. Consider a market that consists of 360 consumers, i = 1,..., 360, each with the following quasi-linear utility function Ui = M¡ + log xị over the numeraire good m (whose price is normalized to one) and x; units of good l; and 10 perfectly competitive firms, j = 1, ..., 10, that produce good l. Each firm j produces q; units of good l using c; (q;) = q² /2 units of the numeraire good. Consumers are price takers, and i's endowment of the numeraire good is wi, i = 1, ..., 360. (a) Derive the individual demand function, x; (p), and aggregate demand function, x (p), of good l. (b) Derive the individual firm supply function, q; (p), and aggregate supply function, q (p), of good l.
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- 2. Consider a market that consists of 10 consumers, i = 1, ..., 10, each with the following quasi- linear utility function Ui = m; + 48 Vx; over the numeraire good m (whose price is normalized to one) and x; units of good l. There are also 40 perfectly competitive firms, j = 1, .., 40, that produce good l. Each firm j produces q; units of good l, which are sold at price p, using c; (q;) = q/3 units of the numeraire good. Consumers are price takers, are endowed with wi units of the numeraire. Cj (a) Derive the individual demand function, x; (p), and aggregate demand function, x (p), of good l. (b) Derive the individual firm supply function, q; (p), and aggregate supply function, q (p), of good l. 6. (c) Find the equilibrium price p* and quantity q* of good l. What is each firm's profit? (d) Find each consumer i's equilibrium consumption of the numeraire m as a function of Wi. (e) Write down the equilibrium utilities u as a function of the initial endowments.1. Consider a market that consists of 50 consumers, i = 1, ..., 50, each with the following quasi- linear utility function Ui = mi + log x; over the numeraire good m (whose price is normalized to one) and x; units of good l; and 50 perfectly competitive firms, j = 1, ..., 50, that produce good l. Each firm j produces q; units of good l using c; (q;) = i's endowment of the numeraire good is wi, i = 1, ...,50. •.. q? /2 units of the numeraire good. Consumers are price takers, and (a) Derive the individual demand function, x; (p), and aggregate demand function, x (p), of good l. (b) Derive the individual firm supply function, q; (p), and aggregate supply function, q (p), of good l. (c) Find the equilibrium price p* and quantity q* of good l. What is each firm's profit? (d) Find each consumer i's equilibrium consumption of the numeraire m; as a function of Wi. Find the condition on w; that yields a strictly positive solution for m . * (e) Write down the equilibrium utilities u as a…5. Consider a market where there are two mers with inverse demand func- consu tions p(q1) = 10 -91 and p(q2) = 5-92. (a) Suppose there is a single firm with inverse supply function p(q) = }q. Find the competitive equilibrium. (b) Find the elasticity of demand and supply at the equilibrium. (c) Suppose instead that there are three firms with the identical inverse sup- ply function given in part (a). Find the competitive equilibrium.
- No written by hand solution Suppose that the market for video games is competitive with demand function Qd = 170 – 4p + 2Y + 3pm – 2pc, where Qd is the quantity demanded, p is the market price, Y is the monthly budget that an average consumer has available for entertainment, pm is the average price of a movie, and pc is the price of a controller that is required to play these games. Given that Y = $100, pm = $30 and pc = $30, use Excel to calculate quantity demanded for p = $10 to p = $80 in $5 increments. Using Excel’s spreadsheet Find Qd = ________ when P=$30. Find Qd = ________ when P=$45. Now, Y increases to $120. Re-calculate the demand schedule and find Qd = ________ when P=$20. Let Y = $100 again, but pm increases to $40. Re-calculate the demand schedule and find Qd = ________ when P=$25. Let Y = $100, pm = $30, and pc increases to $40. Re-calculate the demand schedule and find Qd = ________ when P=$50.Firms can choose a location in the linear city of length 1 with fixed cost of 25. Consumer density at any location x in the linear city is 400. a) Show that a firm each at 0.125, 0.375, 0.625 and 0. 875 is not an equilibrium. b) What is the equilibrium number of firms and th6ir locations? c) Illustrate how entry is no longer profitable at equilibrium? Plz do fastSuppose there are only two firms in a competitive market for a good. Firm 1's marginal cost curve is given by MC = 2.5 +0.5Q and the equation of 4+Q³. What is the equation of the - firm 2's marginal cost curve is MC supply function for this market? - a) MC = 6.5 +1.5Q⁹ b) MC = 0.33Q⁹ +3 c) Q³ = 3p - 9 d) P = 6.5 +1.5Qs
