Chapter 1. Chapter 8 – Question 3

Question 1

Work It Out

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

Question

Consider an economy described by the production function:

Y = F(K, L) = K^0.3L^0.7.

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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.

Question

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.

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Question

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Question

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Question 2

Question

Consider an economy described by the production function:

Y = F(K, L) = K^0.3L^0.7.

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	rujH1K6gnqXhFD4Jj2djIKtFPQlOt+3/rD/5Gw==	rujH1K6gnqXhFD4Jj2djIKtFPQlOt+3/rD/5Gw==	rujH1K6gnqXhFD4Jj2djIKtFPQlOt+3/rD/5Gw==
(0.05)	0.1	a3LbQZv+QkF/GvPBrwnjZXRRhft3WGo4	eusFX0SYx+jm8U6VmQQCEEAcySzWAdzX	zNc6pSlE7GL7oePMTqKvXeSdhdV5LqJB
	0.2	wWOGN4kqjGL0kYF8J7JqRhCvX3cLcM8o	XVyWEG0zsLGs+u5y7gAl1m8Y5Om23qYs	zaNPOGTptZMkMM8+9lvbbJSddV2/Hb6N
	0.3	wdqy5LPrZRk2Snghyo/tK+YJ6JGFINPy	OLyOSnXRQBMXWWcislZzaqazwo4ZdRtA	AMDz9MBPW0vTuT5zfLCZQ+676d9OOart
	0.4	Flm2Zg8NWPfdxfAm3sdTff+7wNF6uJ/y	uwdCvzhIIW6hZIySZ2hzXKfnXGySf+xm	8Xs7Hmhqea0eVCTFtop8upzfPsa1r39U
	0.5	YQUctJJ4wnpqQGOq2ab+YTjvgsNUevpA	Ho0yLBDUXbtBQAFiEjbMNcazS/SkiT+j	0o7C5pKx8dKUC6y6O54RB3wjHNxNIJDU
	0.6	SCL+lr5Ap4jvWz01y5p4yX0Vx2Wo8Hoq	jquwrUGQ3/UmVABqHwgPISvqbXCzxF3h	OiKcI+mFgwuG706x7mFZTCmoBZ39GAjH
	0.7	1oet64nCiFFwAfNtTvej0Vjr1ejBQHkS	B4PBTdiZz80kPMo/Rcw4d7ZvANF7EhxZ	QmtMo464tOFMohhol/KJ3qygKJ9E6KUw
	0.8	0B9ZekVumtvCC9rCVeMD+7y30o7ACvUf	RWKaYB6hy+5IlR0kjBBMYIHIDUjWJ1j6	7ECdmWA5N8ZohOBMLqCAfrQ6LoHS4YXv
	0.9	jmaYPLiht8/iIs98Jqk/FfbIz0TOZ9iz	3JX5XYfq9PirZEnNvNUEhM/ngtjHhvpc	B0ZY4MK1mTz82teGSIKQzYPQk+fmD9rI
	1.0	sGcRdKgcGxTZBma8cHtm9bsJKFIiIJzZ	4LYyE11+th9iohp0CTdTz6pDjpIxaibO	rujH1K6gnqXhFD4Jj2djIKtFPQlOt+3/rD/5Gw==

Question

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

A saving rate of b0g0iQ1whKk= percent maximizes output per worker. A saving rate of udX0h74V+w0= 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.

Question

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	uTo+WvXcUKHV9dW9kE04c4Eqx09ezEay
(0.05)	0.1	2.69	1.35	1.21	GFFCsON5Z92jj3KAvUxh4wdbFMYMmJx1
	0.2	7.25	1.81	1.45	5Q5nmt920j4OX2+CYw+28RND/ET7SXYs
	0.3	12.93	2.16	1.51	rJUqve0sSSBswFMNYkkXSJ2d3a3ap9mq
	0.4	19.50	2.44	1.46	eEsDf95TAOIilio6g33Ak+djgCbdEeygE7GvbQ==
	0.5	26.83	2.68	1.34	cUthh8tRTKDAezOAJHXE5vmAJHQJ5Cdg29PivQ==
	0.6	34.81	2.90	1.16	jwpE0ocwc/+Unt8BbzaEdFyxJtlaei/ikPFWkw==
	0.7	43.38	3.10	0.93	dB2l5SSylypP5zF0hQts7ZQ++EuGP9tU09rh2A==
	0.8	52.50	3.28	0.66	VBurlMBQK8XaIjyxSx4m/hinCqnnSyEpr9uDIA==
	0.9	62.12	3.45	0.35	Xy1mS0oZA9aQ4r5xWFmGb3RcVBvj8qnno1ofKg==
	1.0	72.21	3.61	0.00	Z7V1UV7FQHelHHP5z8UpwwF/AxF01cH5AGZ+bg==

Question

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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.

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