TABLE OF CONTENTS

Question 1 of 2

Work It Out
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You must read each slide, and complete any questions on the slide, in sequence.

Consider an economy described by the production function:

Y = F(K, L) = K0.3L0.7.

What is the per-worker production function?

Review pages 58-61 in Chapter 3 for a discussion of the Cobb-Douglas production function and pages 212-217 in Chapter 8 for a discussion of the per-worker production function and steady-state equilibrium in the Solow growth model.

a. Assuming no population growth or technological progress, find the steady-state capital stock per worker, output per worker, and consumption per worker as a function of the saving rate and the depreciation rate.

k* = _________
Review pages 58-61 in Chapter 3 for a discussion of the Cobb-Douglas production function and pages 212-217 in Chapter 8 for a discussion of the per-worker production function and steady-state equilibrium in the Solow growth model.

y* = _________
Review pages 58-61 in Chapter 3 for a discussion of the Cobb-Douglas production function and pages 212-217 in Chapter 8 for a discussion of the per-worker production function and steady-state equilibrium in the Solow growth model.

c* = _________
Review pages 58-61 in Chapter 3 for a discussion of the Cobb-Douglas production function and pages 212-217 in Chapter 8 for a discussion of the per-worker production function and steady-state equilibrium in the Solow growth model.
Review pages 58-61 in Chapter 3 for a discussion of the Cobb-Douglas production function and pages 212-217 in Chapter 8 for a discussion of the per-worker production function and steady-state equilibrium in the Solow growth model.

Consider an economy described by the production function:

Y = F(K, L) = K0.3L0.7.

Assume that the depreciation rate is 5 percent per year. Make a table showing steady-state capital per worker, output per worker, and consumption per worker for saving rates of 0 percent, 10 percent, 20 percent, 30 percent, and so on. Round your answers to two decimal places.(You might find it easiest to use a computer spreadsheet then transfer your answers to this table.)

Steady State Values for Various Saving Rates
s k* y* c*
Depreciation Rate: 0.0
(0.05) 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0

What saving rate maximizes output per worker? What saving rate maximizes consumption per worker?

A saving rate of percent maximizes output per worker. A saving rate of percent maximizes consumption per worker.

Review Section 8-2 and Table 8-3 for an analysis of the determinants of steady states in the Solow growth model and for a discussion of the Golden Rule steady state that maximizes consumption per worker.

Use information from Chapter 3 to find the marginal product of capital. Round your answers to three decimal places. Add to your table from part (c) the marginal product of capital net of depreciation for each of the saving rates.

Steady State Values for Various Saving Rates
s k* y* c* MPK* - d
Depreciation Rate: 0.0 0.00 0.00 0.00
(0.05) 0.1 2.69 1.35 1.21
0.2 7.25 1.81 1.45
0.3 12.93 2.16 1.51
0.4 19.50 2.44 1.46
0.5 26.83 2.68 1.34
0.6 34.81 2.90 1.16
0.7 43.38 3.10 0.93
0.8 52.50 3.28 0.66
0.9 62.12 3.45 0.35
1.0 72.21 3.61 0.00

What does your table show about the relationship between the net marginal product of capital and steady-state consumption?
The table shows that the net marginal product of capital equals zero when consumption per worker is at its maximum value. To understand why consumption is maximized when the net marginal product of capital equals zero, consider what happens as we increase capital across steady states. When the net marginal product is greater than zero, adding capital produces more output than it costs in depreciation, thereby increasing consumption. When the net marginal product is less than zero, adding capital produces less output than it costs in depreciation, thereby lowering consumption. Accordingly, when the net marginal product of capital equals zero, consumption per worker is at its maximum value.
The table shows that the net marginal product of capital equals zero when consumption per worker is at its maximum value. To understand why consumption is maximized when the net marginal product of capital equals zero, consider what happens as we increase capital across steady states. When the net marginal product is greater than zero, adding capital produces more output than it costs in depreciation, thereby increasing consumption. When the net marginal product is less than zero, adding capital produces less output than it costs in depreciation, thereby lowering consumption. Accordingly, when the net marginal product of capital equals zero, consumption per worker is at its maximum value.