The Macroeconomy in the Long Run The Classical Model

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1 PP556 Macroeconomic Questions The Macroeconomy in the ong Run The Classical Model what determines the economy s total output/income how the prices of the factors of production are determined how total income is distributed what determines the demand for goods and services how equilibrium in the goods market is achieved 0 Economic schools of thought Classical v. Keynesian Many different economic theories and perspectives Classical paradigm is the view of how the economy behaves in the long run, Two central theories in macroeconomics the Classical (or neoclassical) paradigm the Keynesian paradigm while the Keynesian paradigm is the view of how the economy behaves in the short run. The different time horizons is key to understanding the different theories. 2 3 Time horizons Time Horizons ong run (Classical): Prices are flexible and respond to changes in supply or demand Short run (Keynesian): Many prices are sticky at some predetermined level and only adjust over the long run The economy behaves much differently when prices are sticky. In this course, we will start with the long run and understand what determines GDP over this time horizon. Then we will look at the short run (recessions and expansions) and see why GDP varies from its long run value. Toward the end of the course we will look at how GDP grows over many years. 4 5

2 The Classical Model The Classical Model The Classical model is a representation of the relationship between employment, output, wages, and prices in the long run. Our plan is to first understand the pieces of fthe model, then fitthem together, th and then look at how output is determined in the Classical model and what role there is for policy to affect the level of output. The classical model begins by looking at the labor market, where people work to produce something and are paid wages. The labor market is then related to total (aggregate) supply in the economy, since the number of workers determines in part how much is produced (it also depends on how much each worker produces). Combining aggregate supply and aggregate demand, we can determine the equilibrium level of output in the economy. 6 7 Outline of classical model The Production Function A closed economy, market-clearing model Supply side factor markets (supply, demand, price) determination of output/income Demand side determinants of C, I, and G Equilibrium Real interest rate The production function relates inputs (like buildings and machinery, which we call capital and employees, which we call labor) to output. There can be a production function for cars, for computers, for health care, etc., but we will look at an aggregate production function which includes all of these. The aggregate production function relates total labor and capital to total output. 8 9 Factors of production The production function K = capital, tools, machines, and structures used in production = labor, the physical and mental efforts of workers denoted Y = F (K, ) shows how much output (Y ) the economy can produce from K units of capital and units of labor. reflects the economy s level of technology. exhibits constant returns to scale. 0 2

3 Constant Returns to Scale Returns to scale This means that if you double each input, then output will double. As a byproduct, with constant returns to scale, as labor increases with capital fixed, as it is in the short run at least, output increases at a decreasing rate. The intuition is that if you have a certain number of machines, if you add workers you will get more output. If you double the number of workers and the number of machines they have to work with, you can double output. But as you add more and more workers and don't increase the number of machines, you get less and less from each additional worker because they have to wait their turn for the machine or they bump into each other and break things, etc. This is the "law of diminishing returns". You get less and less additional output from each additional worker. Initially Y = F (K, ) Scale all inputs by the same factor z: K 2 = zk and 2 = z (If z =.25, then all inputs are increased by 25%) What happens to output, Y 2 = F (K 2, 2 )? If constant returns to scale, Y 2 = zy If increasing returns to scale, Y 2 > zy If decreasing returns to scale, Y 2 < zy 2 3 Assumptions of the model Determining GDP. Technology is fixed. 2. The economy s supplies of capital and labor are fixed at Output is determined by the fixed factor supplies and the fixed state of technology: K K and Y F ( K, ) 4 5 The distribution of national income Notation determined by factor prices, the prices per unit that firms pay for the factors of production. The wage is the price of, the rental rate is the price of K. W R P W /P = nominal wage = nominal rental rate = price of output = real wage (measured in units of output) R /P = real rental rate 6 7 3

