Question

Imagine an economy with production function Y = F(K) = and 400 units of capital. If the fraction of output invested in new capital is γ = 0.2, the depreciation rate is δ = .05, and the economy starts with output of 20, what does the Solow model predict will happen to output in the long run?

A) Output will decrease.
B) Output will increase indefinitely.
C) Output will remain constant.
D) Output will increase to a certain level and then stabilize.

Answer 1

According to the Solow model, output in the given economy with a fixed amount of capital will rise initially due to investment exceeding depreciation but will eventually stabilize when investment equals depreciation.

Step-by-step explanation:

The Solow model predicts that output in the economy will initially increase due to capital deepening, which is the increase of capital per worker, but will eventually stabilize due to the diminishing marginal returns of capital. With 400 units of capital and a fraction of output invested in new capital (γ) equal to 0.2, and a depreciation rate (δ) of 0.05, the economy will reach a steady state where output grows enough to compensate for the depreciation of capital but not enough to increase indefinitely.

This steady state happens when investment equals depreciation, and in this scenario, the output will increase to a certain level and then remain constant. The correct answer to the student's question is D) Output will increase to a certain level and then stabilize.