Econ 320 Lecture 09 PPTX

Capital Accumulation and Labor Demand

If the capitalists do not invest domestically due to political instability etc., the TPM would not shift up. SEE GRAPH PG 72

The Solow Model So Far

In the Solow model so far: -Worker productivity is held constant. -income per capita is constant in the steady state. Neither point is true in the real world: ‐‐Worker productivity rises frequently -1904‐2004: U.S. real GDP per person grew by a factor of 7.6, or 2% per year. Next: We will allow worker productivity to change.

Lewis Model and Stagnation

In this case, labor demand does not rise. The Lewis economy stagnates. SEE GRAPH PG 74 Lewis gives us an interesting model of development, but ... Lewis Economic Development Process is Not Guaranteed!

Answer to Problem

Per Worker Capital Stock and Per Workers Income: k* = (sA/(δ+n +g))^1/(1-a) y* = A^1/(1-a) (s/(δ+n +g))^a/(1-a) y*R / y*P = {[ 𝑠𝑅/δ+𝑛𝑅+𝑔]/ [ 𝑠𝑃/δ+𝑛𝑃+𝑔]}^α/(1-α) = {[ 0.32/0.05+0.01+0.02]/ [ 0.10/0.05+0.03+0.02]}^α/(1-α) = 4^α/(1-α) If α = 1/3, the expression becomes: 4^1/2 = 2 Richland is twice as rich as Poorland. If, in reality, Richland is 16 times as rich as Poorland, then = 4^α/(1-α) = 16 Which means: α/(1-α) = 2, or, α= 2/3 Capital has 2/3 weight. This may mean that human capital is more important or that technology biased toward human capital is more important.

Recall that production function looks like this (K is fixed here)

SEE GRAPH ON PPTX PG 60

A Graphical Intuitive Understanding

SEE GRAPH PG 10 Adding the labor productivity growth rate, g, shifts the (δ+ n) curve anti-clockwise. It may appear that the new steady state goes from A to C. But it really goes from A to B when we take productivity growth of labor into account

Roadblocks to the Lewis Development Process

What if the new investment is not labor-biased at all? What if investment takes place, but such investment is biased toward high tech capital? (See the next slide).

The newer equation of motion for k

With population growth, the equation of motion for k is ∆k = s f(k) − (δ + n + g) k s f(k) = ACTUAL INVESTMENT (δ + n + g) = BREAK EVEN INVESTMENT •But keep in mind that the values of y, k we get from this model, must be multiplied by the labor productivity index: h. •Also remember that h grows at g percent (Solow's assumption) •This new h = old h(1+g)^t

The Steady State Condition in the Solow Model

s/(δ+ n + g) = k/f(k) This is the final version of the Solow Steady State Condition

Solow Model Steady State Formulas - What is y*?

y* = A(k*)^a substituting y* = A(A0)^a/(1-a) = (A)^(1+(a/1-a))0^a/(1-a) OR y* = (A)^1/(1-a)0^a/(1-a) Given, s, n, δ, A and α, we can find steady state values of per capita GDP and per capita capital stock. Substituting for 0, the steady state value of per capita income y* becomes: y* = A^1/(1-a) (s/(δ+n +g))^a/(1-a) • This formula will be used in the following example.

More Capital = Workers More Productive

• Addition of new machines will make each worker more productive than before. • Because each worker becomes more productive, labor demand curve shifts out in the next period.

Dynamics of the Lewis Economy (2)

• As capitalists reinvest, they raise (shift up) the industrial demand curve continuously. SEE GRAPH PG 69 • After some time, the flat part of industrial labor supply curve will no longer be relevant. • The industrial sector labor demand curve will intersect the industrial sector labor supply curve at the upward sloping part of the industrial labor supply curve. See n or n'. • What happens in the rural sector at that time? • Rural sector no longer pays the institutionally fixed wage, it starts using the marginal productivity rule -it slowly but surely becomes more capitalistic!

