Principles of Macroeconomics 2017 Productivity and Growth. Takeki Sunakawa

Transcription

1 Principles of Macroeconomics 2017 Productivity and Growth Takeki Sunakawa

2 What will be covered Preliminary mathematics: Growth rate, the rule of 70, and the ratio scale Data and questions Productivity, capital and technology Firm s profit maximization Cobb- Douglas production function

3 Growth rate Growth rate of a variable Y from period t to period t+1 is defined as: g " = Y " Y "&' ln Y Y " Y "&' "&' We are usually interested in the growth rate of the GDP, not the level itself.

4 Average growth rate If GDP grows at g percent from year 0, GDP in year t becomes Y " = Y - (1 + g ) ". The formula for computing average growth rate is g = Y " Y '/" - 1.

5 Growth rates of ratios, products, and powers 1. If Z = X Y, then g 6 = g 7 + g If Z = X Y, then g 6 = g 7 g If Z = X 9 Y :, then g 6 = ag 7 + bg 8.

6 The rule of 70 If GDP grows at g percent from year 0, GDP in year t becomes Y " = Y - (1 + g ) ". We are asking how many years does it take before GDP doubles. If it is after t years, 2 = (1 + g ) " holds (why?). This equation can be written as t = -.G DE.

7 Quiz If the economy grows 2% per year, how long does it take before the GDP doubles? If the GDP doubles in 35 years, what is the average of the growth rates during these years? t = G- '--DE.

8 Ratio scale We squish the vertical axis of the plot so that the key points- - - the 10-, 20-, 40- points- - - are equally far apart. An ever- steepening curve has turned into a straight line. The slope is one plus the growth rate

9 Ratio scale U.S. per capita GDP grows at 2% in average. In the ratio scale, the level of GDP is on a straight line. 50,000 44,000 38,000 32,000 26,000 20,000 14,000 8,000 2, ,000 32,000 16,000 8,000 4,000 2,

10 Data set for economic growth Most well- known data set for economic growth: Penn World Table (PWT) Takes into account differences in prices across countries. The following is based on version 8.1 (released on April 13, 2015).

11 GDP per GDP per Growth capita, 1970 capita, 2011 rate Singapore United States FACT 1: There are vast differences in living standards around the world. Germany Canada Japan Republic of Korea Portugal Hungary Brazil China, People's Republic of Uzbekistan NA NA Indonesia Philippines Viet Nam Kyrgyzstan NA NA Bangladesh Nepal Ethiopia

12 GDP per GDP per Growth capita, 1970 capita, 2011 rate Singapore United States FACT 2: There is also great variation in growth rates across countries. Germany Canada Japan Republic of Korea Portugal Hungary Brazil China, People's Republic of Uzbekistan NA NA Indonesia Philippines Viet Nam Kyrgyzstan NA NA Bangladesh Nepal Ethiopia

13 8.0 Levels vs. growth rates of per capita GDP Growth rate, Republic of Korea 6.0 China, People's Republic of Singapore Viet Nam Indonesia Norway Hungary 3.0 Brazil Portugal Japan Germany Ethiopia Nepal Bangladesh Philippines Columbia Canada United States Per capita GDP, 2011 (US=1) 0.0 1/64 1/32 1/16 1/8 1/4 1/2 1 2

14 Incomes and Growth Around the World Since growth rates vary, the country rankings can change over time: Poor countries are not necessarily doomed to poverty forever, e.g. Singapore incomes were low in 1970 and are quite high now. Rich countries can t take their status for granted: They may be overtaken by poorer but faster- growing countries.

15 Incomes and Growth Around the World Questions: Why are some countries richer than others? Why do some countries grow quickly while others seem stuck in a poverty trap? What policies may help raise growth rates and long- run living standards? To answer these questions, economists use models with some assumptions.

16 Two sides of the goods market Aggregate Supply (AS) side How much do firms wish to produce? = the production capacity. Aggregate Demand (AD) side How much do households, firms and the government wish to purchase? We start with the Aggregate Supply side, because

17 In the Long Run, Aggregate Output is determined by Aggregate Supply Long Run means when all the price adjustments are finished. The production capacity in the long run is determined independent of the prices. Short- Run theories explain how the price adjustments affect output fluctuations.

18 Productivity The ability to produce goods and services depends on [labor] productivity, the average quantity of goods and services produced per unit of labor input. Y = real GDP = quantity of output produced L = quantity of labor so productivity = Y/L (output per worker)

19 Why Productivity Is So Important When a nation s workers are very productive, real GDP is large and incomes are high. When productivity grows rapidly, so do living standards. What, then, determines productivity and its growth rate? We will look at capital per worker and technology.

20 Capital Per Worker Capital: The stock of equipment used to produce goods and services is called, denoted by K. K/L = capital per worker (equipment rate). Productivity is higher when the average worker has more capital (machines, equipment, etc.). i.e., an increase in K/L causes an increase in Y/L.

21 Technology Technology: Society s understanding of the best ways to produce goods and services Technological progress does not only mean a faster computer, a higher- definition TV, or a smaller cell phone. It means any advance in knowledge that boosts productivity (allows society to get more output from its resources).

