Exam #1 Study Guide (Lectures 8 – 12)Lecture 8 (January 13)Understand what causes differences in income over time and across countries.Factors of production - capital and laborProduction of technologyDifferences in income must come from differences in capital, labor and technologySolow growth model –Consists of the production function and consumption functionShows how growth in capital stock and labor force, and advances in technology interact in an economy as well as how they affect a nation’s total output of goods and services.Supply of goods in the Solow Growth model is based on the production function – Y = F(K,L)Output depends on capital stock and the labor forceOutput per worker = some function of country’s capital per workerAssumes that the production function has constant returns to scalezY = F(zK, zL) – if capital and labor are multiplied by z, the amount of output is also multiplied by z.All quantities are denoted in “per-worker” terms - lowercase lettersy = Y/L : output per workerk = K/L: capital per workerMore capital  increase in output – f’(k) > 0Production function – y = f(k)The slope of function shows how much extra output a worker produces when given an extra unit of capital.The production function becomes flatter as k increases, indicating diminishing MPKMPK= f(k+1) - f(k)The demand for goods in the Solow growth model comes from consumption and investment.y = c + iGrowth in the Capital Stock and the Steady StateTwo forces influence the capital stock –Investment – expenditure on new plant and equipment, causes capital stock to riseDepreciation (δ) – wearing out of old capital, causes capital stock to fallAccumulation of CapitalThe demand for goods in the Solow model comes from consumption and investment.Output per worker is divided between consumption per worker c and iy = c + iThe Solow model assumes that each year people save a fraction s of their income and consume a fraction (1-s).Consumption function: c = (1 – s)y, where s, the savings rate is a number between 0 – 1.Substitute (1 – s)y for c to see what the consumption function implies for investment.y = (1 – s)y + i  i = syThis equation shows that investment = savingsGrowth in Capital Stock and the Steady StateCapital stock is the key determinant of the economy’s outputEffected by two forces: investment and depreciationInvestment per worker – i = syBy substituting the production function for y, we can express investment per worker as a function of the capital stock per workeri = sf(k) – this equation relates the existing stock of capital k to the accumulation of new capital i.To incorporate depreciation into the model, we assume that a certain fraction δ (depreciation rate) of the capital stock wears out each year.δk – the amount of capital that depreciates each year; this depreciation equation also shows that the amount of depreciation depends on the capital stock.Change in Capital Stock = Investment – DepreciationΔk = i – δk  Δk = s • f(k) – δkAt the steady state (k*) Δk = 0At this point, investment = depreciationThe steady state represents the long-run equilibrium of the economy.In any steady state:i = δ • kf(k) = y = √kThe saving rate is the ratio of saving to outputThe Golden Rule Steady State – savings rate that maximizes consumption contingent on being in a steady state.To maximize: take the derivative and set to 0* be familiar with different starting points (too much capital, too little capital)Population growthInvestment raises the capital stock and depreciation reduces it.The growth in the number of workers causes capital per worker to fallk = K/L – capital per workery = Y/L – output per workerKeep in mind that the number of workers is growing over time.Change in the capital stock per worker is: Δk = i – (δ + n)kEffects of Population GrowthPopulation Growth alters the Solow Model in three ways:Brings us closer to explaining sustained economic growth.Explanation as to why some countries are rich and others are poorAffects our criteria for determining the Golden Rule (consumption-maximizing) level of capital.Alternative Perspectives on Population GrowthMalthusian – Thomas Malthusn > growth rate of food productionHe did not take technology into considerationKremerian – Michael KremerPopulation growth generates technological growthEconomic growth has been much more rapid since 1800 than before 1800.Most economically advanced civilizations prior to 1500 were in Eurasia and parts of Africa.People are what drive economic growth.Lecture 9 (January 22)Four tasks of the Solow Model:Make the Solow model more general and realisticAdd technology to the Solow model – initially only included change in capital and change in labor forceMove from theory to empiricsExamine how a nation’s public policies can influence the level and growth of its citizens’ standard of living5 questions:Should society save more or less?How can policy influence the rate of saving?Are there some types of investment that policy should especially encourage?What institutions ensure that the economy’s resources are being put to their best use?How can policy increase the rate of technological progress?Consider what the Solow model leaves outThe Efficiency of Labor- “anything that multiplies”:Alters current production function: Y = F(K,L)Production function is now: Y= F(K,L x E) where “E” is the efficiency of laborThe term “L x E” can be interpreted as measuring the effective number of workers, where “L” is the actual number of workers and “E” is their level of efficiencyAssumption:Technological progress causes the efficiency of labor to grow at some constant rate g.Ex. g = 0.02; each labor unit becomes 2% more efficient each year: output increases as if the labor force had increased by 2 percent more than it really did.This technological progress is called labor-augmenting and g is called the rate of labor-augmenting technological progress.Because the labor force (L) is growing at rate n and the efficiency of each labor unit (E) is growing at rate g, the effective number of workers (L x E) is growing at rate n + gThe Steady State with Technological ProgressModeled as labor augmenting, therefore fits into the model similarly as population growth.Causes the effective number of workers to increase.~k = K/(L x E) – capital per effective worker~y = Y/(L x E) – output per effective workery = f(k)Δk = sf(k) – (δ + n +