The ethanol industry is perfectly competitive, and each producer has the long-run marginal cost function MC(Q) = 48 - 24Q +3Q². The corresponding long-run average cost function is AC(Q) = 48 12Q+Q². The market demand curve for ethanol is QD = 240 - 10P. - 1. What is one firm's inverse long-run supply curve with the minimum level of price for the firm to operate? 2. What is the optimal level of quantity produced by each firm in the long-run? 3. What is the long-run equilibrium price in this industry?
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- 2. You are the Southeastern Michigan regional manager at Coca-Cola, responsible forproduction and pricing in the Metro Detroit area. Your primary competitor is Pepsi. The marketresearch team at Coca-Cola is thinking about launching a new product, Orange Vanilla Coke, toboost the brand. The cost function to produce a 12-pack of 12 fl. oz. cans of Orange VanillaCoke is C(qcoke) = 0.25qcoke and the market research team has estimated inverse market demandfor a 12-pack of this new “pop” in Southeastern Michigan to be P = 10.25 – 0.00025Q. a. Assuming Pepsi decides not to produce a similar product, allowing Coca-Cola to maintainmonopoly power in the market for orange vanilla cola, what price and quantity will youchoose to maximize profit? How much profit does Coca-Cola earn?b. What price and quantity you would choose to maximize profit if Pepsi spies discover yourproduct before launch, allowing Pepsi to produce and launch an identical product at the sametime. For your answer, assume the cost…A local newspaper currently has 84,000 subscribers at a quarterly charge of $30.Market research has suggested that if the owners raise the price to $32, they wouldlose 5,000 subscribers. Assuming that subscriptions are linearly related to theprice, what price should the newspaper charge for a quarterly subscription tomaximize their revenue?a) Find the cost function (Hint: find slope and use point-slope form to find thecost function) b) Find the revenue function c) Find the maximum revenue d) Find the profit functionA local company is planning to manufacture and market a four-slice toaster. For this toaster, the research department’s estimates are aweekly demand of 300 toasters at a price of $25 per toaster and a weekly demand of 400 toasters at a price of $20. The financial department’s estimates are fixed weekly costs of$5,000 and variable costs of $5 per toaster. a) Assume that the relationship between price ? and demand ? is linear. Use the research department’s estimates to express ? as a function of ? and determine the domain of the function. b) Using your knowledge from Finite Math, determine the Revenue function in terms of ?. c) Determine the Marginal Revenue at 2 different production levels for example 250 and 500 units. Interpret these results. (HINT: Consider what a positive or negative first derivative implies) d) Assume that the cost function is linear. Use the financial department’s estimates to express the cost function interms of ?. e) Determinethe Marginal costand interpret the…
- 1. Consider the perfectly competitive market for guitar tuners. The mar- ket price for a guitar tuner is $20 and the cost functions are: TC (q) = .01q² + .2q + 4950 %3D MC (q) = .02g +.2 (a) Find the profit-maximizing quantity of guitar tuners produced by a firm in this market. (b) Calculate the profit each firm will earn in this market (c) Graphically depict the firm's profit-maximization problem. (note: this doesn't need to be to scale but should accurately reflect the sign of the profit) (d) Will firms enter into this market in the long run? (e) Graphically show how the price will change as the market pro- gresses towards a long-run equilibrium. (There's no need to find the exact long-run equilibrium price. Just follow similar steps to what we did in class)A small firm operating in a purely competitive market has fixed costs of $45 per day compensates each employee $96 per day and has daily input and raw material costs as indicated in the table below. A. What would be the profit maximizing level of production if demand increased such that each unit sold for $130?, will the company make an economic profit producing this quantity of output? b: suppose the demand significantly decreased so that price for a unit of ouput sold to $115 each. What should the firm do? Why?Suppose that over the