Lecture 6 - Economic Growth – 1(B). The main contents of the chapter consist of the following: An increase in the saving rate leads to higher output in the long run, faster growth temporarily, but not faster steady state growth.
Review of the previous lecture The Solow growth model shows that, in the long run, a country’s standard of living depends • positively on its saving rate • negatively on its population growth rate Lecture Economic Growth – 1(B) Instructor: Prof Dr.Qaisar Abbas Lecture Contents • Steady state • Golden Rule The equation of motion for k k = s f(k) – k • The Solow model’s central equation • Determines behavior of capital over time… • …which, in turn, determines behavior of all of the other endogenous variables because they all depend on k E.g., income per person: consump per person: y = f(k) c = (1–s) f(k) The steady state k = s f(k) – k If investment is just enough to cover depreciation [sf(k) = k ], then capital per worker will remain constant: k = This constant value, denoted k*, is called the steady state capital stock The steady state Investment and depreciation k sf(k) k* Capital per worker, k Moving toward the steady state Investment and depreciation k = sf(k) k k sf(k) k investment depreciation k1 k* Capital per worker, k Moving toward the steady state Investment and depreciation k = sf(k) k k sf(k) k k1 k2 k* Capital per worker, k Moving toward the steady state Investment and depreciation k = sf(k) k k sf(k) k investment depreciation k2 k* Capital per worker, k Moving toward the steady state Investment and depreciation k = sf(k) k k sf(k) k k2 k3 k* Capital per worker, k The Golden Rule Capital Stock steady state output and depreciation Then, graph f(k*) and k*, and look for the point where the gap between them is biggest. * * y gold = f (k gold ) k* f(k*) * c gold * * i gold = δ k gold * k gold steady-state capital per worker, k* The Golden Rule Capital Stock c* = f(k*) k* is biggest where the slope of the production func equals the slope of the depreciation line: k* f(k*) * c gold MPK = * k gold steady-state capital per worker, k* Use calculus to find golden rule We want to maximize: c* = f(k*) k* From calculus, at the maximum we know the derivative equals zero Find derivative: dc*/dk*= MPK Set equal to zero: MPK = 0 or MPK = The transition to the Golden Rule Steady State • The economy does NOT have a tendency to move toward the Golden Rule steady state • Achieving the Golden Rule requires that policymakers adjust s • This adjustment leads to a new steady state with higher consumption • But what happens to consumption during the transition to the Golden Rule? Starting with too much capital * If k * > k gold y then increasing c* requires a fall in s In the transition to the Golden Rule, consumption is higher at all points in time c i t0 time Starting with too little capital * If k * < k gold then increasing c* requires an increase in s Future generations enjoy higher consumption, but the current one experiences an initial drop in consumption y c i t0 time Population Growth • Assume that the population and labor force grow at rate n exogenous) (n is ∆L = n L EX: Suppose L = 1000 in year 1 and the population is growing at 2%/year (n = 0.02). Then L = n L = 0.02 1000 = 20, so L = 1020 in year 2 Break-even investment ( + n)k = break-even investment, the amount of investment necessary to keep k constant Break-even investment includes: k to replace capital as it wears out • n k to equip new workers with capital (otherwise, k would fall as the existing capital stock would be spread more thinly over a larger population of workers) The equation of motion for k • With population growth, the equation of motion for k is k = s f(k) actual investment ( + n) k breakeven investment The Solow Model diagram Investment, break-even investment k = s f(k) ( +n)k ( + n ) k sf(k) k* Capital per worker, k The impact of population growth Investment, break-even investment ( +n2) k ( +n1) k An increase in n causes an increase in breakeven investment, leading to a lower steady-state level of k sf(k) k2* k1* Capital per worker, k Prediction • Higher n • And since y = f(k) , lower k* lower y* • Thus, the Solow model predicts that countries with higher population growth rates will have lower levels of capital and income per worker in the long run lower k* International Evidence on Population Growth and Income per Person Income per person i n 1992 (l ogari thmic scal e) 100,000 Germany U.S Denmark Canada Israel 10,000 U.K Italy Japan Finland France Mexico Singapore Egypt Brazil Pakistan Peru Indonesia 1,000 Cameroon India Ivory Coast Kenya Zimbabwe Chad 100 Uganda Popul ati on growth (percent per year) (average 1960 –1992) The Golden Rule with Population Growth To find the Golden Rule capital stock, we again express c* in terms of k*: c* = y* i* = f (k* ) ( + n) k* c* is maximized when MPK = + n or equivalently, MPK = n In In the the Golden Golden Rule Rule Steady Steady State, State, the the marginal marginal product product of of capital capital net net of of depreciation depreciation equals equals the the population population growth growth rate rate Summary An increase in the saving rate leads to higher output in the long run faster growth temporarily but not faster steady state growth ... 0.189 0.189 0.184 0.184 5.602 5.602 2.3 67 2.3 67 1.6 57 1.6 57 0 .71 0 0 .71 0 0.560 0.560 0.150 0.150 7. 351 7. 351 2 .70 6 2 .70 6 1.894 1.894 0.812 0.812 0 .73 2 0 .73 2 0.080 0.080 8.962 8.962 2.994 2.994.. .Lecture Economic Growth – 1(B) Instructor: Prof Dr.Qaisar Abbas Lecture Contents • Steady state • Golden Rule The equation of motion... L = n L = 0.02 1000 = 20, so L = 1020 in year 2 Break-even investment ( + n)k = break-even investment, the amount of investment necessary to keep k constant Break-even investment includes: k to replace capital