Macroeconomic AnalysisEcon 6022

Level I

Lecture 3

Fall, 2011

1 / 41

Overview

• The Production Function• Labor Market

- The Demand for Labor- The Supply of Labor- Labor Market Equilibrium

2 / 41

The Production Function

• Roughly speaking, goods and services produced by theeconomy is GDP.

• How do we describe this production process?• It is rather complicated ...• Simplification: One goods economy!• Factors of production

- Capital (K)- Labor (N)- Others (raw materials, land, energy)- Productivity of factors depends on technology and

management

• Production function: relationship between input (productionfactors) and output

3 / 41

The Production Function

• The production function

Y = A · F (K ,N) (3.1)

- Parameter A is "total factor productivity" (the effectivenesswith which capital and labor are used)

- Variable N is labor input- Variable K is capital

• We define as capital the tools needed for production, i.e.,the physical objects that extend our ability or do work forus.

4 / 41

Five features of capital:

1. It is productive: it raises the amount of output that aworker can produce.

2. It is produced: Capital has itself been produced throughthe process of investment (private or public).

3. It is rival in its use: only a limited number of people canuse a given piece of capital at one time.

4. It yields a return: Since it makes a worker moreproductive, the worker or its firm will be willing to pay (theowner) to use it.

5. It wears out: Using capital causes it to wear down a little,which is called depreciation.

5 / 41

The properties of the Production Function

• Two general Properties- Slopes upward: more of any input produces more output- Slope becomes flatter as input rises: diminishing marginal

product as input increases• Show them graphically

- Graph production function- Output vs. one input- hold other input and A fixed

• Show them mathmatically

6 / 41

Figure 3.1 The Production Function Relating Output andCapital

7 / 41

Marginal Product of Capital

• Marginal product of capital, MPK = ∆Y/∆K

- Equal to slope of production function graph (Y vs. K)- MPK always positive- Diminishing marginal productivity of capital: MPK declines

as K rises

8 / 41

Figure 3.2 The marginal product of capital

9 / 41

Marginal Product of Labor

• Marginal product of labor, MPN = ∆Y/∆N

- Equal to slope of production function graph (Y vs. N)- MPN always positive- Diminishing marginal product of labor: MPN declines as L

rises

10 / 41

Figure 3.3 The production function relating output and labor

11 / 41

The Cobb-Douglas Production Function

• Cobb-Douglas production function is most often used inmacroeconomics.

Y = A · KαN1−α

• The relationship between input and output in industrialeconomies is described reasonably well by Cobb-Douglasproduction function.

• The key is to estimate the parameter α• Data show: α ≈ 0.3• We could also show theoretically that 0 < α < 1

12 / 41

Math Representation

• Actually, all the discussion on production function can besummarized with a few equations.

- Property 1: MPK =∂Y∂K

> 0; MPN =∂Y∂N

> 0

- Property 2:∂MPK∂K

< 0;∂MPN∂N

< 0

• Take Cobb-Douglas production function for example:- Property 1: MPK = A · α · Kα−1 · N1−α > 0

- Property 2:∂MPK∂K

= A · α · (α− 1) · Kα−2 · N1−α < 0

13 / 41

Constant Returns to Scale

• Additional property of production function• Def: If we multiply the quantities of each input by some

factor, the quantity of output will increase by the samefactor.

F (zK , zN) = zF (K ,N)

• Intuitively, it makes sense: double all the inputs ofproduction and output doubles

• That’s “the standard replication argument ” .

14 / 41

Constant Returns to Scale

• It is also useful and often used later on:• Transform production function in aggregate term to per

worker term

1N

Y =1N

F (K ,N) = F(

KN,NN

)= F

(KN,1

)...or defining k = K

N and y = YN , rewrite

1N

Y = F(

KN,1

)• Output per worker is a function only of capital per worker.

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

15 / 41

Supply shocks

• We have been discussing about K ,N, α and now we turnto the other element of the production function.

• Supply shocks: change in productivity parameter A

- Supply shock = productivity shock = a change in aneconomy’s production function

- Supply shocks affect the amount of output that can beproduced for a given amount of inputs

- Shocks may be positive (increasing output) or negative(decreasing output)

- Examples: weather, inventions and innovations,government regulations, oil prices

16 / 41

Supply shocks

• Show supply shocks graphically• Supply shocks shift graph of production function (Fig. 3.4)

• Negative (adverse) shock: Usually slope of productionfunction decreases at each level of input (for example, ifshock causes parameter A to decline)

• Positive shock: Usually slope of production functionincreases at each level of output (for example, if parameterA increases)

17 / 41

Figure 3.4 An adverse supply shock that lowers the MPN

18 / 41

Labor Market

• Discussion on labor market is closely linked withproduction function. We will see immediately.

• Market for labor v.s. market for ice cream.• Labor input is demanded by FIRMS.• Labor input is supplied by INDIVIDUALS.• Equilibrium wage clears the market.

