Question

In one version of the basic neoclassical model of investment, the marginal product of capital in equilibrium equals the real rate of interest (r) plus the depreciation rate (ẟ). The statements below are about the firm’s production technology Q=F(K,L) and the equilibrium condition MPK*=r+ẟ. Which of the following is incorrect?

a. When Q=[0.5K⁻¹+0.5L⁻¹]⁻¹, then log(K*/Q)=-0.5log(2)-0.5log(r+ẟ);

b. When Q=K¹/³L²/³ , then log(K*/Q)=log(2/3)-log(r+ẟ);

c. When Q=K¹/²+L¹/², then 0.5/(K*¹/²)=r+ẟ;

d. When Q=K¹/²L¹/², then log(K*/Q)=-log(2)-log(r+ẟ);

Answer 1

Evaluating the given production functions and equilibrium condition, it was determined that statement (a) is incorrect as it does not logically follow from the given function Q=[0.5K⁻¹+0.5L⁻¹]⁻¹.

Step-by-step explanation:

The student's question is related to a neoclassical model of investment where the marginal product of capital (MPK) in equilibrium is equal to the real rate of interest (r) plus the depreciation rate (δ). The provided statements involve different production functions Q=F(K,L) and their corresponding equilibrium conditions when MPK* = r + δ.

Let's analyze each statement to identify the incorrect one

In conclusion, statement (a) is the only one that does not logically follow from the given production function, which mean that statement (a) is the incorrect one.