ii. Given U = 5x₁0.7x₂0. s. t 100 = = 5x₁ + 10x₂ Find the equilibrium value of x₁ & x₂. also use the bordered hessian matrix to check second order conditions. iii. A two-product firm faces the demand and cost functions below: 91 = 50-3p₁ - P2 92 = 40-P₁-3p2 c=q² + 2q² + 10 a. Find the output levels that satisfy the first-order condition for maximum profit. b. Check the second-order sufficient condition. Can you conclude that this problem possess a unique absolute maximum? c. What is maximal profit?
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- Road Runner Co is a Pakistani manufacturer making Bicycles. It exports to two markets,Bangladesh and Sri Lanka. Demand for Bicycles in thesetwo markets is given by the following Functions: Bangladesh Q1 = 12 – P1 Sri Lanka Q2 = 8 – P2 Where Q1 and Q2 are respective quantities sold (in thousands) andP1 and P2 are the respective prices (in Pak. Rupees per unit) in the two markets. Total cost function is C = 5 + 2 (Q1+ Q2) Determine the company’s total profit function. Also, (i) What are the profit maximizing levels of price and output for the two markets? (ii) Calculate the marginal revenues in each market. Now consider two cases: (i) Company is effectively able to price discriminate in thetwo markets. What will be the total profits? (ii) Suppose the company does not engage in price discrimination. By charging thesameprice in the two markets what are the profit maximizing levels of price,output, and the total profits?…Road Runner Co is a Pakistani manufacturer making Bicycles. It exports to two markets, Bangladesh and Sri Lanka. Demand for Bicycles in these two markets is given by the following Functions: Bangladesh Q1 = 12 – P1 Sri Lanka Q2 = 8 – P2 Where Q1 and Q2 are respective quantities sold (in thousands) andP1 and P2 are the respective prices (in Pak. Rupees per unit) in the two markets. Total cost function is C = 5 + 2 (Q1+ Q2) Determine the company’s total profit function. Also, (i) What are the profit maximizing levels of price and output for the two markets? (ii) Calculate the marginal revenues in each market. Now consider two cases: (i) Company is effectively able to price discriminate in the two markets. What will be the total profits? (ii) Suppose the company does not engage in price discrimination. By charging the same price in the two markets what are the profit maximizing levels of price, output, and the total profits?…Road Runner Co is a Pakistani manufacturer making Bicycles. It exports to two markets,Bangladesh and Sri Lanka. Demand for Bicycles in thesetwo markets is given by the following Functions: Bangladesh Q1 = 12 – P1Sri Lanka Q2 = 8 – P2 Where Q1 and Q2 are respective quantities sold (in thousands) andP1 and P2 are the respective prices (in Pak. Rupees per unit) in the two markets. Total cost function is C = 5 + 2 (Q1+ Q2) Required. Determine the company’s total profit function. Also, (i) What are the profit maximizing levels of price and output for the two markets? (ii) Calculate the marginal revenues in each market.? 2. Now consider two cases: (i) Company is effectively able to price discriminate in the two markets. What will be the total profits? (ii) Suppose the company does not engage in price discrimination. By charging thesameprice in the two markets what are the profit…
- Road Runner Co is a Pakistani manufacturer making Bicycles. It exports to two markets,Bangladesh and Sri Lanka. Demand for Bicycles in thesetwo markets is given by the following Functions: Bangladesh Q1 = 12 – P1 Sri Lanka Q2 = 8 – P2 Where Q1 and Q2 are respective quantities sold (in thousands) andP1 and P2 are the respective prices (in Pak. Rupees per unit) in the two markets. Total cost function is C = 5 + 2 (Q1+ Q2) a. Determine the company’s total profit function. Also, (i) What are the profit maximizing levels of price and output for the two markets? (ii) Calculate the marginal revenues in each market.Road Runner Co is a Pakistani manufacturer making Bicycles. It exports to two markets,Bangladesh and Sri Lanka. Demand for Bicycles in thesetwo markets is given by the following Functions: Bangladesh Q1 = 12 – P1 Sri Lanka Q2 = 8 – P2 Where Q1 and Q2 are respective quantities sold (in thousands) andP1 and P2 are the respective prices (in Pak. Rupees per unit) in the two markets. Total cost function is C = 5 + 2 (Q1+ Q2) A.Determine the company’s total profit function. Also, (i) What are the profit maximizing levels of price and output for the two markets? (ii) Calculate the marginal revenues in each market. B.Now consider two cases: (i) Company is effectively able to price discriminate in thetwo markets. What will be the total profits? (ii) Suppose the company does not engage in price discrimination. By charging thesameprice in the two markets what are the profit maximizing levels of price,output, and the total profits?…Question Road Runner Co is a Pakistani manufacturer making Bicycles. It exports to two markets,Bangladesh and Sri Lanka. Demand for Bicycles in thesetwo markets is given by the following Functions: Bangladesh Q1 = 12 – P1 Sri Lanka Q2 = 8 – P2 Where Q1 and Q2 are respective quantities sold (in thousands) andP1 and P2 are the respective prices (in Pak. Rupees per unit) in the two markets. Total cost function is C = 5 + 2 (Q1+ Q2) Now consider two cases (i) Company is effectively able to price discriminate in the two markets. What will be the total profits? (ii) Suppose the company does not engage in price discrimination. By charging the same price in the two markets what are the profit maximizing levels of price, output, and the total profits? c. Analyze, with graphs, the two alternative pricing strategies…
