>	Econ 100b Created 4/30/1996 Go to Brad De Long's Home Page

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Lecture Twenty Five

Long Run Growth I
(Economics 100b; Spring 1996)

Professor of Economics J. Bradford DeLong
601 Evans, University of California at Berkeley
Berkeley, CA 94720
(510) 643-4027 phone (510) 642-6615 fax
delong@econ.berkeley.edu
http://www.j-bradford-delong.net

April 1, 1996

• It would not be a mistake to say, roughly, that we today are at least 4.5 times as well-off as our predecessors who lived in the U.S. in 1890. In fact, the factor of 4.5 is almost surely an underestimate. We can today purchase or use a much broader range of goods and services than people could in 1890, real GDP measures take no account of the extra welfare produced by an enhanced range of choice among different types of commodities. The work year has also dropped from perhaps 2400 hours a year on average then to perhaps 1800 hours a year on average now.
• Make your guesses as to how much the expanded range of capabilities and powers produced over the past century--as opposed to increased quantities of things we knew how to make a century ago--has contributed to your welfare, and adjust for the declining workweek, and come up with estimates that range from my favorite of 10 to as high as 30 for the multiplication of the average productivity of the American worker over the past century.

Now let's look at the production function:

Let's think of a hypothetical economy in which there are just two kinds of resources used in production--capital (think of it as something like machine tools or assembly lines; large pieces of shaped metal out of which come final products), and the labor of those who tend the machines. Let's write capital K for the capital stock, and L for the inputs of labor-power into the production process. And let's suppose that the economy's "production function" is more-or-less as follows:


What's the content of this assumption?

• Diminishing returns to labor, holding capital fixed
• Diminishing returns to capital, holding labor fixed
• Constant returns to scale

We are going to use particular production functions that have simple mathematical expressions because they are simple to write down, allow us to do a number of experiments and consider a number of cases quickly, and make up a powerful shorthand.

But always remember that the map is not the territory...

A few more words about constant returns to scale...

(1) Y = F(K, L)

(2) Y/L = F(K/L, L/L) = F(K/L, 1)

(3) y = F(k, 1) = f(k)

Properties of f(k); diminishing marginal product of capital.

(4) Y = yL = f(k)L

Approximate international standards of living, 1990:

GDP per capita (1990 prices):

U.S. $22,000
Japan $18,000
Germany $17,000
Mexico $6,000
Brazil $5,000
India $1,300
Nigeria $900

How fast does the economy approach its steady state? Look at the gap between sf(k) and dk:

Suppose that:

• the marginal product of capital at k* is 10% per year
• the savings rate s is 30%
• the depreciation rate d is 6% per year

Then if k = k*-1; depreciation will be lower than at k* by .06 units per year; y will be lower than at k* by .1 units per year, and so sy will be lower than at k* by .03 units per year

• So the annual rate of change of k will be roughly .06 - .03 = .03 units per year--meaning that the economy will close 1/33 of the gap to the steady state in every year. Meaning it will take a very long time to get there...