19 / 41

The Demand for Labor

• How much labor do firms want to use? Assumptions- Hold capital stock fixed (short-run analysis)- Workers are all alike (simplification)- Labor market is competitive (taking price as given)- Firms maximize profits (optimization)

• A thought experiment: marginal benefit and cost of hiringan additional unit of labor (MPN and real wage)

• Analysis at the margin: costs and benefits of hiring oneextra worker (Fig. 3.5)

- If w > MPN, profit rises if number of workers declines- If w < MPN, profit rises if number of workers increases- Firms’ profits are highest when w = MPN

20 / 41

Figure 3.5 The determination of labor demand

21 / 41

The Demand for Labor

• The marginal product of labor and the labor demand curve

- Labor demand curve shows relationship between the realwage rate and the quantity of labor demanded

- It is the same as the MPN curve, since w = MPN atequilibrium

- So the labor demand curve is downward sloping; firms wantto hire less labor, the higher the real wage

22 / 41

The Demand for Labor

• Factors that shift the labor demand curve

- Note: A change in the wage causes a movement along thelabor demand curve, not a shift of the curve

- Supply shocks: Beneficial supply shock raises MPN, soshifts labor demand curve to the right; opposite for adversesupply shock

- Size of capital stock: Higher capital stock raises MPN, soshifts labor demand curve to the right; opposite for lowercapital stock

23 / 41

The Demand for Labor

• Aggregate labor demand

- Aggregate labor demand is the sum of all firms’ labordemand

- Same factors (supply shocks, size of capital stock) that shiftfirms’ labor demand cause shifts in aggregate labordemand

24 / 41

Figure 3.6 The effect of a beneficial supply shock on labordemand

25 / 41

The Supply of Labor

• Supply of labor is determined by individuals

- Aggregate supply of labor is the sum of individuals’ laborsupply

- Labor supply of individuals depends on labor-leisure choice- Total available time = working time + leisure time

26 / 41

The Supply of Labor

• The income-leisure trade-off

- Utility depends on consumption and leisure- U(c, l): c consumption and l leisure time- Price of leisure time relative to consumption good?- Real wage rate, w , and nominal real wage rate , W ,

- w =WP

27 / 41

Real wages and labor supply

• An increase in the real wage has offsetting income andsubstitution effects

- Substitution effect: Higher real wage encourages work,since the price of leisure time is higher

- Income effect: Higher real wage increases income for sameamount of work time, so person can afford more leisure, sowill supply less labor

28 / 41

The Supply of Labor

• A pure substitution effect: a one-day rise in the real wage- A temporary real wage increase has just a pure substitution

effect, since the effect on wealth is negligible• A pure income effect: winning the lottery

- Winning the lottery doesn’t have a substitution effect,because it doesn’t affect the reward for working

- But winning the lottery makes a person wealthier, so aperson will both consume more goods and take moreleisure; this is a pure income effect

29 / 41

The Supply of Labor

• A long-term increase in the real wage- The reward to working is greater: a substitution effect

toward more work- But with higher wage, a person doesn’t need to work as

much: an income effect toward less work- The longer the high wage is expected to last, the stronger

the income effect; thus labor supply will increase by less ordecrease by more than for a temporary reduction in the realwage

30 / 41

The Supply of Labor

• Empirical evidence on real wages and labor supply- Overall result: Labor supply increases with a temporary rise

in the real wage- Labor supply falls with a permanent increase in the real

wage

31 / 41

The Labor Supply Curve

• Increase in the current real wage should raise quantity oflabor supplied?

• YES, NO or It depends?• Labor supply curve relates quantity of labor supplied to

current real wage by holding other things equal (includingfuture wage rates).

• Labor supply curve slopes upward because higher currentwage encourages people to work more

• Future wage rate is a curve shifter.

32 / 41

Figure 3.7 The labor supply curve of an individual worker

33 / 41

The Supply of Labor

• Factors that shift the labor supply curve

- Wealth: Higher wealth reduces labor supply (shifts laborsupply curve to the left, as in Fig. 3.8)

- Expected future real wage: Higher expected future realwage is like an increase in wealth, so reduces labor supply(shifts labor supply curve to the left)

34 / 41

Figure 3.8 The effect on labor supply of an increase in wealth

35 / 41

Aggregate labor supply

• Aggregate labor supply rises when current real wage rises- Some people work more hours- Other people enter labor force- Result: Aggregate labor supply curve slopes upward

36 / 41

Factors increasing labor supply

• Decrease in wealth• Decrease in expected future real wage• Increase in working-age population (higher birth rate,

immigration)• Increase in labor force participation (increased female

labor participation, elimination of mandatory retirement)

37 / 41

Labor Market Equilibrium

• Labor market equilibrium: Labor supply equals labordemand

• Equilibrium wage, w• Equilibrium labor input, N• How does the labor market respond to shocks?

38 / 41

Figure 3.10 Labor market equilibrium

39 / 41

Figure 3.11 Effects of a temporary adverse supplyshock on the labor market

40 / 41

Labor Market Equilibrium

• Full-employment output• Full-employment output = potential output = level of output

when labor market is in equilibrium

Y = A · F (K , N) (3.4)

• affected by changes in full employment level or productionfunction (example: supply shock, Fig. 3.11)

41 / 41