- Igrushka is a profit-maximizing firm producing wooden dolls-a capital-intensive good-which are sold in its home country, Russia, and abroad in France. Igrushka chose foreign production as a method of penetrating the French market and has to decide whether it is more efficient to directly invest in France to establish a production subsidiary or to license the technology to a French firm to produce its goods. On the following graph, AVCFrance is the average variable cost curve of a French firm producing wooden dolls. (This curve represents costs such as labor and materials.) The curve ATCSubsidiary represents the total unit costs Igrushka will face if it establishes a subsidiary in France. PER-UNIT COST (Dollars) 10 9 8 1 0 0 ATC 15 Subsidiary 30 45 60 75 90 105 120 PRODUCT (Thousands) AVC France 135 150 ? 4Exercise A.9 In a market only two firms produce a homogeneous good. You work on one of them and are tasked with drawing up the production strategy for the coming year. The two companies in the market have the same information and the objective of both is the maximization of their profit. You know: the inverse market demand curve of the good: P(Q)=200-2Q where Q = q₁ + q₂ , the function that represents the costs of your company and the rival company: C(qᵢ) = 20qᵢ (for i=1, 2), and the data in the following table, with the optimal decisions according to the different types of competition:C(qᵢ) = 20qᵢ and the data in the following table, with the optimal decisions according to the different types of competition: q1 q2 P Bertrand 45 45 20 Cournot 30 30 80 Collusion 22,5 22,5 110 a) What is more in your company's interest to compete or cooperate with the rival company? Keep in mind that explicit collusion agreements are illegal, so each…(b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p = 40−4q2where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass. (i) Write an equation giving profit as a function of the number of lightweight compasses produced. (ii) At the moment the company produces 2 million lightweight compasses and makes a profit of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit?
- The soluation avilible I believe it is wrong so please solve it carefully Carl and Simon are the only sellers of pumpkins at the market, where the total demand function for pumpkins is q =3 ,200−1,600p. The total number of pumpkins sold at the market is q = qC + qS, where qC is the number that Carl sells, qS is the number that Simon sells. The cost of producing pumpkins for each farmer is $.50 per pumpkin; the fixed costs are zero. .a. Find the Cournot equilibrium price and quantities. .b. Find the Bertrand equilibrium price and quantities. . .c. Suppose now that every spring the snow thaws off of Carl’s pumpkin field a week before it thaws off of Simon’s. Therefore, Carl can plant his pumpkins one week earlier than Simon while predicting Simon’s choice based on the previous year information. Simon observes Carl’s choice and chooses how much pumpkin to plant. Find the new equilibrium price and quantities. .d. Compare the quantities and prices in parts a, b, and c. Rank these outcomes…Suppose you are an analyst for the Coca-Cola Company. An individuals' inverse demand for Coca-Cola is estimated to be P = 98- 4Q (in cents). If Coca-Cola is produced according to the following cost function C(Q)= 1,000+ 2Q (in cents), compute the optimal price and the number of cans to sell as a single package. O $1200 per package and 12 cans O $11.52 per package and 12 cans O $15 per package and 16.67 cans O $12 per package and 24 cans1. It is 1908 and you are the CEO of Ford Motor Company. General Motors startedproducing cars this year and has quickly become your chief rival. Their recent entrance, as wellas your assembly line methods, allows you the advantage of producing cars faster and choosingyour output levels first. Assume the 1908 inverse demand function for cars is P = 3900 - Q(customers view cars as identical products at this point in time) and production costs are C(qi) =100qi. a. What is Ford’s profit-maximizing output level? GM's?b. What is the market equilibrium price?c. How much profit does each firm earn?d. As the assembly line is used by other firms, the first-mover advantage disappears (fast forward100 years to present day), and more firms have entered the market (e.g. FCA, Tesla, Hyundai,Toyota, Honda, etc.), what do you expect to happen to Ford’s profit (assume demand andcosts are the same)? Explain.e. From 1908 into the 1920s, Ford offered customers one car: the Model T. Further, Henry isfamous…