An increase in total factor productivity involves a better technology for converting factor inputs into aggregate output. As we see in this section, increases in total factor productivity increase consumption and aggregate output, but there is an ambiguous effect on employment. This ambiguity is the result of opposing income and substitution effects on labor supply. While an increase in government spending essentially produces only an income effect on consumer behavior, an increase in total factor productivity generates both an income effect and a substitution effect.
Suppose that total factor productivity z increases. As mentioned previously, the interpretation of an increase in z is as a technological innovation (a new invention or an advance in management techniques), a spell of good weather, a relaxation in
government regulations, or a decrease in the price of energy. The interpretation of the increase in z and the resulting effects depend on what we take one period in the model to represent relative to time in the real world. One period could be many years—
in which case, we interpret the results from the model as capturing what happens over the long run—or one period could be a month, a quarter, or a year—in which case, we are studying short-run effects. After we examine what the model tells us, we provide interpretations in terms of the short-run and long-run economic implications.
In general, the short run in macroeconomics typically refers to effects that occur within a year’s time, whereas the long run refers to effects occurring beyond a year’s time.
However, what is taken to be the boundary between the short run and the long run can vary considerably in different contexts.
The effect of an increase in z is to shift the production function up, as in Figure 5.8.
An increase in z not only permits more output to be produced given the quantity of labor input, but it also increases the marginal product of labor for each quantity of labor input; that is, the slope of the production function increases for each N. In Figure 5.8, z increases from z1to z2. We can show exactly the same shift in the production function as a shift outward in the PPF in Figure 5.9 from AB to AD. Here, more consumption is attainable given the better technology, for any quantity of leisure consumed. Further, the trade-off between consumption and leisure has improved, in that the new PPF is steeper for any given quantity of leisure. That is, because MPNincreases and the slope of the PPF is-MPN, the PPF is steeper when z increases.
Figure 5.8 Increase in Total Factor Productivity
An increase in total factor productivity shifts the production function up and increases the marginal product of labor for each quantity of the labor input.
(0,0)
Labor Input, N z2F(K, N)
z1F(K, N)
Ouput, Y
Figure 5.9 Competitive Equilibrium Effects of an Increase in Total Factor Productivity
An increase in total factor productivity shifts the PPF from AB to AD. The competitive equilibrium changes from F to H as a result. Output and consumption increase, the real wage increases, and leisure may rise or fall. Because employment is N= h - l, employment may rise or fall.
h (0,0)
–G
Leisure, l I1
I2 H
F B
D
A l1
C1
z2F(K, h – l ) – G
z1F(K, h – l ) – G C2
Consumption, C
Figure 5.9 allows us to determine all the equilibrium effects of an increase in z.
Here, indifference curve I1is tangent to the initial PPF at point F. After the shift in the PPF, the economy is at a point such as H, where there is a tangency between the new PPF and indifference curve I2. What must be the case is that consumption increases in moving from F to H, in this case increasing from C1to C2. Leisure, however, may increase or decrease, and here we have shown the case where it remains the same at l1. Because Y= C+G in equilibrium and because G remains constant and C increases, there is an increase in aggregate output, and because N= h - l, employment is unchanged (but employment could have increased or decreased). The equilibrium real wage is minus the slope of the PPF at point H (i.e., w= MPN). When we separate the income and substitution effects of the increase in z, in the next stage of our analysis, we show that the real wage must increase in equilibrium. In Figure 5.9, the PPF clearly is steeper at H than at F, so that the real wage is higher in equilibrium, but we show how this must be true in general, even when the quantities of leisure and employment change.
To see why consumption has to increase and why the change in leisure is ambigu-ous, we separate the shift in the PPF into an income effect and a substitution effect. In Figure 5.10, PPF1is the original PPF, and it shifts to PPF2when z increases from z1to
Figure 5.10 Income and Substitution Effects of an Increase in Total Factor Productivity
Here, the effects of an increase in total factor productivity are separated into substitution and income effects. The increase in total factor productivity involves a shift from PPF1to PPF2. The curve PPF3is an artificial PPF, and it is PPF2
with the income effect of the increase in z taken out. The substitution effect is the movement from A to D, and the income effect is the movement from D to B.
h (0,0)
–G
Leisure, l I1
I2
l1
C1 C2
PPF2
PPF3
A D
B
PPF1
Consumption, C
z2. The initial equilibrium is at point A, and the final equilibrium is at point B after z increases. The equation for PPF2is given by
C= z2F(K, h- l) - G.
Now consider constructing an artificial PPF, called PPF3, which is obtained by shifting PPF2downward by a constant amount. That is, the equation for PPF3is given by
C= z2F(K, h- l) - G - C0.
