Question

Describe how, if at all, each of the following developments affects the break-even and actual investment lines in the basic Solow growth model diagram: (a) The rate of depreciation falls. (b) The rate of technological progress rises. (c) The production function is Cobb-Douglas, f(k)=k°

, and capital's share, α, rises. (d) Workers exert more effort, so that output per unit of effective labour for a given value of capital per unit of effective labour is higher than before.

Answer 1

The rate of depreciation falling reduces the break-even investment and requires less investment to maintain the same output. An increase in technological progress leads to a higher level of output for a given amount of capital. In a Cobb-Douglas production function, an increase in capital's share raises the break-even investment and requires more investment to maintain the same output. When workers exert more effort, the break-even investment decreases and less investment is needed to maintain the same output.

Step-by-step explanation:

(a) The rate of depreciation falls: A decrease in the rate of depreciation means that the capital stock will depreciate at a slower rate. This results in a lower break-even investment, as the firm will need to replace its capital stock less frequently. The actual investment line will shift upward, indicating that a lower level of investment is needed to maintain the same level of output.

(b) The rate of technological progress rises: An increase in the rate of technological progress leads to a higher level of output for a given amount of capital. This causes the actual investment line to shift upward, as firms can achieve higher levels of output without investing more in capital.

(c) The production function is Cobb-Douglas and capital's share, α, rises: In a Cobb-Douglas production function, increasing the share of capital (α) will increase the productivity of capital. This results in a higher break-even investment, as more capital is required to achieve the same level of output. The actual investment line will shift upward, indicating that a higher level of investment is needed to maintain the same level of output.

(d) Workers exert more effort: When workers exert more effort, output per unit of effective labor increases. This is represented by an upward shift of the production function curve. The break-even investment line will shift downward, as less capital is needed to achieve the same level of output. The actual investment line will also shift downward, indicating that a lower level of investment is needed to maintain the same level of output.