Solow's Basic Results

• Basic Solow Model: -Late starters have higher growth rates (because f(k) increases at a decreasing rate). -Eventually, late starters will have growth rates similar to the growth rates of matured countries. -All countries will eventually stagnate unless technology comes to the rescue. -Higher savings rate in a late-start country will take the country closer to the income level of matured countries. -High savings rate will take a country to a higher level of GDP in the long run. But the savings rate itself does not affect GDP growth rate.

Solow Model General Steady State Formulas

• Consider the Cobb-Douglas production function: Y=AK^aL^1-a • Which can be re-written as y=Ak^a • Using the steady state condition we get: s/(δ+n +g ) = k/y Let s/(δ+n +g ) = 0 Thus 0=k/y • This gives us the steady state capital stock, k* (a "*" shows that it a steady state variable.) 0=k*/y* OR 0=k*/A(k*)^a OR A0=(k*)^1-a OR k* = (A0)^1/(1-a) OR if you substitute for 0 k* = ((sA)/(δ+n +g ))^1/(1-a)

Useful Info: Working with Percentages

• Examples: • If GDP grows at 5% and Population grows at 2%,per capita GDP grows approximately at (5-2)% =3%. • GDP will double approximately in 70/5 = 14 years. • Per Capita GDP will double approximately in 70/3= 23.3 years. • Now back to the Solow model.

The Nature of Productivity Growth

• First, note that each worker today is more efficient than a generic worker in 1750. • In 1750, farmers used rudimentary agricultural tools, they used inefficient machines and equipment. • One reason why workers today are more efficient than the workers in 1750 is because they have better education, better knowledge, better skills, they also work with different - more efficient - K. • One way to capture all this is to assume that each worker gets a productivity or human capital package called "h." If h is 1, then that's the baseline scenario - i.e., the productivity package of workers in 1750 had an index value of h = 1. • As time went on, h started rising. So a worker in, say, 1850 was 10 times as productive as a typical worker in 1750. • This means: • A worker in 1850 = (10)(worker in 1750) as far as his/her contribution to GDP was concerned. • The human capital index h will rise for various reasons: people get more skilled and educated, the underlying technology changes, the nature of capital changes, etc.

A Different Paradigm

• If other family members consistently help the rural street vendor, the model then will not follow the typical economics models. • In rational economics, wage = value of your marginal product. If your work adds 5 widgets to a factory's production, and widgets can be sold for $2/piece, then your wage is (5)(2) =$10 or less.

Socially Different Agricultural Sector

• If the extended family members share their incomes, the vendor's true wage is equal to whatever he earns selling his stuff plus the amount the family provides for his upkeep. • If he earns less one week, the family probably gives him more that week. • If he earns more one week, the family probably gives him less that week. • His subsistence wage is thus institutionally fixed. • How does the family provide for him? Where does the family get the extra resources? • If there are L workers in the extended family, all L workers pool their resources and divide their income equally. • Some of these workers have high marginal product, some have low marginal product -but in reality they share their total wage. • This may not be totally accurate, but something similar to wage sharing happens which ensures that everyone gets a minimum institutionally fixed wage. • What is the institutionally fixed wage? • Wage = Total product/L = average product of labor or, APL. • This is different from the modern, professional urban manufacturing sector where wage = value of marginal product.

The Capitalists Can Invest Their Income

• If they reinvest their income in new machines, what happens? SEE GRAPH PG 67

Solow Model: ConcludingComments

• In addition to A, K, L, s, δ, n, g, α, many other things influence economic growth. • Role of geography, social environment, political environment, corruption, and a host of other things must matter. • Solow model is a one-sector model -which may not be realistic. • Solow may have just scratched the surface of growth theory.

The Nature of Technological Progress

• Let's go back to the Cobb-Douglas Production Function: Y = A.K^αL^β • There are two ways of thinking of technological progress here: • If "A" rises, same values of K and L will increase Y. this is called a neutral technological progress.

