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 ′ > 0, 𝑓 ′′ < 0, $lim\\\\_{ 𝐾→0 }$ 𝑓 ′ (𝐾) = ∞ , $lim\\\\_{ 𝐾→∞}$ 𝑓 ′ (𝐾) = 0.
The firm has positive capital stock 𝐾̅ to start with, and can buy and sell capital at price 𝑟 per unit of capital. If the firm is maximizing profit then which of the following statements is NOT CORRECT?

• A. If 𝐾̅ is large enough, profit maximizing 𝑦 = 0 and the profit is 𝑟𝐾̅
• B. If 𝑓′(𝐾̅) > 𝑟, the firm will buy additional capital
• C. If 𝑓′(𝐾̅) < 𝑟, the firm will sell some of its capital
• D. If 𝑓 ′(𝐾̅) = 𝑟, the firm will neither buy nor sell any capital

Answer 1

Answer: (A)

If 𝐾̅ is large enough, profit maximizing 𝑦 = 0 and the profit is 𝑟𝐾̅

Answer 2

The correct option is (A): If 𝐾̅ is large enough, profit maximizing 𝑦 = 0 and the profit is 𝑟𝐾̅