Question

Use the basic Solow growth model, without population growth or technological progress.

(1) Draw a diagram with per worker output, y, consumption, c, saving, s and investment, i, on the vertical axis and capital per worker, k, on the horizontal condition. On this diagram, clearly indicate steady-state values for c, i, and y. Briefly outline the condition that holds in the steadystate (i.e. what is the relationship between investment and the depreciation of capital?).

(2) Suppose that society becomes thriftier, resulting in a higher rate of savings, s. Using the above diagram, how does the new steady-state capital stock per worker, k, compare to the steady-state stock in part (1)? How does output per worker compare? How does consumption per worker compare? [Note: Even if output per worker increases, consumption per worker need not increase. Why not?]

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Answer 1

solow onodel the demand amount. all the leprechalion of cabinal). uween verlmene -> In the goods comes froom consumption and for investmene. Y- ati Y = output per worker we are assume closed economy. C = (1-sy that is people save a fraction of thels income and consume remaining an our goal is to find one what saving rate is desirable for the country. Y=(1-syti we know investorient equal saving. the rate of saving is a fraction of oudpur woe for investment. i=sy for any , given stock of capital, I production function y=f(K) determine how much output economy produces and what saving rates determines investonent. Depreciation refers to the weaver at of old cabital & which means every started to fall. year capital stock - Stck) Investment per fan ction of capit Stment per worker is a tion of capital Stock per worker

output per workery fig-1 output f(K) a I consumption per worser Stlk) Investment per 00гке capital per workerk The Saving rate s determines What amount omrestment should I be needed from output after consumption. FSK (Depreciation ( per worker) Depreciation, Sk Fig-2 A constant fraction s of the capital Stoak wears out every year. Change in capital Stock - Investment - 2 Depreciation DIS = i SK We know i=SA (K) . Ak - st(k) - SK

+ f(k) The negher the capital stoas the greater the amount of investment abo greater amount of depreciation. Inventement, depreciation SK2 СК) fig-3 Ski- SK PSIS F(K) KI ber ki capital capital stock increases Stocks decreasen becouse investment Steady stoute level exceeds depreciation. of capital per woriser The Steady state level of capital stoak KA where investment equals depreciation. Investment, a Depreciation ould 6) SK Depre - Sof(K) Figa Sif(K) capital per Ky workerk minerease in the saving rate cs) omplies amount of rivestment for an given capital stock is higher saving enction shifts upward from si to s2... Initial steady stale ko after that capita stock prises until it get Kat with more capital and output.

steady state output "and depreciation SKA Steady state depreciation f(KA Steady state output icgold I k gold Steady State capital per Policymaker want to worker, ka choose the steady state with highest level of consumption. The Steady state value of is that maximper consumption is called Golden Rule level of capital and denoted knygoid @* = f(K . SK It the capital stock is below the Colden Rule level, an increase in capital stock reaises output more than depreciation sothat consumption ruses. V