Lewis Dual Economy Model (also Known as the Labor Surplus Model)

• Models of Economic Growth : Growth Models for Developing Countries. • 1954. "Economic Development with Unlimited Supplies of Labour." Manchester School 22 (May): 139-191. • 1955. The Theory of Economic Growth. London: Allen and Unwin.

Right Side of the Production Function

• Notice that to the right of c, total product does not rise. • This means that to the right of c, the marginal product is zero. • Average product (total product/labor) is still positive to the right of c. • The next slide shows this.

The Steady State

• Recall the definitions of k and y in this expanded version. They have no real life meanings, they are just algebraic variables. Let's try to understand the meaning of steady state in this context. • By definition, steady state is where, k and y do not change, i.e., they grow at 0%. • But since Y/L = h.y, and h grows at g%, Y/L, the real per capita income grows at g% at steady state. • Since Y = h.y.L, and L grows at n%, Y, the real income of a country grows at g% at steady state.

Poor People Have to Share

• Since marginal product of rural subsistence level workers is very low (may be even zero), Wage should be zero or close to zero. • Near zero wage means starvation and death. • So what does he do? • His poor siblings, parents and others must share food with him so that he does not die. • The the poor have to share • They share because they think about their mutual insurance. If the lucky (relatively) high- wage-earner loses his/her job tomorrow, he/she may need help from the extended family at that time. So the high-wage earner shares his wage. • So everybody tries to help everybody else in an extended family type setup.

Is the Solow Model Appropriate for Very Poor Countries?

• Solow model was a one-sector model. • Arthur Lewis proposed a two-sector model with characteristics of less developed countries. • Two sectors: agriculture and industry/manufacturing. • In the Lewis model, the traditional agriculture sector is socially different from the modern industrial sector. • There is disguised unemployment in the agricultural sector where food is shared. • Disguised Unemployment in agriculture has two similar connotations: (1) Zero Marginal Product : the last worker does not increase total product at all or, (2) The last worker adds very little (less than his wage) to total product.

The Romer Model

• The Romer model assumes that societies through R&D create knowledge and such knowledge benefits everyone in the society. • The knowledge variable enhances the K variable in the Cobb-Douglas production function. • So the Romer equation is: • Y = K^α L^1- α K^β where K^β is a knowledge enhancing component of Y. The equation can be written as: Y = K^α+ β L^1- α A curious feature of this model is that α+ β is not necessarily less than 1 and that exponents add up to more than 1. This violates the constant returns to scale assumption we mentioned earlier. We can now have a graph such as this: SEE GRAPH ON PPTX PG 47

The Economy Begins from Low Wages

• The equilibrium wage in the previous slide is k. • In this case, both agriculture and industry pay the institutionally fixed wage. • There is a lot of disguised unemployment in the agricultural sector e.g., there are people who really contribute nothing to agricultural production (their marginal product is zero).

Solow model with population growth and lab productivity growth

• The graphs are the same, except that δ is replaced with δ+ n + g. • Look at the next slide and confirm the following: • If s rises, s f(k) shifts out, and the steady state k and y rise. • If δ or n or g rises, (δ+ n + g) k shift up, y and k fall.

Human Capital in the Solow Model

• Thus a new variable: h = labor efficiency (human capital) is introduced directly in the Solow model. • Assume first that h increases exogenously: human capital progress is labor-augmenting: it increases labor efficiency at the exogenous rate g: • g = ∆h/h • We now write the production function as: • Y = F(K, hL) • where hL = the number of effective workers. • Interestingly, and counter-intuitively, increases in labor efficiency have the same effect on output as increases in the labor force. • Although you are one worker, you are effectively like h times the worker in 1750. • So if you produce 100 units, and your h is 10, it is as if each 1750 worker has produced 10 units each.

