1. Physical Geography: Proximity Ecology Mineral and energy resource Geopolitical Relations: Conquest Imitation Threat Social institutions: Economic Political Cultural Technology: Science Belief systems Innovation and diffusion Demography: Age structure Mortality Morbidity Fertility Economic and Social outcomes: Economic growth Distribution of income This flowchart is an example of a model that shows how different variables that affect Economic Growth relate to each other.

2. To get a better understanding of how these variables relate to each other we will need to distinguish between mechanisms and contexts and institutions. In the rest of this lecture we will study one particular mechanism of economic growth more deeply. Mechanisms of Economic Growth accumulation of capital division of labor innovation resource exploitation and depletion (pseudo growth) income transfers (e.g..from rich to poor) (pseudo growth) Social, Physical, and Geopolitical Context and the effects on mechanisms of growth Kinds of Social Institutions Economic Political Cultural (norms, religious beliefs, governed by sanction) Scientific

3. Let us Consider these Mechanisms in More Detail 1. More “capital” per person Capital includes durable assets that contribute to production. Thus, capital includes land, machinery and factories. It also includes “human capital,” which are durable investments in people – such as education or on-the-job training, which increase their skills. 2. Increased specialization and division of labor Specialization allows individuals to become proficient at particular skills and then to trade their output with others. 3. Increased knowledge. By learning how to improve the varieties of seeds, farmers learned how to produce more food for any given inputs of water, soil, and fertilizer. Engineers learned how to tap coal, oil, wind, water, solar energy for power to replace human and animal power. 4. More rapid depletion of the environment (pseudo growth) Some measured GNP growth is simply the depletion of “natural capital.” Income may collapse as a result of over-exploitation of the physical environment. 5. Income transfers (pseudo growth) Exploitation of slaves increases the “income growth” of slaveholders. Colonial powers may increase their wealth by depleting the wealth of their colonies.

4. A simple model based on Capital Accumulation (mechanism #1). Quantities of the Economy. Y =output K = capital stock I =investment D = depreciation S = saving C =consumption A =level of technology

5. Fundamental Equations (1)Y = A K Production function. This tells us how much income may be produced from any given amount of capital. (2) Y = C + S Output equals Consumption plus Saving. This is an Identity; it is true by definition. (3) I = S Investment equals Saving (4) S = s Y Saving is a fixed fraction of Income. S is a stock, s is a flow. (5) D = d K Depreciation is a fixed fraction of capital (6) K(next year) = K(this year) + I (this year) - D (this year) This equation tells us how capital accumulates over time.

6. Working out what next year’s income is as a function of this year’s income. We begin with our equation (6) which tells us the relationship between this year’s Capital stock and next year’s capital stock. (1) K(next year) = K(this year) + I (this year) - D (this year) We then replace I with sY (since I=S=sY) (2) K(next year) = K (this year) + s Y (this year) - d K (this year) We may then multiply through by A (3) AK(next year) = AK (this year) + sA Y (this year) - d AK (this year) Recognizing that Y=AK we can write this as: (4) Y(next year) = Y(this year) + sAY(this year) - dY(this year) Finally, gathering terms together gives: (5) Y (next year) = (1 + s A - d ) Y (this year)

7. Writing this result in a more general manner We have found out how to write next year’s income as a function of this year’s income. Can we also write the income 5, 10 or 20 years from now as a function of this years income? It turns out that we can. We begin by taking our equation from the last slide: (1) Y (next year) = (1 + s A - d ) Y (this year) And we replace “this year” with t and “next year” with t+1 (2) Y (t+1) = (1 + s A - d) Y (t) If we then ask the question, what will income be in two years time we find: (3) Y (t + 2 ) = (1 + s A - d ) Y(t+1) = (1 + s A - d) 2 Y (t) And if we keep asking questions of this form, we find that income “n” years from now may be written: (4) Y (t + n ) = ( 1 + s A - d) n Y(t ) Hence the economy has geometric growth like what we saw in last Week’s lecture.

8. A NUMERICAL EXAMPLE s = 0.2 d = 0.05 A = 2 K(2001) = 1 This example generates the graphs that you see on the next two slides.