Chapter 1. Chapter 8 – Problem 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) = K0.3L0.7.

CtyO0UklDD2SGxES57vMl62tKHmUXYT7b6t3LcUTVzUUy2lUtnlku0kkIFvwqNDSKI6E5/81EqreSrIgUB+R74hPoLnDzONMD71piEB0AMFfksBXnRP8Sqkt9FnOVYe5LHCSNBJkPPcvSuqVAKpFqeH917uMkaOEDAVqmfy4OzVLgAdJW1UbAcHFcOG/eY5Ay87xrqXf8u3Kl6yTVUB/dobCOEkT8P8jqpXDExAHEhrrW0afKBzY+1yNWmm79uTTgV2H9rj1ox/Q/13C

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

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.

KINmChPBFrLCWN3/ocr6+4w54iJaJvfVrn836dCkTUJ1t5NaQn2GE8sS/D5MW6l09lyIMixyLFwYXQyipWh96/aziFmGdt7ln8H3S+y+sn/VgTu2L4JM7zkmCrKXfRXU1PDtdVTdftyHe//W5wOzE/cXzdXxj24FtnKX6Fy3naS5hfxw8hl2vm1Q81mNnw5ACruJORUKiButedyS/Inr8HiWai9iL1ANg+S26WcIA1k7nL2pkCau7wI6307KK5v421/BB/rJ5sv7qHarLKdZZ/GsvF4U6eDL+QA1Bqn/PYo7BCqpZI2WNbejydP64MF5fpWI2hoyp4DwzIO1b9Mkx3+6KxXeWDofnupKxOGlpsrbXZPw
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

K3tVH7ECmFucEkcp7EGzFq62freIOUuDqilgMdCNeFyNybuDJhLH/WtHNsRUoX1DgHtqQ6BwwLGaLyaK4ipsVpFPjGjm3gbPKSK3jogyLZmdcXSaZhPrk4B4h/IqE5AcMRJX8d+3EamecuO8NBAb5rvN4HyPMs0RBbsBaAVqzQoWqIdksgA83nCwG3t/x1+9EeX8qa3OVgjoqBLFI5Y/amEozs7/gZZnvr61EzYV9IMV+REC+WVT201NumZrY00C/w2AJD9r/PMTdfK5vT32Nlotz4gk4aHFXKqtjCQ6ACU=
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

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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.
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Question 2

Question

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 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 the marginal product of capital net of depreciation for each of the 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 6BioFgrgcaLyz8Yo
0.2 7.25 1.81 1.45 Twgk/O9+C/I81wTH
0.3 12.93 2.16 1.51 YEasaHtUpz+8GKcP
0.4 19.50 2.44 1.46 vQ161FAka0b8o2td
0.5 26.83 2.68 1.34 WAk2GoTLixcP4oCf
0.6 34.81 2.90 1.16 bsdl/4b49bAffNK8
0.7 43.38 3.10 0.93 CkfIKFaeicsUyICP
0.8 52.50 3.28 0.66 CK1qwhHSimh0NduC
0.9 62.12 3.45 0.35 J/7GPOdPwaUkF/eJ
1.0 72.21 3.61 0.00 4XgI5lJ9Ln+7aBnf
Table
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