3. A public utility set up two electric generating facilities: Q₁ kilowatts are produced at facility 1 and Q₂ kilowatts are produced at facility 2 (so Q = Q₁ + Q₂. The costs of producing electricity at each facility are estimated as C₁Q₁ = 8000 + 6Q² and C₂Q₂ = 6000 + 3Q²/². Determine the profit-maximizing quantities produced at the two facilities, and the price.
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- The FIA Formula 1 World Championship to be held during the 2021 Mexico City Grand Prix has a total cost function equal to CT = Q33 + Q2 + 125Q and an inverse demand function of P = 200−2Q. Now suppose there is a new company managing this event, so the total cost function becomes CT = 4Q. This new company intends to sell at two different prices depending on the place that the spectators occupy at the Hermanos Rodríguez Autodrome. For the Red Zone Boxes. The estimated demand will be q1 = 32−12p1 and for the Green Zone Boxes It will be q2 = 42 − p2. The number of tickets sold for the Red Zone and Green Zone will be: 15; 84 23; 16 15; 19 33; 45|1.6.1 A company manufactures and sells x dellphones per week. The weekly price-demand and cost equations are given below. p= 400 - 0.5x and C(x) = 20,000 + 140x (A) What price should the company charge for the phones, and how many phones should be produced to maximize the weekly revenue? What is the maximum weekly revenue? The company should produce (Round to the nearest cent as needed.) phones each week at a price of $ The maximum weekly revenue is $ (Round to the nearest cent as needed.) (B) What price should the company charge for the phones, and how many phones should be produced to maximize the weekly profit? What is the maximum weekly profit? The company should produce (Round to the nearest cent as needed.) phones each week at a price of $ The maximum weekly profit is $ (Round to the nearest cent as needed.)Ticket Price, Cost ($) 10 8 00 D₁ = Dx+DA MC = ATC MRT 20 28 38 10 0 Adult Tickets DK 6 4 MC = ATC MRK Children's Tickets 20 20 1. The Figure above describes demand and cost conditions facing the Salinas Cinema-Plex. Note that marginal costs are constant ($). The demand for Cinema-Plex movie tickets by adult patrons is given by DA and by child patrons Dk. a) Calculate total revenue from ticket sales IF the Cinema-Plex did NOT practice 3rd degree price discrimination, but rather charged a single price to adult and child patrons. b) Calculate the total number of tickets sold if the Cinema-Plex DID practice 3rd degree price discrimination. c) Calculate the change in consumer surplus (CS) received by adult patrons if the Cinema-Plex shifted from a single price to a 3rd degree price discrimination regime. d) How much (economic) profit does the Cinema-Plex stand to gain by engaging in 3rd degree price discrimination?
- Consider a wholesale electricity market with two types of generators: coal plants and natural gasplants. There are 10 generators for each fuel type. Each generator has a capacity of 1,000 MW.Marginal costs vary across generation types: $10 per MWh for coal and $20 per MWh for naturalgas. During peak hours, demand is given by Q = 30,000 – 100P (measured in MWh). During semipeak hours, demand is given by Q = 22,000 – 100P. During off-peak hours, demand is given by Q= 20,000 – 100P. Assume that a day consists of one off-peak hour and either a semi-peak or apeak hour (so a day contains two hours only!). Probabilities of semi-peak vs. peak hours are 50%-50%. For now, assume that the market is competitive.a. Calculate the peak, the semi-peak, and the off-peak prices of electricity.b. What are the expected daily profits for each plant?The Independent System Operator (ISO) is worried that the peak price is too high, and asksinvestors to build an additional 1,000 MW natural gas fired plant.c.