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- A price-taking firm in a competitive industry of a good that is continuously divisible (like sand) has a total cost function TC(Q) = 3.5Q^2 + 100Q + 500. The market price for the good is p = $240. a: Carefully write out this firm’s profit maximization problem, using the particulars of thisproblem. b: Give the marginal condition (equation) that characterizes the solution to this problem. Solvethis condition for the firm’s optimal quantity Q*. c: Calculate the firm’s maximized profit. d: On a graph with quantity on the horizontal axis, neatly plot the marginal revenue curve andmarginal cost curve. Show Q* on your graph. e: Label areas on your graph using a, b, c, etc. and indicate the areas that correspond to totalrevenue and variable cost.What is the optimal price to charge?Exercise 2.9 Firms in a competitive industry have production costs C(q)=q²+20q+100 and the industry demand is QD(P)=1200-10P; a) Find the price, the production of the representative company, the production of the industry and the number of companies that will be part of the industry it in the long-term equilibrium. b) Suppose that demand shifts to Qº'(P) = 1.800 - 12P. Find the price, quantity and profits of companies in the short term. Calculate the social welfare corresponding to this equilibrium. (c) Calculate the final long-term equilibrium. Describe the adjustment process in a graph.
- Exercise 2.9 Firms in a competitive industry have production costs C(q) =q²+20q+100 and the industry demand is Qº(P)=1200-10P; a) Find the price, the production of the representative company, the production of the industry and the number of companies that will be part of the industry it in the long-term equilibrium. b) Suppose that demand shifts to Qº'(P) = 1.800 - 12P. Find the price, quantity and profits of companies in the short term. Calculate the social welfare corresponding to this equilibrium. (c) Calculate the final long-term equilibrium. Describe the adjustment process in a graph.HP has developed a new, high-end, high-resolution printer, which can print 40 pages per minute. Its market research identified two target segments of customers: 3,500 large businesses and 6,500 university labs. A large business has a valuation of $900 for the new printer, whereas a university lab has a valuation of $630. HP’s variable cost for the printer is $450/unit; all fixed costs are sunk. Assume that each customer needs at most one new HP printer (i.e., no customer will buy multiple units). (a) Suppose that HP cannot price discriminate the two segments of customers, i.e., it can charge only one price for its printer. What is HP’s optimal price for the new printer? What is its maximum profit? (b) Suppose that HP can install an extra chip in the printer to slow down printing to 15 pages per minute. Such a chip costs HP $20 to make and install for each printer. The slower version of the printer is valued at $700 by a large business customer and $600 by a university lab. With…C2) Company A is the only supplier of glass in Big Apple City used for tall buildings’ exteriors. Its marginal cost of production is cA=1, and it has no other production costs. The demand for such glass in Big Apple city is QD=2-P. Company B in Jersey City produces the same glass and is considering whether to expand to Big Apple city. If it enters, it needs to get a permit to allow it to be a supplier in the Big-Apple city at a cost of L=0.5, which does not vary with quantity of output, and its marginal cost of production is cB=0.5. If it expands to the Big-Apple city, companies A and B both supply to the market, and the market price P satisfies QA+QB=2-P, where QA is company A’s production level and QB is company B’s. a) If company B expands to the Big-Apple city, what is the resulting price in a Nash equilibrium? b) Company B hires a consulting company to advise whether it should expand to the Big-Apple city. If you’re running the consulting company, what is your advice? Explain…
- C2) Company A is the only supplier of glass in Big Apple City used for tall buildings’ exteriors. Its marginal cost of production is cA=1, and it has no other production costs. The demand for such glass in Big Apple city is QD=2-P. Company B in Jersey City produces the same glass and is considering whether to expand to Big Apple city. If it enters, it needs to get a permit to allow it to be a supplier in the Big-Apple city at a cost of L=0.5, which does not vary with quantity of output, and its marginal cost of production is cB=0.5. If it expands to the Big-Apple city, companies A and B both supply to the market, and the market price P satisfies QA+QB=2-P, where QA is company A’s production level and QB is company B’s. a) If company B expands to the Big-Apple city, what is the resulting price in a Nash equilibrium? b) Company B hires a consulting company to advise whether it should expand to the Big-Apple city. If you’re running the consulting company, what is your advice? Explain…AOF is the only firm selling beer around Isla Vitas, which has a beer fountain in the backyard so the marginal cost of producing beer is 0. There are two groups of consumers: students and non students. The students' beer inverse demand function is p = 60 – 6q , and the non-students' beer inverse demand function is p = 10 – 2q. AOF sells beer in two sizes: 10 ounces bottle and 5 ounces can. Due to a local act, the consumers can only buy either 1 bottle or 1 can of beer. AOF can charge different prices on each bottle and each can of beer, while it cannot tell whether a customer is a student or not. In order to maximize the profits, how much should AOF charge its 10 ounces bottle? Answer: 37.5 The correct answer is: 100.0In a market that produces hotdogs operates in the long-run, and that each firm and potential entrant has a LRAC AC = 10Q2 − 5Q + 20 and a LRMC MC = 30Q3 - 10Q + 20, where Q is thousands of units per year. The demand for hotdogs is given as D(P) = 39,000 - 2,000P. (a) Solve for the market clearing condition.
- You own a business that operates in perfect competition, and the market price of the product is $15 per unit. Q is the number of units for production. Your costs of production are shown below. The time period is fixed at one month All revenues and costs are calculated at the monthly rate. A. determine the number of units that you will select. Justify and support your answer using the information on this problem. Select only whole numbers of Q B. calculate the profit that will be earned in Part A. Q FC VC MC TC AFC AVC ATC 0 $40.00 $0.00 xxx $40.00 xxx xxx xxx 1 $40.00 $30.00 $30.00 $70.00 $40.00 $30.00 $70.00 2 $40.00 $44.00 $14.00 $84.00 $20.00 $22.00 $42.00 3 $40.00 $60.00 $16.00 $100.00 $13.33 $20.00 $33.33 4 $40.00 $80.00 $20.00 $120.00 $10.00 $20.00 $30.00 5 $40.00 $110.00 $30.00 $150.00 $8.00 $22.00 $30.00 6 $40.00…KidzPoses Inc., a profit-maximizing business, is the only photography business in town that specializes in portraits of small children. James, who owns and runs KidzPoses, expects to encounter an average of eight customers per day, each with a reservation price (shown in the following table). Assume James has no fixed costs, and his cost of producing each portrait is $12. Customer Reservation Price ($ per photo) 1 50 2 46 3 42 4 38 5 34 6 30 7…AOF is the only firm selling beer around Isla Vitas, which has a beer fountain in the backyard so the marginal cost of producing beer is 0. There are two groups of consumers: students and non students. The students' beer inverse demand function is p=50-5q, and the non-students' beer inverse demand function is p=10-2q. AOF sells beer in two sizes: 10 ounces bottle and 5 ounces can. Due to a local act, the consumers can only buy either 1 bottle or 1 can of beer. AOF can charge different prices on each bottle and each can of beer, while it cannot tell whether a customer is a student or not. In order to maximize the profits, how much should AOF charge its 10 ounces bottle? Answer: 87.5