APPLIED MACROECONOMICS

Outline of the Lecture Review of Solow Model. Development Accounting Going beyond Solow Model First part of the assignment presentation

Solow production function We begin with a production function and assume constant returns. Y=A.F(K,L) so…zY=F(zK,zL) By setting z=1/L we create a per worker function. Y/L=F(K/L,1) So, output per worker is a function of capital per worker. We write this as, y=f(k)

y=f(k) Change in k Change in y

The slope of this function is the marginal product of capital per worker. MPK = f(k+1)– f(k). It tells us the change in output per worker that results when we increase the capital per worker by one.

The function of production of Solow model tell us how the variation output per worker is due to the variation of capital per worker. Y=F(k) Let us see how Solow explain the variation of capital.

where k is capital per worker y is real gross domestic product (real GDP) per worker y/k is the average product of capital s is the saving rate δ is the depreciation rate n is the population growth rate. We assumed that everything on the right-hand side was constant except for y/k. We found that, in the transition to the steady state, the rise in k led to a fall in y/k and, hence, to a fall in ∆k/k. In the steady state, k was constant and, therefore, y/k was constant. Hence, ∆k/k was constant and equal to zero

Measuring Productivity Productivity is the effectiveness with which factors of production are converted into output. In other word, productivity is the ratio of the output produced to the amount of input. We talk of total factor productivity when referring to the overall productivity of an economy. That is the percentage change in real GDP equal the percentage change in total factor productivity plus the percentage change in labor and capital multiplied by the share of GDP taken by labor and capital.

Measuring countries productivity growth. We use growth accounting which equation show how given a country’s growth rates of output, physical capital and human capital, we can measure its growth rate of productivity.

Growth accounting 10

Consider our by-now familiar production function: Applying our rules for growth rates What is the economic interpretation of this equation? The growth rate of output is the sum of TFP growth and input growth. Input growth is itself a weighted average of the growth rates of the inputs; weights are factor shares. 11

Measuring productivity difference among countries. We use development accounting which is a technique of breaking down difference in income into the part that is accounted for difference in productivity and the part accounted for by difference in factor accumulation. This expression says that, in determining the productivity difference between two countries, we look at their level of output and levels of factor accumulation. The large the ratio of output in the two countries, the larger the productivity gap we would infer. Conversely, the larger the gap in the accumulation of factors, the smaller the productivity gap we would infer.

Development Accounting

Output per worker,y Physical capital per worker, k Human capital per worker, h country country2111

The table above tell us that. First, there are surprisingly large difference in the level of productivity, among countries. Capture interesting variation in countries relative strengths and weaknesses. If there is a deficiency with these productivity measures?

The Endogenous Growth Theory rejects Solow’s basic assumption of exogenous technological change

Start with a simple production function: Y = AK, where Y is output, K is the capital stock, and A is a constant measuring the amount of output produced for each unit of capital (noticing this production function does not have diminishing returns to capital). One extra unit of capital produces A extra units of output regardless of how much capital there is. This absence of diminishing returns to capital is the key difference between this endogenous growth model and the Solow model. Let’s describe capital accumulation with an equation similar to those we’ve been using:  K = s Y -  K. This equation states that the change in the capital stock (  K) equals investment ( s Y) minus depreciation (  K). We combine this equation with the production function, do some rearranging, and we get:  Y/Y =  K/K = s A - 

This equation shows what determines the growth rate of output  Y/Y. Notice that as long as sA > , the economy’s income grows forever, even without the assumption of exogenous technological progress. In the Solow model, saving leads to growth temporarily, but diminishing returns to capital eventually force the economy to approach a steady state in which growth depends only on exogenous technological progress. By contrast, in this endogenous growth model, saving and investment can lead to persistent growth.  Y/Y =  K/K = s A - 