areproduced and sold?d. How many refrigerators must be sold to breakeven on this product?
- Find the total revenue and marginal revenue schedules for the firm and complete the following table. Price/ Pounrd Quanitity TR MR 25 0 0 18 1,000 18,000 18.00 16 2,000 14 3,000 12 4,000 10 5,000 8 6,000 6 7,000 4 8,000 2 9,000 Fixed costs of manufactoring beryllium are $14,000 per period. The firm's variable cost schedule is as follows: Determine the average total cost and marginal cost schedules for the firm and complete the following table. Output VC TC MC 0 0 0 1,000 10.00 24,000 24.00 2,000 8.50 3,000 7.33 4,000 6.25 5,000 5.40 6,000 5.00 7,000 5.14 8,000 5.88 9,000 7.00 Exotic Metals maximizes profits when the price is $ per pound and the output level is pounds per peroid. What is Exotic's profit (or Loss) at the profit-maximizing…2) A perfectly competitive market has demand given by Qp market, and cach firm has a different cost structure as shown below: 4850-70P.There are four firms in this TC (q) = 5000 + 4q + 0.02q? MC(q) = 4+ 0.04q Client 9 & Co. TC(q) = ? MC(q) = 1+0.05q BTVS Inc 6000 +q + 0.025q TC(q) = 5000 + 2q + 0.02q? MC(q) = 2+ 0.04q The Fred Firm TC (q) = 15000 + 5q + 0.005q2 MC(q) = 5+0.01q OTT (a) What is the market price and market quantity? Hint: Start by determining the individual supply for each firm, and then add them to get the market supply (b) How many units does cach firm produce, and how much profit does each firm make? (c) In the long-run competitive equilibrium, what is the market price and market quantity? (d) In the long-run competitive equilibrium, how many units docs cach firm produce, and how much profit docs cach firm make?The graph below depicts the cost curves faced by all firms in a particular industry. While the second graph show the total market demand (in thousands). Initially there are 500 firms. 10 B N 5 20 40 60 80 100 120 140 160 180 200 9 50 100 150 200 250 300 350 400 450 500 Demand in thousands What is the SR profit per firm? -80 240 0300 400