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Econ 100b

Created 4/30/1996
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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


Administration
Review: Pace of Long-Run Growth; The Production Function; International Income Differentials
Capital Accumulation
Changes in the Savings Rate



Administration

Schedule for rest of semester: hand it out; talk about it briefly

Review: Pace of Long-Run Growth; The Production Function; International Income Differentials

When we look at the figure below, what do we see? It has gone up a lot over the past century. In 1890, real GDP per worker (at 1995's prices) was only some $12,000 a year. Take what the average worker produced in 1890, bring it forward in time to 1995, and sell it--and you will get some $12,000 for it. By contrast, real GDP per worker crossed $50,000 a year sometime early in this decade, and continues to rise.



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?

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


Capital Accumulation:

(5) i = sy, where s is the savings rate. Per-worker rate of investment; back to a closed economy.

Depreciation rate d: a constant fraction of the capital stock.

(6) Change in capital stock: = sy - dk = sf(k) - dk

If sf(k) > dk, then the per-worker capital stock will be growing over time...

If sf(k) < dk, then the per-worker capital stock will be shrinking over time...

If sf(k) = dk, then the per-worker capital stock will be constant. k*

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

Suppose that:

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


Changes in the Savings Rate


Steady-state condition: 0 = sy* - dk*

Or: k*/y* = s/d

Suppose: f(k*) = k*a

Then: k*1-a = s/d

Or: k* = (s/d)SUP>(1/(1-a))

Boost s by one-tenth, say, and you find that you have boosted k* by roughly (1/(1-a)) tenths, and have boosted y* by roughly (a/(1-a)) tenths...


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Econ 100b

Created 4/30/1996
Go to
Brad De Long's Home Page


Professor of Economics J. Bradford DeLong, 601 Evans
University of California at Berkeley
Berkeley, CA 94720-3880
(510) 643-4027 phone (510) 642-6615 fax
delong@econ.berkeley.edu
http://www.j-bradford-delong.net/