Chapter 3

PRODUCTIVITY, OUTPUT, AND EMPLOYMENT.

Introduction.

  • Measuring economic activity is only part of the job. We also have to analyze how economic growth is generated in order to know how to stimulate it and solve some of its problems.

(e.g.: how to fight the inflation associated with rapid economic growth)

  • We are going to start with how the labor market works.

3.1 The Production Function.

  • In order to produce goods and services, which market value the GDP records, we need to use inputs such as:

-Raw materials

-Energy

-Machines (physical capital, K)

-Workers (labor, N)

  • The last two factors of production are the most important ones and we can represent how we use them to produce goods and services through the production function:

Y = A . F (K , N)

where:Y = GDP = Output = Production of goods and services

K = physical capital stock

N = labor employed

F = the production function itself, the mathematical expression that tells us how we combine N and K to produce Y.

A = total factor productivity (technology)

  • Note that A relates actual output with the production function and that it is independent from F, K and N. If A increases (technology improves) for the same uses of K and N we can obtain higher Y.
  • Productivity is the key to economic growth. Workers are the same all around the world, machines can be bought, copied or stolen, so the real key factor is how well these factors are combined, how productive they are.
  • Some economists speculate with the idea of productivity being endogenous. That would create self-sustained growth.

The Shape of the Production Function.

  • We can calculate (estimate) the production function for the US economy.
  • It looks like this: Y = A. K 0.3. N 0.7

-If we use real data about the output produced, capital used and labor employed we can obtain a table like Table 3.1

(Notice the evolution of A. When A grows, the economy grows. When it decreases the economy is in a recession)

-If we plot the production function into a graph we can get a better understanding about how it works.

(Problem: how do we plot Y, K and N all at the same time in a two-dimensional graph?)

We will plot just two variables at a time

The Production Function Relating Output and Capital. Figure 3.1

  • Keeping N fixed we can see what happens to output when we increase the use of capital:

-More capital generates higher output (marginal productivity of K is positive)

-As we keep on increasing K (for a fixed level of N), output grows at a slower pace (K exhibits diminishing marginal returns)

  • The marginal product of capital (MPK = Y / K) is always positive but declines as the capital stock increases.
  • The MPK shows as the slope of the production function. The production function is upward sloping, so MPK>0. At the same time, the slope slightly declines as K, so capital exhibits diminishing marginal returns (MPK'<0)
  • Example: You have to write a paper (Y) and start out only with a pencil (K). If you are given a typewriter (K), you write more pages per hour (Y) If you use a computer (K) you are even faster (Y) but if you are given two computers (K) to use at the same time your speed is not going to increase by that much (Y)
  • Supply shocks (changes in A)can change the slope of the production function.

-A positive supply shock (a technology improvement) will shift the production function up

(e.g.: the introduction of computers)

The Production Function Relating Output and Labor. Figure 3.2

  • Keeping K fixed we can see what happens to output when we increase the use of labor:

-More labor generates higher output (marginal productivity of N is positive)

-As we keep on increasing N (for a fixed level of K), output grows at a slower pace (N exhibits diminishing marginal returns)

  • The marginal product of labor (MPN = Y / N) is always positive but declines as the labor employed increases.
  • The MPN shows as the slope of the production function. The production function is upward sloping, so MPN>0. At the same time, the slope slightly declines as N, so labor exhibits diminishing marginal returns (MPN'<0)
  • Example: You have a piece of land (K) to farm where to harvest a crop (Y) You start out only with one worker (N). If another worker joins you (N), the crop increases (Y) If more workers join you (N), harvesting is faster and the crops larger (Y) but if the number of workers on that limited piece of land keeps on increasing (N) they will start obstructing each other and the increase in crops will not be as large (Y)
  • Supply shocks (changes in A)can change the slope of the production function.

-A positive supply shock (a technology improvement) will shift the production function up

(e.g.: the invention of electricity)

3.2 The Demand for Labor.

  • We will consider the capital stock as being fixed in the short-run since depreciation is negligible on a monthly basis and new additions take significant time.
  • Labor employed, on the other hand, is quite flexible due to the availability of overtime, layoffs and other similar resources available to firms.
  • Therefore, when we think of the production function we will assume that K is fixed and only N changes.
  • In that case, we saw that each additional unit of labor employed by firms rendered marginally smaller additional units of output. Total labor productivity is always positive, but its marginal productivity declines as N increases.
  • If a firm knows that the last worker they are hiring is not going to bring the same increase to total output than the first worker they hired, they will be willing to offer a smaller wage to the last worker than to the first one.
  • This is why we can identify the labor demand curve with the marginal productivity of labor:

-As MPN with each additional worker, firms offer wages. Only with wages they can N

(the labor demand curve is downward sloping: wages QND and wages QND)

-Changes in the real wage will increase or decrease N (we will move along ND)

-Changes in the productivity of labor will increase or decrease ND (we will shift ND)

i.e.: better technology makes worker produce goods faster: ND shifts right.

3.3 The Supply of Labor.

  • The amount of labor supplied by workers is an individual decision that takes into consideration two different effects:

-The substitution effect: every time the wage offered to a worker is increased by a $ amount the worker faces the tradeoff of giving up some unpaid leisure time to work an extra hour.

-The income effect: every time the wage offered to a worker is increased by a $ amount the worker's wealth increases and the need to work longer hours decreases.

  • In general terms we should expect the substitution effect to incite the worker to work more hours as the wage increases and the income effect to reduce the amount of hours worked as the wage increases:

-If the wage increase is temporary the substitution effect will overrun the income effect because the worker will want to seize the brief opportunity to accumulate wealth.

-If the wage increase is permanent, it is very likely that the income effect will overcome the substitution effect and the number of hours worked will decrease.

  • The labor supply curve will show the relationship between wages and the amount of labor offered by workers:

(the labor supply curve is upward sloping: wages QNS and wages QNS)

-Changes in the real wage will increase or decrease QNS (we will move along NS)

-Changes in other factors will increase or decrease NS (we will shift NS)

e.g.: winning the lottery increases our wealth and reduces the need to work: NS shifts left.

e.g.: population growth increases the total amount of hours worked: NS shifts right.

  • How many hours are worked in the US per week? See Figure 3.9
  • How much do US workers work compared to other countries? See Figure 3.10

3.4 Labor Market Equilibrium.

  • At any given moment in time the total amount of people employed in the economy will be determined by the intersection of the labor demand curve and the labor supply curve.
  • That point is called labor market equilibrium:

-At the equilibrium wage firms can hire as many workers as they need.

-At the equilibrium wage workers can work as many hours as they want.

-At the equilibrium level of employment the economy produces at the equilibrium level of output.

  • A number of factors can make QND < QNS and so produce unemployment:

-If the government sets a minimum wage that is above the equilibrium wage.

-If there is a temporary supply shock (a hurricane) there will be frictional unemployment.

-If there is a permanent supply shock (foreign competition in steel manufacturing) there will be structural unemployment.

-If people decide to quit their jobs and take a break there will be voluntary unemployment.

  • For all these reasons there will always be some level of unemployment.
  • The volume of unemployment in the economy is measured through the unemployment rate:

"The fraction of the labor force that was actively looking for a job during the last month but was not able to find one"

  • This measure of unemployment is deficient for a number of reasons:

-If a worker gives up on looking for jobs after a while he/she is considered "discouraged" and is no longer considered unemployed.

-The labor force is composed of the non-retired population above 16, but does not account for people in jail, hospitals or college. If an unemployed worker becomes discouraged and returns to college for additional training he/she also drops from the labor force.