…The price-demand equation for the production of bluetooth speakers is: p = 250 - 1/20x, for 0 is less than or equal to x and x is less than or equal to 5000 where x speakers can be sold at $p per each speaker. The cost to produce x speakers is given as C(x) = 150,000 + 30x, where both C(x) and p are represented in dollars ($). - find the profit function and the marginal profit and interpret the quantity P'(4500) - find the marginal cost and interpret the quantity C'(3000) - find the revenue function and the marginal revenue and interpret the quantity R'(3000)Assume that Gas & Minerals is the only copper mining firm in Chile. The national demand for copper in thousands of tonnes per month is: q^d(p) = 15 - pThe total costs in millions of dollars are: c(q) = 5q(a) What would be the profit-maximising level of production for this firm? Determine the monopoly price and quantify the profits. Graph the demand, marginal revenue and marginal cost, identifying their values along with determining the social loss generated and identifying it in the graph above. Assume now that due to a bad internal restructuring, the operations manager was fired and a professional with little mining experience was hired. The new manager does not know environmental protocol and mining waste (tailings) has gotten out of control and has been dumped into a river. This generated a negative externality on copper production. The estimated damage is US$5 million per 1,000 tonnes.(b) Obtain the social marginal cost of this mining activity.(c) What level of production will…
- Consider a wholesale electricity market with two types of generators: coal plants and natural gas plants. There are 10 generators for each fuel type. Each generator has a capacity of 1,000 MW. Marginal costs vary across generation types: $10 per MWh for coal and $20 per MWh for natural gas. During peak hours, demand is given by Q = 30,000 – 100P (measured in MWh). During semi- peak hours, demand is given by Q = 22,000 – 100P. During off-peak hours, demand is given by Q = 20,000 – 100P. Assume that a day consists of one off-peak hour and either a semi-peak or a peak hour (so a day contains two hours only!). Probabilities of semi-peak vs. peak hours are 50%- 50%. For now, assume that the market is competitive. Calculate the peak, the semi-peak, and the off-peak prices of electricity. What are the expected daily profits for each plant?. The second-largest public utility in the nation is the sole provider of electricity in 32 counties of southern Florida. To meet the monthly demand for electricity in these counties, which is given by the inverse demand function P = 1,200 − 4Q, the utility company has set up two electric generating facilities: Q1 kilowatts are produced at facility 1 and Q2 kilowatts are produced at facility 2 (so Q = Q1 + Q2). The costs of producing electricity at each facility are given by C1(Q1) = 8,000 + 6Q21and C2(Q2) = 6,000 + 3Q22, respectively. Determine the profit-maximizing amounts of electricity to produce at the two facilities, the optimal price, and the utility company’s profits.Consider PNW Airlines, an airline focused on transporting cargo. Their fleet is composed of four cargo airplanes. Total cargo capacity of the fleet is 100,000 cubic feet. The monthly cost of maintaining and operating the fleet is $50,000. Market research indicated that the demand curve for cargo capacity is d=300,000-25,000p where d is the demand across all segments and p is the transport price per cubic foot. Question 1: What is the price that maximizes profit for PNW Airlines if all the demand comes from a single segment? What is the demand if PNW sets price to be the value found in Question 1? How much profit does PNW Airlines make?
- A manufacturer of a new patented product has found that he can sell 70 units a week to the customer if the price is $48. In error, the price was recently advertised at $78 and as a result, only 40 units were sold in a week. The manufacturers fixed costs of production are $1,710 a week and variable costs are $9 per unit. You are required to: a. Show the equation of the demand function linking price (P) to quantity demanded (X) assuming it to be a straight line is P = 118-x4. Windies Cricket manufactures Windies supporter jerseys. The quantity q, of these jerseys demanded weekly is related to the wholesale price per jersey p, by the following equation: p=-0.006q+15 The weekly total cost incurred by Windies Cricket for producing q jerseys is: C(q) = 38q0.02q² + 30,000 a. Determine an expression to represent the weekly Revenue function. b. Determine an expression to represent the weekly Profit function. c. Calculate the weekly Revenue when ten dozen jerseys are produced and sold.TNBest is the only electricity company in a suburban area. Suppose that the demand for electricity for this area is ? = 500 − 10? and the cost of producing electricity is ?? = 500 + 2?.(i) If the city council want to ensure that TNBest doesn’t lose money, comment on the lowest price they can impose and TNBest’s profit and output level with this new price.