22 Production function

23 The Production Function We assume that the production capacity is characterized by a mathematical relationship called the production function. The production function is a graph or equation showing the relation between output and inputs Y = A F(L, K) F( ) is a function that shows how inputs are combined to produce output L: labor input K: [physical] capital A: the level of technology

24 The Production Function Y = A F(L, K) A multiplies the function F( ), so improvements in technology (increases in A ) allow more output (Y) to be produced from any given combination of inputs. For the function F( ), we assume: 1. Constant Returns to Scale (CRS). 2. Marginal product of capital (MPK) is positive and diminishing. 3. Marginal product of labor (MPL) is positive and diminishing.

25 The Production Function: CRS The production function has the property constant returns to scale (CRS): Changing all inputs by the same percentage causes output to change by that percentage. For example, doubling all inputs (multiplying each by 2) causes output to double: 2Y = A F(2L, 2K) Also, increasing all inputs 10% (multiplying each by 1.1) causes output to increase by 10%: 1.1Y = A F(1.1L, 1.1K)

26 The Production Function: CRS If we multiply each input by 1/L, then output is multiplied by 1/L: y = A F(1, k) This equation shows that productivity (output per worker) y=y/l depends on: the level of technology (A) Y/L = A F(1, K/L) physical capital per worker (k=k/l)

27 What is MPK and MPL? MPK: Marginal Product of Capital (Holding constant L,) if we add 1 more K, how much extra Y do we get? MPL: Marginal Product of Labor (Holding constant K,) if we add 1 more L, how much extra Y can we get? Both are positive and diminishing.

28 The Production Function & Diminishing Returns If workers Output per have little worker k, giving (productivity) them more increases their productivity a lot. y= A F(k) If workers already have a lot of k, giving them more increases productivity fairly little. k

29 The catch-up effect: the property whereby poor countries tend to grow more rapidly than rich ones Rich country s growth y= A F(k) Poor country s growth Poor country starts here k Rich country starts here

30 Profit maximization with Cobb- Douglas production function

31 Real vs. Nominal Variables Nominal variables are measured in monetary units. Examples: nominal GDP, nominal interest rate (rate of return measured in $) nominal wage ($ per hour worked) Real variables are measured in physical units. Examples: real GDP, real interest rate (measured in output) real wage (measured in output)

32 Real vs. Nominal Variables Prices are normally measured in terms of money. Price of a compact disc: $15/cd Price of a pepperoni pizza: $10/pizza A relative price is the price of one good relative to (divided by) another: Relative price of CDs in terms of pizza: price of cd price of pizza = $15/cd $10/pizza = 1.5 pizzas per cd Relative prices are measured in physical units, so they are real variables.

33 Real vs. Nominal Wages An important relative price is the real wage: W = nominal wage = price of labor, e.g., $15/hour P = price level = price of goods & services, e.g., $5/unit of output Real wage is the price of labor relative to the price of output: W P = $15/hour $5/unit of output = 3 units output per hour

34 Firm s decision making Consider a firm s decision making. In each period, firms rent K from outside, paying the rental rate. Firms also hire L, paying the wage. The rental rate per unit of K is denoted by R. The wage per unit of L is denoted by W. Both R and W denoted in the units of money. That is, they are nominal.

35 Firm s decision making Using K and L, firms produce output Y, whose price per unit is denoted P. Assume that R, W and P are all exogenous (given) from the viewpoint of each firm (assumption of price takers). How do firms determine the quantity of inputs (K and L) so as to maximize their profit?

36 Firm s decision making Firms determine their demand for K and L so as to maximize their profits. Firm s nominal profit is where Π = PY RK WL, Y = AF(K, L).

37 Firm s decision making By solving this problem, we obtain and r = R S = MPK w = V S = MPL where MPK = A WX(Y,Z) and MPL = A WX(Y,Z). WY WZ r and w are real input prices.

38 Firm s decision making A firm demands inputs (K and L) up to the point where Why? (Real Input Price) = (Its marginal product). Imagine that (Input price) < (Marginal product). What should the firm do to increase its profit? What if (Input price) > (Marginal product)?

39 Cobb- Douglas production function Y = A F(L, K) has a following specific functional form: Y = AK [ L '&[ where 0 < α < 1. Then, we have r = MPK = αak`&' L '&[ and w = MPL = (1 α)ak`l &[ (to be explained on the board)

40 Numerical example Let A=L=1 and alpha=0.5 then we get Y = K -.a K Y

41 Numerical example If the level of technology is doubled Y = AK -.a

42 Numerical example Let A=L=1 and alpha=0.5 then we get MRK = 0.5K &-.a K YMRK 0.00 NA

43 Input prices under the Cobb- Douglas technology In the technical appendix (optional), it is shown that MPK, and thus r, is decreasing in K/L and increasing in A. MPL, and thus w, is increasing in K/L and increasing in A. That is, it is the ratio K/L that matters.

44 Capital share under the Cobb- Douglas technology In the technical appendix, it is also shown that alpha should be equal to the share of capital income in total income, α = rk/y. Capital s share is very similar (around ) across countries and stable over time for most countries, giving us a rationale for using the Cobb- Douglas production function. So we can safely assume that alpha in the real world is around