ECO403 Highlighted Handouts Lectures 19-45 by Mr Shahbaz

Lesson 19 ECONOMIC GROWTH

PER CAPITA INCOME OF SELECTED COUNTRIES, 2004 (IN US $)

Norway 43,350 Saudi Arabia 8,530 Switzerland 39,880 Mexico 6,230 United States 37,610 Malaysia 3,780 Japan 34,510 Brazil 2,710 United Kingdom 28,350 Russia 2,610 Belgium 25,820 Egypt 1,390 Germany 25,250 China 1,100 France 24,770 Indonesia Australia 21,650 India Italy 21,560 Pakistan Kuwait 16,340 Bangladesh Korea 12,020 Nigeria

THE SOLOW GROWTH MODEL

Robert Solow won Nobel Prize for contributions to the study of economic growth. It is a major paradigm which is widely used in policy making and a benchmark against which most recent growth theories are compared. The Solow Growth Model is designed to show how growth in the capital stock, growth in the labor force, and advances in technology interact in an economy, and how they affect a nation’s total output of goods and services.

HOW SOLOW MODEL IS DIFFERENT: ASSUMPTIONS

K is no longer fixed: investment causes it to grow, depreciation causes it to shrink. L is no longer fixed: population growth causes it to grow. The consumption function is simpler. No G or T (only to simplify presentation; we can still do fiscal policy experiments) Cosmetic differences.

THE PRODUCTION FUNCTION

Let’s analyze the supply and demand for goods, and see how much output is produced at any given time and how this output is allocated among alternative uses. The production function represents the transformation of inputs (labor (L), capital (K), and production technology) into outputs (final goods and services for a certain time period).

In aggregate terms: Y = F (K, L) y = Y/L = output per worker k = K/L = capital per worker

Assume constant returns to scale: zY = F (zK, zL) for any z > 0 Pick z = 1/L. Then Y/L = F (K/L, 1) y = F (k, 1) y f (k)

Where f (k) = F (k, 1)

THE NATIONAL INCOME IDENTITY

Y = C + I (remember, no G) In “per worker” terms: y = c + i where c = C/L and i = I/L

THE CONSUMPTION FUNCTION

s = the saving rate, the fraction of income that is saved (s is an exogenous parameter). Note: s is the only lowercase variable that is not equal to its uppercase version divided by L. Consumption function: c = (1–s) y (per worker)

SAVING AND INVESTMENT

Saving (per worker) = sy National income identity is y = c + i Rearrange to get: i = y – c = sy (investment = saving) Using the results above, i = sy = sf (k)

OUTPUT, CONSUMPTION, AND INVESTMENT

Output per Worker, y

Worker, k f (k)

sf (k)

k1 y1

i1 c1

Output per

worker, y

worker, k

f(k)

Note: this production function exhibits diminishing MPK.

MPK =f(k +1) – f(k)

CAPITAL ACCUMULATION

Investment makes the capital stock bigger, depreciation makes it smaller. Change in capital stock= investment – depreciation k i k Since i = sf (k), this becomes: k = s f (k) – k

THE EQUATION OF MOTION FOR k

The equation of motion for k can be written as: k = s f (k) – k It is the Solow model’s central equation. It determines behavior of capital over time which, in turn, determines behavior of all of the other endogenous variables because they all depend on k. e.g. Income per person: y = f (k), Consumption per person: c = (1–s) f (k)

If investment is just enough to cover depreciation, [sf (k) = k], then capital per worker will remain constant: k = 0. This constant value, denoted k*, is called the steady state capital stock. worker, k k  = the rate of depreciation = the fraction of the capital stock that wears out each period

Worker, k sf (k) k

k*