Consider a single output firm which uses three factors of production. Its production function is 1/2 1/2 ƒ (21, 22, 23) = 21 +2₂² +23² for z = +23² for z = (21, 22, 23) € R³. Given factor prices w₁ = 2, w2 > 0, and w3 > 0, the cost of producing output q = 6 is minimized at z₁ = 1, 22 = 4, 23 = 9. DETERMINE W2 and w3.
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- In the market for foam fire retardant there is only one firm. The demand func-tion for the product is Q = 15,000 – 10P where Q is the annual sales quantity in tons and P is the price per ton. The firm’s total cost function (in dollars) is C = 1,400,000 + 300Q + 0.05Q2.a) How much foam fire retardant should this firm produce and sell in order to maximize its profit? What price should it charge?b) Compute the firm’s total profit.c) Suppose now that the firm faces a 20% increase in variable costs. Determine what impact this will have on the firm’s optimal choice.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…Now suppose firm X undertakes a process innovation that reduces its marginal cost ofproduction from $20 to $15. The fixed cost of undertaking this process innovation is F > 0. Is this atough commitment or a soft commitment? Why? For what values of F would it make sense for firm Xto make this commitment?
- A 62 metre length of rope is cut into pieces whose lengths are in arithmetic progressionwitha common difference of d metres. Given that the lengths of the shortest and thelongest pieces are 0.5 and 3.5 metres respectively, find d.(C) For a firm’s product, the demand function isp = 72 2 0.04qand the average cost function isc¯ =500q+ 30 At what level of output would profit be maximized?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) b. 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? c. Analyze, with graphs, the two alternative pricing strategies available to the company.Phillips Industries manufactures a certain product that can be sold directly to retail outlets or to the Superior Company for further processing and eventual sale as a completely different product. The demand function for each of these markets isRetail Outlets: P1 = 60 - 2Q1Superior Company: P2 = 40 - Q2where P1 and P2 are the prices charged and Q1 and Q2 are the quantities sold in the respective markets. Phillips’ total cost function for the manufacture of this product isTC = 10 + 8(Q1 + Q2)a. Determine Phillips’ total profit function.b. What are the profit-maximizing price and output levels for the product in the two markets?c. At these levels of output, calculate the marginal revenue in each market.d. What are Phillips’ total profits if the firm is effectively able to charge different prices in the two markets?e. Calculate the profit-maximizing level of price and output if Phillips is required to charge the same price per unit in each market. What are Phillips’ profits under this…
- 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…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?…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) (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? (iii) Analyze, with graphs, the two alternative pricing strategies available to the company.
- 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) 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 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…