Econ 322 1 st Edition 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 labor Production of technology Differences in income must come from differences in capital labor and technology Solow growth model Consists of the production function and consumption function Shows 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 o Supply of goods in the Solow Growth model is based on the production function Y F K L o Output depends on capital stock and the labor force Output per worker some function of country s capital per worker o Assumes that the production function has constant returns to scale zY F zK zL if capital and labor are multiplied by z the amount of output is also multiplied by z o All quantities are denoted in per worker terms lowercase letters o y Y L output per worker o k K L capital per worker o More capital increase in output f k 0 o Production 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 MPK MPK f k 1 f k The demand for goods in the Solow growth model comes from consumption and investment o y c i Growth in the Capital Stock and the Steady State o Two forces influence the capital stock Investment expenditure on new plant and equipment causes capital stock to rise Depreciation wearing out of old capital causes capital stock to fall Accumulation of Capital The demand for goods in the Solow model comes from consumption and investment o Output per worker is divided between consumption per worker c and i y c i o The 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 sy This equation shows that investment savings Growth in Capital Stock and the Steady State Capital stock is the key determinant of the economy s output o Effected by two forces investment and depreciation o Investment per worker i sy By substituting the production function for y we can express investment per worker as a function of the capital stock per worker i 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 depreciation rate of the capital stock wears out each year k the amount of capital that depreciates each year this depreciation equation also shows that the amount of depreciation depends on the capital stock o Change in Capital Stock Investment Depreciation k i k k s f k k At the steady state k k 0 At this point investment depreciation The steady state represents the long run equilibrium of the economy In any steady state i k f k y k o The saving rate is the ratio of saving to output o The 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 growth o Investment raises the capital stock and depreciation reduces it o The growth in the number of workers causes capital per worker to fall o k K L capital per worker o y Y L output per worker Keep in mind that the number of workers is growing over time Change in the capital stock per worker is k i n k Effects of Population Growth o Population 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 poor Affects our criteria for determining the Golden Rule consumptionmaximizing level of capital Alternative Perspectives on Population Growth o Malthusian Thomas Malthus n growth rate of food production He did not take technology into consideration o Kremerian Michael Kremer Population growth generates technological growth Economic 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 realistic o Add technology to the Solow model initially only included change in capital and change in labor force Move from theory to empirics Examine how a nation s public policies can influence the level and growth of its citizens standard of living o 5 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 out The Efficiency of Labor anything that multiplies o Alters current production function Y F K L o Production function is now Y F K L x E where E is the efficiency of labor The 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 efficiency o Assumption 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 g The Steady State with Technological Progress o Modeled as labor augmenting therefore fits into the model similarly as population growth o 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 worker y f k k sf k n g k sf k investment n g k break even investment o If g technology increases output per worker and capital per worker will decrease o In a steady state with effective workers change in capital per effective worker and change in output per effective