Steady State in the Expanded Solow Model

• Thus, formally, this expanded model is very similar to the original model we started with which had no population growth and no Productivity growth. • In that original model the steady state equation was: ∆k = sf(k) -δk = 0; • Or, s/δ= k/f(k) • The expanded model now becomes (the new steady state condition): s/(δ+ n + g) = k/f(k)

Richland-Poorland Example

• Two countries, Richland and Poorland, are described by the Solow growth model. They have the same Cobb-Douglas production function, F(K,L) = A K^αL^1−α, but with different quantities of capital and labor. Richland saves 32 percent of its income, while Poorland saves 10 percent. Richland has population growth of 1 percent per year, while Poorland has population growth of 3 percent. (The numbers in this problem are chosen to be approximately realistic descriptions of rich and poor nations.) Both nations have technological progress at a rate of 2 percent per year and depreciation at a rate of 5 percent per year. a. What is the per worker production function f(k)? b. Solve for the ratio of Richland's steady-state income per worker to Poorland's. c. If the Cobb-Douglas parameter α takes the conventional value of about 1/3, how much higher should income per worker be in Richland compared to Poorland? d. Income per worker in Richland is actually 16 times income per worker in Poorland. Can you explain this fact by changing the value of the parameter α? What must it be? e. Can you think of any way of justifying such a value for this parameter? How else might you explain the large difference in income between Richland and Poorland?

The Lewis Dual Economy Model

• Two sectors: -Sector 1: • Agricultural, rural, informal, traditional sector providing subsistence level wages and "bad"jobs. -Sector 2: • Manufacturing, urban, formal, modern sector providing above-subsistence level wages and "good" jobs.

Labor Supply in Industry

• Wages are not allowed to fall below an institutionally fixed level which is probably close to the subsistence level. • This is the situation in agriculture. • So how does the labor supply curve to industry look like? • No one works for the industry if industry offers a wage below the institutionally fixed wage in agriculture. • Wage rate in industry must not be less than the wage rate at h (next slide). SEE GRAPH PG 63 Demand for Labor in Industry • Demand curve for labor in industry is like any other labor demand curve. Capitalists are hard-nosed and rational. They don't share anything. SEE GRAPH PG 64

Some attempts to Model Technology: Romer and Others

• We did not say much about A. • If "A" rises continuously, there will be no steady state either! • Can "A" rise continuously? • Solow, Romer and others seem to have gone back to Adam Smith and are asking: • Can technology rescue us and break the curse of steady state? SEE GRAPHS ON PPTX PG 40, 41, 42, 43

Solow Model with Labor Productivity Growth

• We started with the basic Solow model without labor force growth, without technological growth. • We then added population growth. • We now add worker productivity growth.

Dynamics of the Lewis Economy

• What happens in the next period? • Recall that capitalists are the only ones making extra income. • Hopefully, they reinvest their income. • They use more machines in the next period. • As they use more machines, each worker becomes more productive.

Street Vendors in Poor Countries

• You see street vendors like this (next slide) in the villages of less developed countries. • Do they make enough money to support themselves? SEE PIC PG 52 • Look at what he is selling. • How much money does he make per day? • Is it enough to support himself? • Probably he makes one or two dollars worth of profit/day -not enough to support himself. • Other family members help him out. May be the parents help. May be the siblings help.

The Nature of Technological Progress (2)

•In the basic Solow model, per capita income grows at g% which is the rate of growth of h. •What determines h? •Note that the determination of "A" and the determination of "h" are similar problems: •Y = AK^α (hL)^1- α = A. (h)^1- α K^α (L)^1- α ≡ A*K^α L^1- α

How Does Technology/Labor Productivity Change?

•Is technology like a fish-pond (and have we already overfished?) •Is it multiplicative from the last period? •Is it exponential?

Labor Productivity: h

•What if each worker becomes more efficient over time? •Higher productivity: Each worker behaves as if the worker is doing h times the work of the previous worker. •In other words, h = index of human capital. It was implicitly h = 1 before. •Will consider this issue first.

Human Capital in the Solow Model GRAPH

∆k = s f(k) −(δ+n +g )k