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(c) Suppose that only two firms supply the market and each firm chooses its output in period t + 1 to maximize profit in the belief that the other firm will maintain its output level at the period t value. Let the demand function be p(x + y) = 126 - (x + y) Now suppose the firms have cost functions given by 1 1 C(x) = 2x², C(y) = y² (1) (ii) Derive the linear second order difference equation. Given x(0) = 28 and x(1) = 56, solve the difference equation for x.

(c) Suppose that only two firms supply the market and each firm chooses its output in period t + 1 to maximize profit in the belief that the other firm will maintain its output level at the period t value. Let the demand function be p(x + y) = 126 - (x + y) Now suppose the firms have cost functions given by 1 1 C(x) = 2x², C(y) = y² (1) (ii) Derive the linear second order difference equation. Given x(0) = 28 and x(1) = 56, solve the difference equation for x.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(c) Suppose that only two firms supply the market and each firm chooses its output in period t + 1 to maximize profit in the belief that the other firm will maintain its output level at the period t value. Let the demand function be p(x + y) = 126 - (x + y) Now suppose the firms have cost functions given by 1 C(x) = x², C(y) = y² (i) (ii) Derive the linear second order difference equation. Given x (0) = 28 and x(1) = 56, solve the difference equation for x.
Transcribed Image Text:(c) Suppose that only two firms supply the market and each firm chooses its output in period t + 1 to maximize profit in the belief that the other firm will maintain its output level at the period t value. Let the demand function be p(x + y) = 126 - (x + y) Now suppose the firms have cost functions given by 1 C(x) = x², C(y) = y² (i) (ii) Derive the linear second order difference equation. Given x (0) = 28 and x(1) = 56, solve the difference equation for x.
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