Suppose a monopoly supplied its market from two plants, with cost functions: C₁-18 q₁ and C₂ (92) — 392. The monopolist faces a linear demand p = 238 - 5 Q, where is the amount sold in this market, which is the total amount produced by both plants. Find the quantities produced at each plant to maximize the monopolist's profit. 91 · 92 Number Number Now check the second order conditions:
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- A monopoly that produces beer has estimated the following demand function: 1 p(q) = 300 q + 20t 3000 The variables are defined as follows: p is the price of a liter of beer, q is production, and t is the monthly average temperature in degrees centigrade. The estimated cost of producing a liter of beer is $12. Below is a table with the average temperature recorded in Arizona during March and April. Month Temperature March 35 April 38 a) Find the optimal price for the monopolist in each month b) Calculate the Mark-up for April and according to it estimate the elasticity of demand. Comment on the results. C) Determine the efficiency loss in the month of March.A firm is a profit-maximizing monopolist in the market of a patented computer software. As an economic analyst,you observe the following data:a) The monopoly’s price is set at $50 per copy.b) The monopoly’s total revenue is $300,000.c) The monopoly’s marginal cost at the profit-maximizing quantity is at $30 per copy.Based on the observed data, please determine the linear inverse demand function.Fill in the blanks. Suppose the inverse demand function is of the formwhere a, b are both positive constants, determine the value for a: 1 and b: 2 .Hint: a should be an integer, the answer for b should round to four decimal places.Consider the relationship between monopoly pricing and the price elasticity of demand. If demand is inelastic and a monopolist raises its price, quantity would fall by a percentage than the rise in price, causing profit to Therefore, a monopolist will produce a quantity at which the demand curve is elastic. Use the purple segment (diamond symbols) to indicate the portion of the demand curve that is inelastic. (Hint: The answer is related to the marginal- revenue (MR) curve.) Then use the black point (plus symbol) to show the quantity and price that maximizes total revenue (TR). (? 10 Demand Inelastic Demand 6 5 Max TR 3 2 1 -1 -2 Marginal Revenue -3 -4 1 2 3 4 5 7 8 9 10 Quantity
- Consider a monopolist local movie theater which has two distinct client groups, adults and seniors. The inverse demands for the two group are given by:p(qA) = a − b · qAp(qB) = a/3-b/3.qB(a) Describe the demand function in the two markets graphically and then compute the demand elasticity in each market.(b) Compute the demand function qP under the assumption that the movie theather canonly offer a single price to both segments of the market. (Hint: at a given price addthe demand of the adults and senior market. You need to go from the inverse demand function to the demand function.) Illustrate the aggregate demand function in contrast to the demand functions in each segment. Now compute the optimal price of the movie theater when it can only offer a single and common price to the market segments. Who goes to the movies and who does not?(c) Next allow the movie theater to offer different prices in each segment and customerscannot mispresent their identity. What is the optimal price in…You are the manager of a monopolist that produces women shoes and faces a random marginal cost. The demand for women shoes is O = 1000 - 0.1P Marginal cost can be constant at either $60 with a probability of 50% or $40 with a probability of probability of 50%. Draw a graph and plot the demand for shoes. Derive the marginal revenue curve and plot it on the graph. Find the price and output that maximize profits. Find the firm's profits.A monopolist has a single customer with the demand curve P=20-Q. (So this customer will buy different quantities at different prices.) Suppose the monopolist’s marginal cost is MC=0. (And assume FC=0 to keep things simple.) The monopolist uses “standard” pricing, i.e., it sets a single price for all units that the customer buys. The graph below shows the demand curve and MC curve. Solve graphically for the price & quantity that will maximize profit for the monopolist. Shade the areas on your graph that represent consumer surplus and the monopolist’s profit.
- Consider the relationship between monopoly pricing and the price elasticity of demand. If demand is inelastic and a monopolist raises its price, quantity would fall by a ▼. Therefore, a monopolist will Use the purple segment (diamond symbols) to indicate the portion of the demand curve that is inelastic. (Hint: The answer is related to the marginal- revenue (MR) curve.) Then use the black point (plus symbol) to show the quantity and price that maximizes total revenue (TR). Price 10 9 CO 7 6 S E 2 0 -2 Demand Search percentage than the rise in price, causing profit to produce a quantity at which the demand curve is elastic. Marginal Revenue 86 Inelastic Demand e + Max TR C ? (CC Speaker/Headph AThe market demand function for Pierogi in Pittsburgh Pennsylvania has a constant elasticity of -3. More precisely the actual daily demand was estimated to be Q=34560p3, where p is the price per pound. Each pound costs c-$8 to produce. Pittsburgh is served by a local monopoly producer. Compute the monopoly's profit-maximizing price and the monopoly's profit level. Show your computations.A monopoly sells 30 units of output when price Ksh 12 and 40 units when price is Ksh 10. If its demand schedule is linear, what is the specific form of the actual demand function? Use this function to predict quantity sold when price is Ksh 8. What domain restrictions would you put on this demand function?
- Barnacle Industries was awarded a patent over 15 years ago for a unique industrial-strength cleaner that removes barnacles and other particles from the hulls of ships. Thanks to its monopoly position, Barnacle has earned more than $160 million over the past decade. Its customers—spanning the gamut from cruise lines to freighters—use the product because it reduces their fuel bills. The annual (inverse) demand function for Barnacle’s product is given by P = 400 – .0005Q, and Barnacle’s cost function is given by C(Q) = 250Q. Thanks to subsidies stemming from an energy bill passed by Congress nearly two decades ago, Barnacle does not have any fixed costs: The federal government essentially pays for the plant and capital equipment required to make this energy-saving product.Absent this subsidy, Barnacle’s fixed costs would be about $4 million annually. Knowing that the company’s patent will soon expire, Marge, Barnacle’s manager, is concerned that entrants will qualify for the subsidy,…A monopoly sells 30 units of output when price is GH¢12 and 40 units when price is GH¢10. If its demand schedule is linear, what is the specific form of the actual demand function? Use this function to predict quantity sold when price is GH¢8. What domain restrictions would you put on this demand function?Barnacle Industries was awarded a patent over 15 years ago for a unique industrial strength cleaner that removes barnacles and other particles from the hulls of ships. Thanks to its monopoly position, Barnacle has earned more than $160 million over the past decade. Its customers—spanning the gamut from cruise lines to freighters—use the product because it reduces their fuel bills. The annual (inverse) demand function for Barnacle’s product is given by P = 380 -0.00009Q,and Barnacle’s cost function is given by C(Q) = 270Q. Thanks to subsidies stemming from an energy bill passed by Congress nearly two decades ago, Barnacle does not have any fixed costs: The federal government essentially pays for the plant and capital equipment required to make this energy-saving product. Absent this subsidy, Barnacle’s fixed costs would be about $9 million annually. Knowing that the company’s patent will soon expire, Marge, Barnacle’s manager, is concerned that entrants will qualify for the subsidy,…