Here C0is a constant that is large enough so that PPF3is just tangent to the initial indif-ference curve I1. What we are doing here is taking consumption (i.e., “income”) away from the representative consumer to obtain the pure substitution effect of an increase in z. In Figure 5.10 the substitution effect is then the movement from A to D, and the income effect is the movement from D to B. Much the same as when we considered income and substitution effects for a consumer facing an increase in his or her wage rate, here the substitution effect is for consumption to increase and leisure to decrease, so that hours worked increase. Also, the income effect is for both consumption and
leisure to increase. As before, consumption must increase as both goods are normal, but leisure may increase or decrease because of opposing income and substitution effects.
Why must the real wage increase in moving from A to B, even if the quantities of leisure and employment rise or fall? First, the substitution effect involves an increase in MRSl,C (the indifference curve gets steeper) in moving along the indifference curve from A to D. Second, because PPF2is just PPF3shifted up by a fixed amount, the slope of PPF2 is the same as the slope of PPF3 for each quantity of leisure. As the quantity of leisure is higher at point B than at point D, the PPF is steeper at B than at D, and so MRSl,Calso increases in moving from D to B. Thus, the real wage, which is equal to the marginal rate of substitution in equilibrium, must be higher in equilibrium when z is higher.
The increase in total factor productivity causes an increase in the marginal productivity of labor, which increases the demand for labor by firms, driving up the real wage. Workers now have more income given the number of hours worked, and they spend the increased income on consumption goods. Because there are offsetting income and substitution effects on the quantity of labor supplied, however, hours worked may increase or decrease. An important feature of the increase in total fac-tor productivity is that the welfare of the representative consumer must increase. That is, the representative consumer must consume on a higher indifference curve when z increases. Therefore, increases in total factor productivity unambiguously increase the aggregate standard of living.
Interpretation of the Model’s Predictions
Figure 5.9 tells a story about the long-term economic effects of long-run improve-ments in technology, such as those that have occurred in the United States since World War II. There have been many important technological innovations since World War II, particularly in electronics and information technology. Also, some key observations from post–World War II U.S. data are that aggregate output has increased steadily, consumption has increased, the real wage has increased, and hours worked per employed person has remained roughly constant. Figure 5.9 matches these observations in that it predicts that a technological advance leads to increased output, increased consumption, a higher real wage, and ambiguous effects on hours worked. Thus, if income and substitution effects roughly cancel over the long run, then the model is consistent with the fact that hours worked per person have remained roughly constant over the post–World War II period in the United States. There may have been many other factors in addition to technological change affecting output, consumption, the real wage, and hours worked over this period in U.S. history. Our model, however, tells us that empirical observations for this period are consistent with technological innovations having been an important contributing factor to changes in these key macroeconomic variables.
A second interpretation of Figure 5.9 is in terms of short-run aggregate fluctua-tions in macroeconomic variables. Could fluctuafluctua-tions in total factor productivity be an important cause of business cycles? Recall from Chapter 3 that three key busi-ness cycle facts are that consumption is procyclical, employment is procyclical, and the real wage is procyclical. From Figure 5.9, our model predicts that, in response to an increase in z, aggregate output increases, consumption increases, employment may increase or decrease, and the real wage increases. Therefore, the model is consistent
with procyclical consumption and real wages, as consumption and the real wage always move in the same direction as output when z changes. Employment, however, may be procyclical or countercyclical, depending on the strength of opposing income and substitution effects. For the model to be consistent with the data requires that the sub-stitution effect dominate the income effect, so that the consumer wants to increase labor supply in response to an increase in the market real wage. Thus, it is certainly possible that total factor productivity shocks could be a primary cause of business cycles, but to be consistent with the data requires that workers increase and decrease labor supply in response to increases and decreases in total factor productivity over the business cycle.
Some macroeconomists, the advocates of real business cycle theory, view total factor productivity shocks as the most important cause of business cycles. This view may seem to be contradicted by the long-run evidence that the income and substi-tution effects on labor supply of real wage increases appear to roughly cancel in the post–World War II period. Real business cycle theorists, however, argue that much of the short-run variation in labor supply is the result of intertemporal substitution of labor, which is the substitution of labor over time in response to real wage movements.
For example, a worker may choose to work harder in the present if he or she views his or her wage as being temporarily high, while planning to take more vacation in the future. The worker basically “makes hay while the sun shines.” In this way, even though income and substitution effects may cancel in the long run, in the short run the substitution effect of an increase in the real wage could outweigh the income effect.
We explore intertemporal substitution further in Chapters 9–14.