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- Consider a market where the inverse demand function is P = 400 – 20Q, where Q is the aggregate output. Assume there are three firms which compete à la Bertrand. a)What is the equilibrium price and the corresponding aggregate output if all firms have a constant marginal cost equal to 40? b)What is the equilibrium price and the corresponding aggregate output if one firm has a constant marginal cost equal to 40 and the other firms have a constant marginal cost equal to 100? c)What is the equilibrium price and the corresponding aggregate output if one firm has a constant marginal cost equal to 40 and the other firms have a constant marginal cost equal to 260?Suppose you are an economist working in a watch factory operating in a competitive market. The cost is given by: CT = 200 + Q2, where Q is the level of production and CT is the Total Cost, the CMg (marginal cost) of production is 2Q. The Fixed Cost of production is $ 150. a. If the price of the watches is $ 60. How many watches must they make to maximize profit?b. What would be the level of utility?c. At what minimum price would the company make a positive output?Suppose that the inverse market demand for pumpkins is given by P = $10 - 0.05Q. Pumpkins can be grown by anybody at a marginal cost of $1.
- Suppose that BMW can produce any quantity of cars at a constant marginal cost equal to$50 and a fixed cost of $22,500. You are asked to advise the CEO as to what prices andquantities BMW should set for sales in Europe and in the United States to maximize its profits.The demand for BMWs in each market is given by:QE = 8,000 – 80PE and QU = 4,000 – 20 PU,where the subscript E denotes Europe, the subscript U denotes the United States. Assume thatBMW can restrict U.S. sales to authorized BMW dealers only. Support your answersgraphically as well.a. If, by an international agreement between Europe and United States, BMW wereforced to charge the same price in each market, what would be the quantity sold in eachmarket, the equilibrium price, and the company’s profit?b. Suppose now that Europe and United States signed a new trade package under whichBMW now can charge different prices across the two markets. What quantity of BMWsshould the firm sell in each market, and what should the price be…Consider a “market” with differently substitute goods. Firms1 and 2 produce homogeneous goods, but firm 3 produces a differentiated (imperfectlysubstitute) good. Thus, the inverse demand functions for each of the firms are:P1 = 1 − 2q1 − 2q2− .5q3P2 = 1 − 2q2 − 2q1− .5q3P3 = 1 − 2q3 − .5q1− .5q2All firms have zero costs. They compete in quantities. We want to study this “market” todefine a relevant market as traditionally done by antitrust agencies, and to that end weare going to perform the SSNIP test. The question is whether the product offered by firm3 is in the same “market” as that offered by firms 1 and 2. Thus, we need to know if a“hypothetical” monopoly (or cartel) producing goods 1 and 2 would increase the price bya 5-10% at least. Thus,(a) let us first compute the prices in this “market” as it is. (You can use symmetrybetween firms 1 and 2, so that you expect q1 = q2, to speed up the computationof equilibrium outputs and prices.)(b) Now consider a hypothetical monopoly that…Assume the demand function for a product is given by QD = 20,000 – 10P + 0.4I, where P = price of the product, and I = average income of consumers. Also, assume the supply function of the product is given by QS = 30P. If the market for the product is perfectly competitive, and the average income of consumers is $10,000, what are the equilibrium price and quantity in this market?
- You make delicious cupcakes that you mail to customers across the country. Your cupcakes are so unique and special that you have a great deal of pricing power. Your customers have identical demand curves for your cupcakes, and a representative customer’s demand curve is shown below. (It’s not needed, but the demand curve equation is P=5-0.2Q or Q=25-5P.) Suppose your MC=$1/cupcake, whether you produce lots or just a few cupcakes. To keep things simple, suppose there are no fixed costs, so FC=0. a) Acting as a monopolist, show the standard pricing analysis on the graph below that identifies your profit-mamximing price and quantity for your representative customer. Shade areas representing your profit and CS. (PS and profit are the same here since FC=0). b) Suppose you offer a quantity discount: first 10 cupcakes at $3 each and any cupcakes over 10 are offered at a discounted price. What discount price will maximize your profit? Show this quantity discount arrangement on your graph…Suppose you are the economic adviser ofa company producing three brands of mobile pnones;Nokia 10, Samsung X and iPhone 7. Suppose further that, your company currently sells 120units of iPhone Z at e800 per unit, 150 units of Samsung X at e800 per unit and 200 units ofNokia 10 at e100 per unit, but in a bid to maximize profit, the company's managing directorproposes an increase in price of Samsung X from e800 to e1000 per unit for which quantitydemanded is anticipated to fall from 150 to 100 units; iPhone Z from e800 to e 1200 per unitfor which quantity demanded is anticipated to fall from 120 to 100 units; and Nokia 10 from100 to 200 per unit for which quantity demanded is expected to fall from 200 to 100 unitsUsing the mid-polint formula. compute the price elasticity of demand for each brand.From your answer in i, what is the type and economic interpretatiom of each brand'sii.value of elasticity.Suppose market demand for mobile operators is expressed by Q=90-3P where Q is measured by calls in hours. There are three firms that supply the market: TRCell,VFone, and Avea .Avea provide hourly calls at a unit cost of 20$, where as TRCell& VFone has a unit cost equal to 10 Suppose firms are competing in price( no capacity constraints ) a) What is the market price? Why? b) How much does each firm sell in Bertrand equilibrium? c) What are firms’ profits? Is there any way for all firms to get higher profits
- Economics 1). Suppose a firm faces the demand function q = 600 – 6P. The firm's total production costs are given by MC(q) = 5q / 6 + q2. Further, suppose that the firm can perfectly price discriminate. The output level that maximizes profit for the firm is ____. (You may use the quadratic formula) a. 12.64 b. 10.89 c. 9.51 d. 7.63Suppose the following data represent the market demand for catfish: Price (per unit) $20 19 18 17 16 15 14 13 12 11Quantity demanded (units per day) 12 13 14 15 16 17 18 19 20 21Total revenue — — — — — — — — — —Marginal revenue — — — — — — — — — —Compute total and marginal revenue to complete the table above. At what rate of output is total revenue maximized? At what rate of output is MR less than price? At what rate of output does MR first become negative? Graph the demand and MR curves.c) Suppose the inverse demand curve in a market is D(p) =a-bp, where D(p) is the quantity demanded and p is the market price. Firm 1 is the leader and has a cost function c1(y1)=cy1 while firm 2 is the follower with a cost function c2(y2 )=. Firm 1 sets its price to maximise its profit. Firm 1 correctly forecasts that the follower takes the price leader’s chosen price as given (price taker) and chooses output so as to maximise its own profit. Write down the profit function of the follower. Calculate the profit maximising quantity that the follower selects given the leader’s chosen price p (i.e., calculate the follower’s supply curve S(p)). Interpret the solution to the profit maximising problem. d) The leader is facing the residual demand curve R(p)=D(p)-S(p) with D(p) and S(p) as defined in (c) Calculate the leader’s residual demand curve using the result in (c). Solve for p as a function of the leader’s output y1, i.e. the inverse…