4 How factor prices are determined Demand for abor Factor prices are determined by supply and demand in factor markets. Recall: Supply of each factor is fixed. What about demand? The demand for labor is a relationship that says how many workers will be hired at different wage rates. Clearly, the higher the wage a firm has to pay, the fewer people it will want to hire. Not surprisingly, the demand for labor is related to the production function. The production function told us how much each additional worker produced. Firms look at this and directly see how much the additional worker is "worth" to them, and this is how much they are willing to pay that worker. If the wage is higher than that amount, they will not hire that last worker who adds less to production than he/she would be paid. Each worker is "worth" the amount that worker adds to output (marginal product), valued at the price at which that unit of output will be sold (the price). So the wage equals the marginal product times the price, or equivalently, the marginal product equals the real wage. 8 9 Demand for labor Marginal product of labor (MP) Assume markets are competitive: each firm takes W, R, and P as given Basic idea: A firm hires each unit of labor if the cost does not exceed the benefit. cost = real wage benefit = marginal product of labor definition: The extra output the firm can produce using an additional unit of labor (holding other inputs fixed): MP = F (K, +) F (K, ) 20 2 The MP and the production function Diminishing marginal returns Y output MP MP MP Slope of the production function equals MP F ( K, ) As more labor is added, MP As a factor input is increased, its marginal product falls (other things equal). Intuition: while holding K fixed fewer machines per worker lower productivity labor

5 MP and the demand for labor abor Supply Units of output Real wage Quantity of labor demanded Each firm hires labor up to the point where MP = W/P MP, abor demand Units of labor, Note that we assume the quantity of labor is fixed, and all that is determined in the labor market is the real wage that is paid to workers. We could imagine that more people want to work at higher wages, but that will not really change our understanding of how output is determined and how workers are paid, etc. For now, assume the labor supply is fixed (i.e., is a certain level, regardless of the wage). This labor supply will then be vertical: The equilibrium real wage The Real Wage Units of output abor supply The nominal wage is how much (in $, Euros, Yen etc.) workers are paid. equilibrium real wage MP, abor demand The real wage is how much they can buy with that wage, so if prices rise but nominal wages don't rise, workers can buy less with their earnings, which is because real wages have fallen. The real wage adjusts to equate labor demand with supply. Units of labor, The real wage is how the firms determine how many people they are willing to hire Unemployment? Reality Check! Together, the demand for labor and the supply of labor determine the equilibrium amount of labor employed and the equilibrium real wage What is unemployment in the classical model? It will only occur if the real wage is too high. According to classical economists, as long as the real wage fell, employment could be eliminated. The place where labor supply and labor demand intersect, where we would "like" to be, and could be, according to the classical economists, was called "full employment, or correspondingly the natural rate of unemployment". We will talk next time about how there can be unemployment at full employment

6 Determining the rental rate The equilibrium real rental rate We have just seen that MP = W/P The same logic shows that MPK = R/P : diminishing returns to capital: MPK as K The MPK curve is the firm s demand curve for renting capital. Units of output Supply of capital The real rental rate adjusts to equate demand for capital with supply. Firms maximize profits by choosing K such that MPK = R/P. equilibrium R/P MPK, demand for capital 30 K Units of capital, K 3 The Neoclassical Theory of Distribution states that each factor input is paid its marginal product accepted by most economists How income is distributed: total labor income = total capital income = W P R K P MP MPK K If production function has constant t returns to scale, then Y MP MPK K national income labor income capital income abor s share of total income The ratio of labor income to total income in the U.S abor s share of income is approximately constant over time. (Hence, capital s share is, too.) 34 What Have We earned So Far? First, we know how much will be produced (GDP) as long as we know how much capital and labor there is. The production function tells us how capital and labor combine to produce output. Second, we know how GDP is distributed. Firms pay workers a real wage equal to their marginal product, and capital is paid its marginal product. For now, we are pretty vague about who "owns" the capital. 35 6

