# The production function is a relationship between amount of labor employed and

To characterize the relationship between the quantity of labor employed and called an aggregate production function, which shows the maximum amount of. It is related to the production function because the marginal product of labor is equal to the slope of the production function (where output is plotted against employment). A temporary increase in the real wage increases the amount of labor . curve because a labor demand curve shows the relationship between labor. The production function illustrates the relationship between the quantity of inputs The marginal product of labor is the increase in the amount of output from an Labor. Supply. Demand. Equilibrium. wage,. W. Equilibrium. employment,. L.

The production function can shift due to supply shocks, which affect overall productivity. Examples include changes in energy supplies, technological breakthroughs, and management practices. Besides knowing the production function, you must also know the quantities of capital and labor the economy has. The upward slope of the production function means that any additional inputs of capital or labor produce more output.

The fact that the slope declines as we move from left to right illustrates the idea of diminishing marginal productivity. For a fixed amount of capital, additional workers each add less additional output as the number of workers increases. For a fixed number of workers, additional capital adds less additional output as the amount of capital increases.

The marginal product of capital MPK is the output produced per unit of additional capital.

The MPK can be shown graphically using the production function. For a fixed level of labor, plot the output provided by different levels of capital; this is the production function. The MPK is just the slope of the production function. The marginal revenue product of labor represents the benefit to a firm of hiring an additional worker, while the nominal wage is the cost.

Comparing the benefit to the cost, the firm will hire additional workers as long as the marginal revenue product of labor exceeds the nominal wage, since doing so increases profits. Profits will be at their highest when the marginal revenue product of labor just equals the nominal wage.

The same condition can be expressed in real terms by dividing through by the price of the good. The marginal revenue product of labor equals the marginal product of labor times the price of the good. The nominal wage equals the real wage times the price of the good.

Dividing each of these through by the price of the good means that an equivalent profit-maximizing condition is the marginal product of labor equals the real wage. The MPN curve shows the marginal product of labor at each level of employment.

It is related to the production function because the marginal product of labor is equal to the slope of the production function where output is plotted against employment.

The MPN curve is related to labor demand, because firms hire workers up to the point at which the real wage equals the marginal product of labor. So the labor demand curve is identical to the MPN curve, except that the vertical axis is the real wage instead of the marginal product of labor. A temporary increase in the real wage increases the amount of labor supplied because the substitution effect is larger than the income effect.

The substitution effect arises because a higher real wage raises the benefit of additional work for a worker. The income effect may be so large that it exceeds the substitution effect, causing the worker to reduce time spent working.

The aggregate labor supply curve relates labor supply and the real wage. Increases in wealth or the expected future real wage shift the aggregate labor supply curve to the left.

### Production function

Increases in the working-age population or in labor-force participation shift the aggregate labor supply curve to the right. Full-employment output is the level of output that firms supply when wages and prices in the economy have fully adjusted; in the classical model of the labor market, this occurs when the labor market is in equilibrium.

As a result, the production processes tend to be highly labor intensive, using a lot of workers relative to the amount of machinery. By contrast, garment manufacture in richer countries where labor is much more expensive tends to use methods of production that require fewer people and more machines.

When we talk about the cost function of a firm, therefore, we are assuming that it gives us the lowest cost for producing each given level of output. The production function tells us what a firm needs in terms of inputs—in this case, labor—to produce a given level of output. The more output a firm wants to produce, the more labor it will hire and the more jobs it will create.

The cost function tells us the cost of producing different levels of output, and the marginal cost function tells us the cost of producing additional output. Marginal cost is the critical ingredient in the next decision made by managers, which is selecting a point on the demand curve. We can think of managers as either choosing the price and then selling the quantity demanded at that price or choosing the level of output and selling it at the price that the market will bear.

In either case, they are picking the point on the demand curve whereThis decision of the firm is also covered in detail in Chapter 7 "Where Do Prices Come From? We show this decision graphically in Figure 9. In our discussion of costs to this point, we have not specified whether we were talking about the nominal wage that is, measured in dollars or the real wage that is, adjusted for inflation. The most important thing is being consistent. If we use the nominal wage when calculating our cost functions, then we end up with nominal costs.

If we use the real wage, then we end up with real costs. And when we equate marginal revenue and marginal cost, we must be sure that we measure in nominal terms or real terms not a mixture.

The distinction becomes important only when the general price level changes, so it is not central to our discussion here. When the price level is constant, we can always just suppose that it is equal to 1, in which case the nominal wage and the real wage are equal. Still, when we draw diagrams of the labor market, we typically put the real wage on the axis, so from here on we will explicitly suppose that we are measuring everything in real terms.

We can now explain labor demand by a firm. There are two steps: As in Figure 9. We already know that the marginal cost of production depends on the real wage: As the real wage decreases, the marginal cost of an additional unit of output decreases, so a firm will choose to produce more output.

The price will decrease because the firm must lower the price to sell the additional output. Because a firm wants to produce more output, it will demand more hours of labor. In other words, a decrease in wages leads to an increase in the quantity of labor demanded. The resulting inverse relationship between the real wage and the amount of labor demanded is shown in Figure 9. The labor demand curve for a single firm is downward sloping. This is true for every firm in the labor market.

The market demand curve for labor is obtained by adding together the demand curves of individual firms. So the market demand for labor is downward sloping as well. Changes in Employment We can now connect our understanding of the labor market with the data on net job creation that we showed in Figure 9. Based on what we have learned, there are three main reasons why jobs might be created or destroyed: Changes in the Real Wage Changes in the cost of labor are one reason firms create or destroy jobs.

Decreases in the real wage lead firms to produce more output and hire more workers, thus creating jobs. Increases in the real wage cause firms to produce less output and lay off workers.