Arnold Kling  

Bryan's Question and Stagnation

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Bryan asked,

Suppose half of the sectors of the economy grow forever at 4%, while the rest completely stagnate. I'm strongly tempted to say that this economy's growth rate equals 2% forever. Anyone tempted to disagree? If so, why?

He received multiple answers, and I can see why. I think that the answer depends on the behavior of demand.

Suppose we think of 100 units of labor producing goods, and 100 units of labor producing services. Initially, each unit of labor can produce one unit of output in each sector.

Next, let productivity growth in the goods sector be 4%, with 0% productivity growth in services. Now think about various configurations of demand.

Case 1: satiation in services. No matter what, people only want 100 units of services. In that case, the goods-producing sector gets to be a larger and larger share of the economy, so that the overall growth rate approaches 4 percent.

Case 2: satiation in goods. No matter what, people only want 100 units of goods. In that case, about 4 percent of labor will be re-allocated to services each year, and the overall growth rate will approach 0 percent.

Case 3: balanced demand. No matter what, people allocate half their incomes to goods and half to services. In that case, about 2 percent of labor will be re-allocated to services each year, and the overall growth rate will be about 2 percent. That is Bryan's answer.

I think that the real world lies somewhere between case 2 and case 3. That is, as Robert Fogel has pointed out, the income elasticity of the demand for goods is about one-half, and that for services is about one and one-half.

Arithmetically, this implies stagnation. The overall growth rate will slow, notwithstanding productivity gains in goods production.

However, I do not think that we are doomed to have low productivity growth forever in education and health care. I think that efficiency in both sectors is held back by cultural norms and government intervention.

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COMMENTS (2 to date)
Becky Hargrove writes:

Working with the problem as it was set up, I tended to initially agree with your assessment.

However, real world circumstances make answers less than clear. On the demand side: We need more goods in our youth, more services as we age, and more services overall in the course of our lives.

On the supply side: Labor produces a far greater degree of goods than services in monetary terms. The actual wealth creation from (institutional)services depends on the products/machines/tools that services transfer from production and derive rent from. With that rent, labor costs are paid.

I think the problem in all this is that we ultimately need more services than goods, whereas goods are more efficient in terms of money. Thus, wealth is distributed from goods production to make up for the efficiency lag in services. To what degree does that wealth transfer actually happen? That needs to be factored into the equation of growth in monetary terms.

JohnE writes:

One reason why there are so many different answers is because everyone is using different meanings of "4% growth of a sector". The way Bryan originally formulated the problem implied that he meant growth in terms of contribution to GDP. This formulation of the problem sweeps any price effects under the rug (whether caused by demand behavior or production technology). The problem becomes one of simple arithmetic, and the answer is that the economy grows at a rate that approaches 4%. Most people who emphatically insist on the 4% answer are probably thinking of growth in these terms.

Then in Bryan's second post, he seemed to imply that he instead meant that the sector in question grew 4% in terms of quantity produced. If that is the case, then there will be price effects and the growth of the economy will be any rate greater than zero (yes, it can theoretically exceed 4%). Anyone who makes a point estimate on the growth of the economy is implicitly assuming a specific price effect (i.e. they are making specific assumptions on marginal rates of substitution). (Note that this formulation of the problem ignores issues due to production technology. So we can think of the economy as an endowment economy.)

In this post, Arnold is making explicit his assumptions on demand behavior to make inferences on the growth rate of the economy, which is the right way to go. However, Arnold seems to be using a new meaning of growth, different from Bryan's two above. Namely he is thinking about growth in labor productivity. This means that our answer not only depends on the behavior of demand, as Arnold points out, but also on technology (i.e. the behavior of supply). So in Case 2 above, Arnold implicitly assumes something about production technology to get at his answer of 0% growth. Namely, he assumes that the marginal productivity of labor in the service sector is zero. In other words he assumes stagnation to reach the conclusion that the economy is stagnant! If the marginal productivity of labor is not zero, then in Case 2, the economy's growth will be positive. In fact it can exceed 4% if there are increasing returns to scale.

To sum up: 1) If we are going to be playing with thought experiments on economic growth, it is important to be clear about definitions of growth. 2) Any answer will depend on assumptions on demand behavior and production technology.

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