Output is homogenous and the demand curve P = 448 - Q. There are two firms with identica %3D costs given by C = q2 i where qi is the %3D production of firm i. The marginal cost of firm i is MCi(qi) = 2qi . (a) Find the Cournot equilibrium firm outputs.
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- An Australian firm and a US firm produce a homogeneous good that is sold only in Japan. The marginal cost of producing the good is constant and equal to 30 in both countries. The demand curve for the good in Japan is: P = 120-Q where Q = QA +QUS represents the sum of the quantities. produced by the Australian and the US firms, respectively. (b) Assume the Australian firm can commit to an output before the US firm. Solve for the Stackelberg Equilibrium price, sales and profits of each firm in Japan. Price profit AUS2 ,output_US2 profit_US2 output_AUS2There are only two driveway paving companies in a small town, Asphalt, Inc. and Blacktop Bros. The inverse demand curve for paving services is ?= 2040 ―20? where quantity is measured in pave jobs per month and price is measured in dollars per job. Assume Asphalt, Inc. has a marginal cost of $100 per driveway and Blacktop Bros. has a marginal cost of $150. Answer the following questions: Determine each firm’s reaction curve and graph it. How many paving jobs will each firm produce in Cournot equilibrium? What will the market price of a pave job be? How much profit does each firm earn?Suppose two firms engage in simultaneous quantity competition. Both firms have 0marginal cost. Firm A : P(Q)= 24-Q Firm B: P(Q)= 24-2Q a) Find the Nash Equilibrium quantities q^NE and profits.(b) Find the Monopoly Quantity QM and Profit.(c) Now suppose the game is repeated infinitely and each firm has a common discountfactor δ. Find the required discount factor to sustain the following grim triggerstrategy as a SPNE: Play Q^M /2 if this has been played in every previous period,otherwise play q^NE.
- Two farmers produce milk for local town with local milk demand given by Q=100-1/3P (P denotes price measured in Rands, Q denotes the quantity measured in litres). Both farmers have the same cost function given by TC=150+2q (where q denotes output)a. What output should farmer 1 produce if he or she expects their rival to produce 20 units?Consider an industry with N firms that compete by setting the quantities of an identical product simultaneously. The resulting market price is given by: p = 1000 − 4Q. The total cost function of each firm is C(qi) = 50 + 20qi . (a) Derive the output reaction of firm i to the belief that its rivals are jointly producing a total output of Q-i . Assuming that every firm produces the same quantity in equilibrium, use your answer to compute that quantity. (b) Suppose firms would enter (exit) this industry if the existing firms were making a profit (loss). Write down a mathematical equation, the solution to which would give you the equilibrium number of firms in this industry. You don’t have to solve this equation.The market inverse demandfor salt is P(Q) = 1000−10Q. There are n firms producing salt, each with the sameconstant marginal cost c. Show that as n increases, the market gets closer to efficiency.
- Consider a market with demand P(Q) = 112 - 3Q in which 9 identical firms compete. All firms face T C(Q) = 52Q. Let X = Q2 + Q3 + . .. + Q9. (a) Write out the residual demand curve for firm 1 in terms of X and Q1. (b) Find the corresponding marginal revenue. (c) What is the reaction function for firm 1 (in terms of X). (d) Find the Cournot equilibrium (market quantity QM* , P* ). (e) Determine profits for each firm.Here is a market with three firms: 1, 2, and 3. The demand curve is P=100-Q. There is no fixed cost but the marginal cost 10 for all firms. Firm 1 is a leader firm so that it decides the quantity Q1 first. Then two firms respectively decide their quantities Q2 and Q3 simultaneously. 1) At an equilibrium (SPE), Q1 is Q2=Q3= 2) At the equilibrium, (the market quantity) Q= and (the market price) P= 3) The profit of firm 1 is while the profit of firm 2 and 3 respectively isan Problem 5. Consider following price competition between 2 firms. Both firms choose their prices (p, and p2) simultaneously and the market demand function given by q 10-min{p₁, P2}. Assume production costs are 0 for both firms. Thus, the payoff (profit) function for firm i is: u.(Pi. Pj) (10-P.)Pi (10-pi)Pi 2 Notice that this function is not continuous in pi 1 if Pi Pj
- Consider a market where two firms produce the same product, and compete by choosing the price to charge consumers. There are no capacity constraints and no fixed costs. Consumers purchase from the firm that charges the lowest price, Pmin Aggregate demand is given by Q(Pmin) = 600 – 30pmin. Both firms have marginal costs of c = 15. What is the aggregate quantity produced in this market? And what price do consumers pay? (a) p₁ = = 15, p2 = 20, Q = 150 (b) P1 = P2 = 15, Q = 150 (c) P₁ = P₂ = 20, Q = 0 (d) p₁ = 10, P2 = 15, Q = 300 (e) None of the above options is correct.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?Ugly Dolls Inc. (UD) is a firm in Mytown that sells its products on a market under monopolistic competition. The cost function of UD is represented by TC = 100+10Q. Lately, because of the UD is making a big amount of profit, some firms enter the market to compete. If the number of firms entering the dolls market increase, we know that, (a) The price of dolls will drop. (b) The average cost of UD will increase. (c) The quantity sold by UD will drop. (d) All the above answers are correct.