7 Aggregate Supply Putting it all together in 4 Graphs To determine how much is supplied at different prices, we have to use the labor market and production function. This isn't surprising since they together determine how much is produced at a given price (which appears in the real wage). The intuition for what we will do graphically is to look at "full employment or natural (sometimes potential)" output (the output level at full employment) at one price, and then vary the price and see what happens to aggregate output. Since we are varying the price in the output market, where output is produced and supplied, we will end up with a supply curve. The first two graphs, the labor market curve and production function, are exactly as we had them before when we looked at them separately, but here we "stack" them since the level of labor in the labor market is the same as the level of labor that is input to the production function (so we can line them up). The third graph is just to turn corners. It is a line where each point on the vertical axis is turned into an equivalent point on the horizontal axis. The last graph relates output (or national income, since income=expenditure as we saw earlier) to the price level ong Run Aggregate Supply What the Graphs Show: Y W/P W /P =W 0/P 0 W 0/P F F F(K,) D F P P P 0 Y F RAS Y F Y Y First we will locate our initial full employment output level (go from intersection in labor market up to production function, across, and down to a point for aggregate supply curve. Now, if we change the price level, the classical model tells us that the nominal wage will adjust to prevent unemployment, keeping us at full employment. (This may not happen immediately, but it will over the long run, since this is how we defined the long run). We can go through the graphs again to see that we get a point in the aggregate supply diagram where income is the same but the price level is different. Note that we refer here to "aggregate supply" which is supply for the whole economy, rather than for a particular product Vertical Aggregate Supply Curve Outline of model The key point from this model is that the classical aggregate supply curve is vertical. The same amount is produced, and employment is the same, no matter what the price level. We will relax the assumption of complete flexibility of the labor market to reach the equilibrium real wage later on and see how the determination of GDP is affected. For now, think of this as a long-run view of the economy, in the sense that in the long run we expect wages to adjust so that we achieve labor market equilibrium. A closed economy, market-clearing model Supply side DONE factor markets (supply, demand, price) DONE determination of output/income Demand side Next determinants of C, I, and G Equilibrium Interest rate

8 Demand for goods & services US GDP Components of aggregate demand: C = consumer demand for goods and services I = demand for investment goods G = government demand for goods and services (closed economy: no net exports, NX ) Components of GDP Consumption CONSUMPTION is determined by how much income people have available, which is total income less the amount they pay to the government in taxes. Returning to the flow diagram, recall that we denoted consumption as C, income as Y, and taxes as T, so consumption is just C = a +c (Y T ) which says that people p always consume some subsistence level of consumption (food, shelter) and then for each dollar of disposable income (Y-T), people spend a fraction c of that dollar. For example, if c is 0.8, then people spend $.80 of each dollar of disposable (after-tax) income. They save the rest. The fraction of after-tax income that is spent on consumption is called the marginal propensity to consume Consumption, C The consumption function def: disposable income is total income minus total taxes: Y T C Consumption function: C = a +c (Y T ) Shows that (Y T ) C C (Y T ) def: The marginal propensity to consume is the increase in C caused by a one-unit increase in disposable income. MPC The slope of the consumption function is the MPC. Y T

9 Investment Investment and the Interest Rate INVESTMENT depends on how much it costs to invest (not surprisingly), which is the interest rate. The interest rate is the cost of investing since often a firm must borrow (and pay interest on the amount borrowed) to make an investment like a new factory or new machine. Even if the firm does not have to borrow, it gives up the interest it would have earned on the money had it not spent it on the factory. Therefore, the interest rate is the cost of investing. In particular, it is the real interest rate denoted as "r" (the "reported" interest rate adjusted for inflation) that is the cost of borrowing. To see this, note that if you borrow and have to pay interest of 0%, but prices are rising by 0%, then each dollar is worth 0% less, and it is therefore easier to pay back the interest (in this case the real interest rate is zero and it has cost you essentially nothing to borrow). We denote the dependence of investment on the interest rate by I(r) Investment, I The investment function The investment function is I = I (r ), where r denotes the real interest rate, the nominal interest rate corrected for inflation. The real interest rate is the cost of borrowing the opportunity cost of using one s own funds to finance investment spending. So, r I r Spending on investment goods is a downwardsloping function of the real interest rate I (r ) I 50 5 Government Government spending, G GOVERNMENT SPENDING is a policy variable that is set by the government, and is therefore called exogenous since it is not determined in combination with C, I, r, Y, etc. We will have to worry later about how the government gets the money to spend, but clearly to some extent this depends on taxes, and a deficit can arise if spending is greater than tax revenue. G includes government spending on goods and services. G excludes transfer payments Assume government spending and total taxes are exogenous: G G and T T