short run (say the next 5 years), demand for OPEC oil is given by P = 165 – 2.5q. Here q is measured in millions of barrels a day. OPEC marginal cost per barrel is $15. What is OPEC’s optimal level of production? What is the prevailing price of oil at that level? Many experts contend that maximizing short-run profit is counterproductive for OPEC in the long run because high price reduces buyers to conserve energy and spur competition and new exploration that increases the overall supply of oil. Suppose that the demand curve just described will remain unchanged only if oil prices stabilize at $65 per barrel or below. If oil price exceeds this threshold, long run demand (over a second five year-period) will be curtailed to P = 135 – 2.5q. OPEC seeks to maximize its total profit over the next decade. What is the optimum output and price policy? (assume all values are present values)
- Suppose that the firm with the costs and revenues shown in the graph below is contemplating whether or not to produce 12 units of output. If it were to produce this many units, what (if anything) would happen to the market price? What would be the firm's marginal revenue for the 12th unit produced? What would be the firm's total revenues per hour? Price and Marginal Cost ($ per unit) $6 E MC 10 11 12 13 14 Output (units per hour) Answer: This firm is in relation to the industry as a whole that its production market price, which would , so its output rate is influence the $6 per unit. The market price the firm's marginal revenue, which therefore would be MR unit. The firm's hourly total revenues if it were to produce 12 units would be TR $72. + $6 per 4Given Question #1 Cost function C= 3000+6Q Q = 4400 - 200Q - This is the demand function Q= 1600 P = 14 Profit= 22400-12600 = 9800 Question #2 Q=$480 - L Q=$1120- SA Question #3 Ed=−1.25 - L Ed=−0.55 - SA 0.5<0.8− markup index it is charging less. - L 0.64<-1/-0.55--markup index it is charging less. - SA Please answer question #5 A-C Given Question #2 Demand Function for San Antiono - Q=$1120- SA Question #3 Elasticity of Demand - Ed=−0.55 Markup - 0.64<-1/-0.55--markup index it is charging lessLI Auto can produce any quantity of cars at a constant marginal cost equal to $100 and a total foxed cost of $10000 globally You are asked to advise the CEO as to what prices and quantties LI Auto should set for car sales in Europe and in the US to maximize its profits The demand for LI Auto in each market is given by Og= 6000-8 P and Q, = 4000-2 P,where the subscript E denotes Europe, the subscript U denotes the US. Assume that LI Auto can restrict Europe or US car sales to authorized LI Auto dealers only. If, by an international agreement between Europe and US, LI Auto was forced to charge the same price in each market, calculate the following (round of to nearest number): Question: 1. Equilibrium Price 2. Quantity of cars sold in Europe and In the US 3. Total Profit
- Discuss the importance of price elasticity of demand, income elasticity of demand and cross price elasticity of demand to a sales manager selling soft drinks like Coca Cola If a firm faces the Marginal Cost schedule MC = 180 + 0.3Q2 and the MR schedule is MR = 540 = 0.6Q2 and that Total Fixed costs are $65. What is the maximum profit it can make? Assume that the second-order condition for maximum is metThe figure deplcts the demand curve for Beautiful Cars, and the marginal cost and Isoprofit curves of the car manufacturer. The quantity and price at polnt E are (Q*. P*) - (30, 5,500). Suppose now that the firm Increases the price to 5,550 and chooses the corresponding level of output from the demand function at the new price. Based on this Information, whlch of the following Is correct? 8,000 Demand curve 100 Quantity of cars, O O The firm will sell 30 cars at the higher price. O The firm's profit remains the same. O The quantity of cars produced reduced. O Tho firm's profit is now incroasod Price, Marginal cost ($)The handmade snuffbox industry is composed of 100 identical firms each having short-run total costs given by , where q is the output per day.20.5105STCqq=++(a) What is the short-run supply curve for each firm? What is the short-run supply curve for the market?(b) Suppose the demand is given by . What will be the equilibrium (both quantity and 110050QP=-price) in this marketplace? (c) What will each firm’s short-run profits be?