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- 1. Consider a two-product firm under pure competition. With pure competition, the prices of both commodities will be taken as exogenous, denoted by P₁ and P₂. The production cost is C (Q₁, Q2) = Q +3Q/²2 where Q₁ and Q₂ represent the output levels of product 1 and product 2. (e) Find the maximum proifit that this firm can earn as a function of P₁ and P₂.2. 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…Suppose you are a perfectly competitive firm producing computer memory chips. Your production capacityis 1000 units per year. Your marginal cost is $10 per chip up to capacity. You have a fixed cost of $10,000 ifproduction is positive and $0 if you shut down. What are your profit-maximizing levels of production andprofit if the market price is ( a ) $5 per chip, ( b ) $15 per chip, and ( c ) $25 per chip? For case ( b ), explainwhy production is positive even though profits are negative?
- Consider a competitive firm with total costs given by T C(q) = 100 + 10q + q^2. The firm faces a market price p = 50. (a) Graph the AT C, AV C, MC, and MR curves in a single graph, and indicate the profit maximizing level of output. If there are profits, shade the region corresponding to profit and label it. (b) If fixed costs increase from 100 to 500, what happens to the profit maximizing level of output, T R, T C, and π? (c) If fixed costs increase from 100 to 500, should the firm continue to operate in the short-run? What about the long-run?The figure deplcts the demand curve for Beautiful Cars, and the marginal cost and Isoprofit curves of the car manufacturer. The quantity and price at polnt E are (Q*. P*) - (30, 5,500). Suppose now that the firm Increases the price to 5,550 and chooses the corresponding level of output from the demand function at the new price. Based on this Information, whlch of the following Is correct? 8,000 Demand curve 100 Quantity of cars, O O The firm will sell 30 cars at the higher price. O The firm's profit remains the same. O The quantity of cars produced reduced. O Tho firm's profit is now incroasod Price, Marginal cost ($)1. There is an industry consisting of 12 firms, each with total cost function given by TC(q) 3q² - 2q +867, where the fixed costs are non-sunk. The demand for the industry's product is given by Q¹ (p) = 448 - p per month. Firms are price takers. (a) Find the short-term equilibrium price, demand, the quantity produced by each firm, as well as firm's profit. What is the consumer surplus? What about the producer's surplus? (b) The government urgently needs to collect some extra tax revenues in the next four months to meet debt payments. This implies that it needs to collect the amount of T = 1000 per month from the industry. Calculate the tax level needed to raise this revenue depending on the type of tax. Which tax type is the better from a welfare perspective? i. An output tax of t per unit sold imposed on the firms. ii. 7-percent tax on firms' profits.
- Attempt all questions. Q1. a) A local Pepsi company has total costs of production given by the equation TC-500+10q+Sq2. This implies that the firm's marginal cost is given by the equation MC 10+10q. The market demand for cold drink is given by the equation QD-105 (1/2)*P. Write the equations showing the company's average total cost and average variable cost and average fixed cost, each as a function of q. Show the firm's MC, ATC and AVC on one graph. What is the breakeven price and breakeven quantity for this firm in the short run? What is the shutdown price and shutdown quantity for this firm in the short run? If the market price of the output is $50, how many units will this firm produce? iv) Assuming the cold drink industry is perfectly competitive, what output would be produced by the firm in long-run equilibrium? What would be the long-run equilibrium price? i) ii)c)Given that the cost function MC=x-2x^2-1 and the revenue function as MR=2x^2-3x-1.Assuming pure competition,determine the point atwhich profit maximized and the total profit made.Mondi Company produces party boxes that are sold in bundles of 1000 boxes. The market is highly competitive, with boxes currently selling for R100 per thousand. The company has a total and marginal cost curve given by: TC = 3,000,000 + 0.001Q2 MC = 0.002Q Q is measured in thousand box bundles per year. [5] a. Determine Mondi's profit maximizing quantity. b. Calculate if the firm is earning a profit or a loss? c. Based on the analysis above, should Mondi Company operate or shut down in the shortrun?
- Suppose market inverse demand function is p(y)=100-Yt where Yt is total production in the market. Assume that there are two firms with following marginal cost MC(firm 1)=Y1 MC(firm 2)=2*Y2+10 Assume that Yt=Y1+Y2 Set up profit function for both firms. What is the best response function of each firm by taking into account action of other firm? What output level is going to be produced by each firm in equilibrium? Assume that Firm 1 is leader in the market and going to act first. What will be the best response and output level of firm 2. What is difference between previous and new situation? Why? What is difference between Bertrand and previous competition? How would you like to find equilibrium price?Question 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) Now consider two cases (i) Company is effectively able to price discriminate in the two markets. What will be the total profits? (ii) Suppose the company does not engage in price discrimination. By charging the same price in the two markets what are the profit maximizing levels of price, output, and the total profits? c. Analyze, with graphs, the two alternative pricing strategies…1. Consider a two-product firm under pure competition. With pure competition, the prices of both commodities will be taken as exogenous, denoted by P₁ and P₂. The production cost is C (Q1, Q2) = Q +3Q²/ where Q₁ and Q₂ represent the output levels of product 1 and product 2. (b) (10) State the first-order necessary conditions for profit maximization.