Two firms, each in a different country, sell homogeneous output in a third country. Government 1 subsidizes its domestic firm by s per unit. The other government does not react. In the absence of government intervention, the market has a Nash- Cournot equilibrium. Suppose demand is linear, p = 1 - q1 - q2, and each firm's marginal an average cost of production are constant at m. Government 1 maximizes net national income (it does not care about transfers between the government and the firm, so it maximizes the firm's profit net of the transfers). Show that Government 1's optimal s results in its firm producing the Stackelberg leader quantity and the other firm producing the Stackelberg follower quantity in equilibrium.

Two firms, each in a different country, sell homogeneous output in a third country. Government 1 subsidizes its domestic firm by s per unit. The other government does not react. In the absence of government intervention, the market has a Nash- Cournot equilibrium. Suppose demand is linear, p = 1 - q1 - q2, and each firm's marginal an average cost of production are constant at m. Government 1 maximizes net national income (it does not care about transfers between the government and the firm, so it maximizes the firm's profit net of the transfers). Show that Government 1's optimal s results in its firm producing the Stackelberg leader quantity and the other firm producing the Stackelberg follower quantity in equilibrium.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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All problems below include an “unknown” parameter A, which is 1.5. Suppose that 2 firms are competing in a heterogeneous market whereby the demand functions of firm 1 and firm 2 are given by q1 = A − 3p1 + 2p2 and q2 = A − 3p2 + 2p1. Both firms have a marginal cost equal to 1. (a) [10] Calculate the optimal profits for the two firms when they compete in prices. (b) [20] If firm 1 spends an amount F to reduce its marginal cost to 0, what is the maximum value of F that it would be willing to pay? For the rest of the problem, suppose, instead, that firm 1 sets the quantity (q1) while simultaneously firm 2 sets the price (p2). (c) [15] Draw the two best response functions in a graph and indicate the Nash equilibrium. Be as detailed as possible in giving intuition. (Note: the graphs will be in the (p2, q1) space, but remember that you are not drawing any demand curves.) (d) [25] Compute both of the firms’ equilibrium prices, quantities, and profits. Which firm makes a higher profit?…
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There are two firms in a market, where quantities are the strategic variable within two periods. In each of the two periods t = 1; 2 the inverse demand function Ptis given by P: (y') = 5-y'. The cost function of firm i is given by C=3+2y, where i=1,2. In the first period firm1 is a protected monopolist. Profits of a firm can be interpreted as the sum of its profits in each period. In order to maximize their profits, firms set quantities. Define the monopoly solution. (i) (ii) Firm1 must choose the same quantity in each period y = yf due to the technological restrictions. Considering ył firm2 thinking to enter in period 2. Define the profit maximizing yi if y is given. (iii) Suppose that firm 2 will enter in the second period. What quantity will firm 1 have? What is the equilibrium P, Q and profit?
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