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- 4. Consider a market that consists of 360 consumers, i 1,..., 360, each with the following quasi-linear utility function Ui = m; + log xi 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. (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 function of the…A7 You are the manager of a bakery that produces and packages gourmet muffins, and you currently sell muffins in packages of 3. A consultant’s report has estimated the (inverse) demand of a typical consumer to: P = 3 − 0.5Q If your cost of producing bran muffins is C(Q) = Q: (a) What is the marginal cost of muffins? (b) Draw the demand and marginal cost on a diagram. (c) Determine the optimal number of muffins to sell in a single package. (d) What price should the firm charge for each park?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.
- Suppose 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 +1.5QsExercise 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…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 fast
- 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.Be sure to explain your answers. 2. Consider a market for a homogenous good with the following inverse demand function: P = 52 – 20 where Qis total sold quantity on the market. + (a) If there is only one firm serving the market and the firm's cost function is C(O) = 4Q, what quantity will be sold on the market? What will be the market price? What is the firm's profits? Is the market outcome efficient? (b) Suddenly, there is a potential rival firm considering entering the market. It would produce the same good as the incumbent firm and would have an identical variable cost but has a fixed cost of entry, F = 100. The two firms would be faced with a problem of simultaneously deciding on how of the good to sell on the market (the inverse demand function is still the same). Derive both firms' best response functions and draw these in a diagram. Explain the Nash equilibrium in the diagram. (c) Following from (b), what would be the new equilibrium quantity sold in the market and what is the…(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?
- Consider two firms that produce the same product and sell it in a market with the following demand function: d(p) = max{0, 12 − p}, where p ≥ 0 is the unit price of the good. Suppose that, for technological reasons, firm 1 can produce either 4 units of output at the total cost of 10, or 6 units at the total cost of 15. Similarly, firm 2 can produce either 3 units of output at the total cost of 8, or 4 units at the total cost of 10. Assume that the firms make their production decisions simultaneously. Characterize the players’ strategy sets. Write down this game in the normal and extensive forms. Find all (if any) Nash equilibria of the game. Now assume that firm 1 makes its decision first. Firm 2 decides how much to produce after it observes firm 1’s output. Characterize the players’ strategy sets. Write down this game in the normal and extensive forms. Find all (if any) Nash equilibria of the game.3. A firm faces a demand curve given by the function: Q = 100 – 2P Marginal and average costs for the firm are constant at KShs.10 per unit. a) What output level should the firm produce to maximize profits and what are the profits at this output level? b) What output level should the firm produce to maximize revenue and what are the profits at this revenue maximizing output level c) Suppose the firm wishes to maximize revenues subject to the constraint that it earns KShs.12 in profits for each of the 64 machines it employs, what level of output should it produce?4. Consider a market where every firm and every potential entrant has the iden- tical cost function C(q) = 3q³-6q² +6q. (a) Find the firm's inverse supply function. (b) Suppose the market demand function is given by QP (P) = 20-2P. Find the long-run equilibrium price, quantity, and the number of firms. (c) Suppose the demand function suddenly becomes perfectly inelastic at quan- tity Q = 7. Find the long-run equilibrium price, quantity and the number of firms. (d) Suppose the demand becomes perfectly inelastic at quantity Q = 7, and the government decides to collect a per unit tax t = 4 from the producers for every unit of the good they sell. Find the long-run equilibrium price, quantity and the number of firms.