ECON102: Principles of Macroeconomics (2021.A.01)

Part I: Labor Demand

• In a competitive market, a firm can sell as much Y as it wants at the going
• price p, and can hire as much N as it wants at the going wage w.
• Facing w and p, a profit maximizing firm hires N to the point where
  $\text{MPN = w/p}$ (the benefit from an additional worker, in terms of additional output, must equal the cost of hiring him). <<This is straight from micro>>

• With Cobb-Douglas: $\text{MPN =.7 Y/N =.7 A (K/N).3}$
• If firms maximize profits: $\text{w/p =.7 Y/N =.7 A (K/N).3}$

The Labor Demand Curve

Notes on the Labor Demand Curve

• For the moment keep A and K constant.
  

• $N_{d}$ slopes downward: $N_{d} =\text{ MPN =.7 A * (K/N)}^{3}$
  

• $N_{d}$shifts up with $A$ and $K$ (complementarity)
  

• Caveat: Who says that there is a demand for more Y?
• Need to look at the demand side of economy (next lectures).
  

Part II: Labor Supply

• Labor Supply N_s Results from Individual Optimization Decisions
  

• Households compare benefits of working (additional lifetime resources) with cost of working (forgone leisure + effort)
  

• How much labor an household will choose to supply as the real wage (before taxes) wp varies?
  

• 2 effects:

1. Substitution effect: higher real wage means higher reward to working, hence you want to work more!
2. Income effect: higher real wage means you are richer, hence you need to work less to consume the same goods!

Refresh your memory from Micro!

• Think of an agent who gets utility from consuming apples and bananas
• From the utility maximization problem you get

$\text{MU(apples)/ MU(bananas) = P(apples)/P(bananas)}$

• If P(apples) increases:

1. Substitution effect: you want to increase MU(apples)/ MU(bananas). By the law of diminishing marginal utility you need to consume less apples and more bananas! You subsitute away from apples towards bananas
2. Income effect: you spend more for the apples that you buy, so you are poorer. You will consume less apples AND bananas!

From Micro to Macro

• The two goods that the household can consume are now consumption (C) and leisure (L)
  

• The household can spend 1 unit of time either working (N) or having fun (L), that is $\text{N + L = 1}$
  

• The budget constraint is $\text{WN = PC (and P(C)=P}$ for simplicity) with $\text{N=1-L}$. Then we can write a static version of the maximization problem as:

$\text{Max U(C,L)}$

$\text{s.t. W = PC + WL}$

• The price of leisure is the foregone wages, that is $P(L) = W$. Then

$\text{MU(L)/ MU(C) = W/ P}$

• If W/P increases:

1. Substitution effect: you want to increase $\text{MU(L)/ MU(C)}$. By the law of diminishing marginal utility you need to subsitute away from leisure towards consumption goods. Then you need to work more!
2. Income effect: you have higher wages, so you are richer. You will consume more C and L. To consume more L, you need to work less!

Back to the Labor Supply

• In reality the household problem is not static. Define $\text{PVLR = present value of life time resources}$, that determines the household income. life time resources, that determines the household income.
  

• For simplicity to graph the Labor Supply we separate income and substitution effects by separating PVLR from the current real wage w/p effects by separating PVLR from the current real wage w/p.
  

• PVLR represents the income effect and w/p the substitution effect.
  

• SHORTCUT: if w/p increases permanently PVLR increases as well, BUT if w/p increases temporarily only, then PVLR increases just a tiny bit so that we assume that $PVLR$ does not change!

The Labor Supply Curve

• Factors Affecting Labor Supply

• Labor Supply (N_s) shows the relationship between real wages and hours worked holding everything else constant (included (PVLR)!)

The Labor Supply Curve: Substitution Effect

The Labor Supply Curve: Income effect

$\text{PVLR → PVLR'(< PVLR) = income effect}!$

What affects the Labor Supply?

• The Real Wage - HOLDING PVLR fixed: A higher w/p encourages individuals to substitute away from leisure toward work (leisure becomes more expensive). This is a substitution effect.  <<This is why the labor supply curve slopes upwards>>
  

• Estimating this substitution effect is difficult since PVLR is not easily held constant. Estimates range from 0 - 2 (For a 1% increase in after-tax w/p holding PVLR fixed, labor supply either increases between 0% and 2%). Very Wide Range – little consensus.
  

• $\text{PVLR = initial wealth + present discounted value of earnings}$
  

• A higher PVLR induces individuals to work less (lower N_s ) for a given after-tax wage, allowing them to enjoy more leisure (If leisure is preferred to work – as I get richer, I can afford to work less). <<This is represented by a shift of the supply curve >>
  

• PVLR is net of taxes and non-work governmental transfers and inclusive of all other transfers.
  

• Marginal tax rate on labor income- Should have same substitution effect as the before tax real wage. Studies of the 1986 U.S. Tax Reform found that only high-earning married women worked more in response to lower marginal income tax rates. income tax rates.

• Marginal tax rate on consumption - see above

• Value of Leisure - If leisure/no-work becomes more/less attractive, households will work less/more (think about welfare programs, child care,…)

• Working Age Population: Usually defined as 16-64 (includes changes in Labor Force Participation Rates)

Recap on Labor Supply

• Substitution Effect:

• This is why Labor Supply Curve Slopes Upward

• Income Effect

• Evidence:

Part III: Labor Market Equilibrium

Temporary Increase in A

Permanent Increase in A

N* < N" → Here income effect is dominated!

Can Technological Progress destroy jobs?

Facts:     

A N w/p are trending up over time A, N, w/p are trending up over time.

N/pop is trending down (except in U.S. since 1980).

Higher A countries have higher w/p and lower N/pop.