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Consider a firm aiming to maximising total profits from time 0 through infinity. The firm's production function is f(k,) where k, is the capital stock at time t. New investment is i,, and costs W₁- max Σ(+) ((k) - wid] t=0 s.t. k+1=(1-6)k, + i. Solve for the condition that determines the firm's optimal investment decision given k₁.

Consider a firm aiming to maximising total profits from time 0 through infinity. The firm's production function is f(k,) where k, is the capital stock at time t. New investment is i,, and costs W₁- max Σ(+) ((k) - wid] t=0 s.t. k+1=(1-6)k, + i. Solve for the condition that determines the firm's optimal investment decision given k₁.

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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1. Consider a firm aiming to maximising total profits from time 0 through infinity. The firm's production function is f(k,) where k, is the capital stock at time t. New investment is i,, and costs w;- 00 max t=0 s.t. kr41 = (1 - 8)k, + i,. Solve for the condition that determines the firm's optimal investment decision given k,.
Transcribed Image Text:1. Consider a firm aiming to maximising total profits from time 0 through infinity. The firm's production function is f(k,) where k, is the capital stock at time t. New investment is i,, and costs w;- 00 max t=0 s.t. kr41 = (1 - 8)k, + i,. Solve for the condition that determines the firm's optimal investment decision given k,.
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