Question:

A competitive firm can sell any output at price 𝑃 = 1. Production depends on capital alone, and the production function 𝑦 = 𝑓(𝐾) is twice continuously differentiable, with
𝑓(0) = 0, 𝑓 β€² > 0, 𝑓 β€²β€² < 0, \(lim\\_{ 𝐾→0 }\) π‘“ β€² (𝐾) = ∞ , \(lim\\_{ πΎβ†’βˆž}\) π‘“ β€² (𝐾) = 0.
The firm has positive capital stock 𝐾̅  to start with, and can buy and sell capital at price π‘Ÿ per unit of capital. If the firm is maximizing profit then which of the following statements is NOT CORRECT?

Updated On: Oct 1, 2024
  • If 𝐾̅ is large enough, profit maximizing 𝑦 = 0 and the profit is π‘ŸπΎΜ…
  • If 𝑓′(𝐾̅) > π‘Ÿ, the firm will buy additional capital
  • If 𝑓′(𝐾̅) < π‘Ÿ, the firm will sell some of its capital
  • If 𝑓 β€²(𝐾̅) = π‘Ÿ, the firm will neither buy nor sell any capital
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The Correct Option is A

Solution and Explanation

The correct option is (A): If 𝐾̅ is large enough, profit maximizing 𝑦 = 0 and the profit is π‘ŸπΎΜ…
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