- The equations that correspond to the following market are as follows: Qd = -200P + 3,000 Qs = 200P - 400 During finals week, Midnight Cookies runs the 'Manager's Special,' which sells the same cookie four-pack for $5. Holding all other variables constant, and assuming that Midnight Cookies changes nothing to their production plans, calculate the deadweight loss generated in the Midnight Cookies market from the store running the Manager's special during finals week. Omit any units and round to the nearest cent.Spinners World is a fitness equipment company that manufactures spin bikes.The market research department recommends that the company manufacture a new model of spin bikes and presents the following demand equation x = 35000-50p, where x is the demand at $p per bike. (a) Solve the demand equation for p. The financial department also provides the cost function C(x)= 8,000+200x. (b) Analyse the revenue and profit function to produce x bikes while Identifying what the marginal revenue and the marginal profit equation signifies. (c) Determine the exact and approximate revenue from manufacturing the 31st spin bike.he Pear Computer Company just developed a totally revolutionary new personal computer. Pear estimates that it will take competitors at least two years to produce equivalent products. The demand function for the computer is estimated to be P=2,500−500Q�=2,500−500� where Q� is millions of computers. The marginal (and average variable) cost of producing the computer is $900. Assuming Pear acts as a monopolist in its market, the profit-maximizing price and output levels are per computer and million computers, respectively. The total contribution to profits and fixed costs at this output level is million. Pear Computer is considering an alternative pricing strategy of price skimming. It plans to set the following schedule of prices over the coming two years: Complete the following table by calculating the contribution to profit and overhead for each of the 10 time periods and prices. Time Period Price Quantity Sold Total Contribution ($) (Million)…
- Tasty Inc. sells table salt to both retail grocery chains and commercial users (e.g., bakeries, snack food makers, etc.). The demand function for each of these markets is: Retail grocery chains: P1 = 180 − 8Q1 Commercial users: P2 = 100 − 4Q2 where P1 and P2 are the prices charged and Q1 and Q2 are the quantities sold in the respective markets. Tasty's total cost function (which includes a "normal" return to the owners) for salt is: TC = 50 + 20(Q1 + Q2) (a) Determine Tasty's total profit function. (b) Assuming that Tasty Inc. is effectively able to charge different prices in the two markets, what are the profit-maximizing price and output levels for the product in the two markets? What is Tasty's total profit under this condition?A price-setting firm faces the following estimated demand and average variable cost functions: Qd= 800,000 − 2,000P + 0.7M + 4,000PR AVC = 500−0.03Q + 0.000001Q2 where Qd is the quantity demanded, P is price, M is income, and PR is the price of a related good. The firm expects income to be $40,000 and PR to be $53. Total fixed cost is $2,600,000. What is the profit-maximizing choice of output? a. 8,000 units b. 20,000 units c. 0 units, the firm shuts down d. 10,000 units e. 12,000 unitsBosch claims to be the leader in terms of energy efficiency in the washing machine market and produces a special-design motor that is used in the manufacturing of its washing machines. The market demand and the total cost for Bosch’s washing machines are estimated as follows: P = 3,200 – 0.20Q TCwashing machine = 60,000 + 1,280 Q + TCMotor In this equation, Q is the number of washing machines sold per month, P is the TL price of washing machines, TCMotor is Bosch’s total cost of manufacturing the special-design motors in TL. In addition, TCMotor is estimated to be TL160 per motor without any additional fixed costs. a. As a result of its special design, the motors can be used only in the manufacturing of Bosch washing machines with no external market. Determine the profit-maximizing number of washing machines Bosch should manufacture and sell. Explicitly state the transfer price that Arçelik should set for the special-design motors.