10 Putting these 3 pieces together Equilibrium We have the allocation of Y (GDP) to consumption, investment, and government spending: Y = C + I + G = a+c(y-t) + I(r) + G We know how much is produced from the production function, since Y = F(K,) Equilibrium is where "supply equals demand", or where the amount produced equals the amount spent as consumption, investment, and government spending. Since K and are given (fixed) and T and G are given (fixed) and a and c are just numbers, the only thing left that can equate supply and demand is the real interest rate The market for goods & services How is equilibrium achieved? Agg. demand: CY ( T) I( r) G Agg. supply: Y F ( K, ) Equilibrium: Y = CY ( T) I( r) G The real interest rate adjusts to equate demand with supply. Think about the capital market box on our original flow chart. Flows into the capital market came from (private, or personal) savings. Flows out of the capital market went to investment by firms (i.e., they borrow from the capital market). The government can either supply funds to the capital market if it has a surplus, or borrow from the capital market if it has a deficit. So the total amount of savings in the economy is (Y-T-C) + (T-G), which is total income less taxes and consumption, which is personal funds left for saving, and the government surplus (if negative, then a deficit and it reduces savings) Algebraically The interest rate Start with Y = C + I + G Re-arranging Y -C-G = I which is equivalent to (Y - T C) + (T G) = I which is equivalent to saying that savings equals investment. Or equivalently, the supply of funds to the capital market (savings) equals the demand for funds from the capital market (investment). Y is fixed by the labor market and production function, T and G are exogenous (determined by the government), and C depends on Y and T which again are fixed. So total savings is fixed by the labor market, production function, and government policy. So how is the capital market kept in equilibrium? The interest rate equates supply and demand in the capital market

11 The Interest Rate The Role of Prices If the interest rate is too high, then investment demand will be low and supply will exceed demand, pushing the interest rate down. If the interest rate is too low, then demand for investment will exceed supply, pushing up the price of investment (the interest rate). So the interest rate keeps the capital market in equilibrium, which is equivalent to keeping supply and demand of output in equilibrium. Note that prices do not accomplish anything here. The price level is not what is equating supply and demand because as we saw earlier, the price level does not affect output, and nowhere in the allocation of output to consumption, investment, and government spending does a price appear. This is captured in the vertical aggregate supply curve which says output is at a fixed level regardless of the price level. Another way of saying this is that real quantities are determined completely separately from prices in the long run. We will return to this idea when we start to introduce money and monetary policy How can we increase output? The role of Productivity increase productivity (shift up the production function to get more output from the same number of workers) increase population working (i.e., increase the labor supply) increase investment (as we will see later, more investment leads to more capital stock, which in the very long run leads to more output). Since it is very difficult to think about how to increase the population working, and investment is actually very complicated (but we will talk about it more during the course), productivity is a hot topic. But the problem is that no one is really sure how to increase productivity, or really what the process is that makes it increase when it does increase. There has been a lot of discussion i of whether computers have increased productivity. Some people say yes since a computer can do things that it used to take a person to do (so there can be more output with the same number of people). Some people say no since now people revise and revise and revise (for example), which doesn t increase output, but does use up labor, thus decreasing output per worker or per worker hour Cross-Country Country Productivity 64

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