Consider an industry composed of two firms producing the same good. Let y be the output...
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Consider an industry composed of two firms producing the same good. Let y₁ be the output of firm 1 and y2 the output of firm 2. For simplicity, assume that the price p of the good does not change with the output produced by the firms; this could be a reasonable assumption if the good is a luxury good. The total cost of producing y₁ in firm 1 is C₁ (9₁); the total cost of producing y2 in firm 2 is C2 (y2). The two functions C₁, C₂ are increasing and convex. Firm 1 is more efficient in the sense that C1(y)< C2(y) for every y > 0. (1) The firms behave as a cartel and jointly choose y₁, 92 to maximize the industry's total profit T(y₁, y2) = px (y₁ + y2) - C₁ (3₁) - C2 (Y2). Show that the solution to that maximization problem need not entail that firm 1 produces more than firm 2. More precisely: exhibit two increasing and convex cost functions C₁, C₂ satisfying (1) for which the output levels y₁, y2 maximizing (y1, y2) are such that y₁ < y2. Hint: this problem involves no computation but isn't easy; the simplest example involves piecewise linear cost functions. Consider an industry composed of two firms producing the same good. Let y₁ be the output of firm 1 and y2 the output of firm 2. For simplicity, assume that the price p of the good does not change with the output produced by the firms; this could be a reasonable assumption if the good is a luxury good. The total cost of producing y₁ in firm 1 is C₁ (9₁); the total cost of producing y2 in firm 2 is C2 (y2). The two functions C₁, C₂ are increasing and convex. Firm 1 is more efficient in the sense that C1(y)< C2(y) for every y > 0. (1) The firms behave as a cartel and jointly choose y₁, 92 to maximize the industry's total profit T(y₁, y2) = px (y₁ + y2) - C₁ (3₁) - C2 (Y2). Show that the solution to that maximization problem need not entail that firm 1 produces more than firm 2. More precisely: exhibit two increasing and convex cost functions C₁, C₂ satisfying (1) for which the output levels y₁, y2 maximizing (y1, y2) are such that y₁ < y2. Hint: this problem involves no computation but isn't easy; the simplest example involves piecewise linear cost functions.
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Answer Total Cost of producing your firm I is Total Cose of produc... View the full answer
Related Book For
Managing Supply Chain and Operations An Integrative Approach
ISBN: 978-0132832403
1st edition
Authors: Thomas Foster, Scott E. Sampson, Cynthia Wallin, Scott W Webb
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