Suppose that one factory inputs its goods from two different plants, A and B, with different costs, 4 and 7 each respective. And suppose the price function in the market is decided as p(x, y) = 100 - x - y where and y are the demand functions and 0 ≤ x, y. Then as y = the factory can attain the maximum profit,
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- Suppose that Quality Widgets Limited is an efficient small firm with cost functionC(q)=q3 - 10q2+100q + 196 and suppose also that the maximum level of weekly production is L=10. Determine:(d) their breakeven point, (e) their supply set.Consider an imperfectly competitive service provider, Muscat Automotive Repair Services (MARS), whose total cost of production is C = 30Q +0. 165Q2. Also, MARS faces two different market segments, A and B, whose demands can be linearly expressed as QA = 240 − PA and QB = 120 − 0.5PB . (Hint: the marginal cost is the slope of the total cost function). 4. If MARS decides to segment the market in accordance with the demands of groups A and B, find the profit-maximizing prices and quantities (PA, QA) and (PB, QB).5. What is the value of the consumer surplus for each group A and B, under this segmentation strategy?6. Draw the situation described in (4) and (5) above, clearly showing each group’s profitmaximizing price and quantity, and the areas that correspond to their consumer surpluses.7. Verify the inverse elasticity rule under each of the scenarios described (1) and (4) above.A commodity has a demand function modeled by p = 106 − 0.5x and a total cost function modeled by C = 30x + 33.75, where x is the number of units. (a) What unit price (in dollars) yields a maximum profit? $ per unit (b) When the profit is maximized, what is the average cost (in dollars) per unit? (Round your answer to two decimal places.) $ per unit
- James mainly sells confectionery items, newspapers, magazines and cigarettes in his convenience store. Noting his small business is not thriving, he thought of selling hot pies and rolls too. Suppose the total cost function for rolls and pies is, TC = 900 + 50Q, Q = Q1 + Q2 Where Q1 and Q2denote the quantities of rolls and pies respectfully. If P1 and P2 denote the corresponding prices, the inverse demand equations are. Q1 = 70 - P1 and 0.5Q2 = 100 - P2 a)If James decides to make a total of 48 rolls and pies per day and charges different prices as above (that is, P1 ≠ P2 ), how many of rolls and pies each should he make in order to maximize the profit of a particular day? Estimate and interpret the Lagrange Multiplier λ [note: assume second-order conditions are satisfied]. b)Using your knowledge of input-output tables, explain which components of the economy will be affected if all convenience stores, including James’, closed down for three months due to the COVID-19. What would…A manufacturer of a new patented product has found that she can sell 70 units a week direct to the customer if the price is $78. In error, the price was advertised as $138, and, as a result only 40 units were sold in a week. The manufacturer's fixed costs of production are $50 a week and variable costs of $18 per unit. You are required to: a. Show the equation of the demand function linking price(P) to quantity demand(X), assuming it to be a straight line, is P+2X=218 b. Find where the manufacturer breaks even c. Find the quantity that maximizes profit d. Recommend a unit price which would maximize profit e. Determine the maximum profit f. Find the equation of new demand function, assuming a sudden change in trading conditions resulting a 20% reduction in demand at all price levelsA firm manufactures two goods labeled 1 and 2. It sells Qi items of good i for a fixed price per unit of pi. The total cost of producing good i is ciQi2.Explain briefly why the profit function is given byπ(Q1, Q2) = p1Q1 + p2Q2 − c1Q12 − c2Q22Find the values of Q1 and Q2 which maximize π and verify that the second-order conditions for a maximum are satisfied. Find an expression for the maximum profit.
- Answer b and c 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? c. Analyze,…A commodity has a demand function modeled by p = 117 − 0.5x and a total cost function modeled by C = 40x + 31.75, where x is the number of units. (a) What price yields a maximum profit? $____________ per unit (b) When the profit is maximized, what is the average cost per unit? (Round your answer to two decimal places.) $_____________ per unit. An electricity producer has a constant marginal cost of production equal to $40 per megawatt. The residual demand for its electricity is given by P (q) = a−bq, where P is the price and q is the quantity of power generated by this producer. The producer knows the slope, b, but he vertical intercept of the residual demand curve, a is unknown. Assume A and B are greater than zero. If you get stuck, you may answer any of the following questions for special case where a = 80 And b = 0.5 for partial credit. (a) What is the marginal revenue, M R(q), for this producer? b) What is the optimal q for this producer? (c) What is the electricity producer’s optimal price? (d) What is the electricity producer’s optimal bid in a uniform price Auction? e) Suppose b is equal to zero. Would the producer have an incentive to submit a bid above its marginal cost? Explain.
- Suppose the profit maximizing firm sells the same good in two individual markets that it is able to keep separate. Since the price elasticity of demand is different in each market, the firm recognizes that rather than charge all customers the same price, it can increase profits by charging different prices in each of the two markets. The demand equations for each market are shown below: Market 1 P=25-2Q Demand The firm's Total Cost Function is: TC=5Q a) What is the optimal output in Market 1? b) What price will be charged in Market 1? Market 2 P=15-Q c) what is the optimal output in market d) what price will be charged in market e) what is the firm's total profit f ) illustrate your answerA firm in a perfectly competitive market has a fixed cost of $5 and a MC function of 9X, where X is the firm's output choice, for X = 0,1,2,3 and 4 units. The current market price of X is P = $30. In this case, the optimal X* for the firm is ______ units, and at this output, the firm faces a total cost of _____. Group of answer choices 3; $59 3; $95 4; $59 4; $95Y6 questions1. A firm produces TVs and ovens witha joint cost function that takes the form:C(x,y) = 3x^2 + 2y^2 + 2xy where x and y are the firm's output of TVs and ovensrespectively. Suppose the cost function is subject to the constraint on the total output ofthe firm in the form 2x + y = 35.a) Find the optimum values x and that minimize the firm's total cost.b) Check your answer in (a) by using the bordered Hessian matrix.c)Determine the optimum value of the Lagrange multiblier À. Interpret your answer.