Inter. Macro Exam 1: One-Period Model

Representative Consumer's Choice

-Chooses quantity to buy in competitive goods market, and quantity to sell in competitive labor market

-Chooses quantities that maximize utility subject to budget constraint, w/ given prices (P, w)

Consumer's Utility Function

-Quantifies satisfaction consumer receives from a certain bundle of consumption and leisure

-Allows consumer to "rank" his choices by assigning preference scores

Slope of the utility function, with respect to consumption or leisure, is the negative marginal utility of consumption/leisure

The additional utility received from one additional unit of consumption or leisure

Properties of consumer utility:

1) Strictly increasing in c and l (first derivatives are positive)

2) Diminishing marginal utility for c and l (second derivatives are negative)

Indifference Curves

-A set of all the (c,l) bundles that generate the same utility, so that consumer is "indifferent" between them

-The slope of an indifference curve is the negative marginal rate of substitution of leisure for consumption

The Budget Constraint

-Dictates what bundles are feasible given h, w, pi, t

Pc=(1-t)W(h-l) + PI

Pc + (1-t)Wl = (1-t)Wh + PI

Slope of the budget constraint is the negative effective real wage

-(1-t)W/P

The "opportunity cost" in consumption of an additional unit of leisure

Utility-maximizing bundle is where the highest possible indifference curve is tangent to the budget constraint-

-Here, the marginal rate of substitution is equal to the wage, so that the "market price" and "internal price" of leisure are equal

The Labor Supply Curve (for given after-tax wages) is backward-bending

At Lower Wages, a wage increase will increase labor supply

Increased wage compensates for disutility of decreased leisure

Substitution Effect>Income Effect

Wage elasticity of Labor is Positive

At Higher Wages, a wage increase will decrease labor supply

Increased wage compensates for disutility of decreased leisure

Income Effect>Substitution Effect

Wage elasticity of Labor is Negative

Frisch Elasticity measures how much labor supply would change if relative prices change while keeping income constant (substitution effect)

Frisch elasticity is higher for "less attached" populations who face a higher opportunity cost (married women, retirees, low-income people, etc.)

Wage, tax, and transfer policies influence Frisch elasticities, determining who shows up to work and how much

Representative Firm's Choice

-Chooses quantity of labor to purchase in competitive labor market based on the quantity sold in competitive goods market that would maximize profits , given k, z, w, P

Firm's Production Function

y = F(z, K, N)

Constant capital and total factor productivity

Determines how much output is produced based off of hours of labor

Properties of Production Function:

1) Positive but diminishing returns to capital and labor

2) Positive cross-partials

3) Returns to scale may be increasing, decreasing, or constant

The Cobb-Douglas Production Function, Constant Returns to Scale:

F(z,K,N) = zK^(alpha)N^(1-alpha)

Firm's Profits

PI = Py - WN + P(1-d)K,

s.t. y=F(z,K,N)

The firm maximizes its profits by choosing the amount of labor so that the marginal product of the last worker is equal to the real wage

Competitive Labor Equilibrium

-Both Firm and Consumer are optimizing and have reached optima

-Labor Supply = Labor Demand

Properties of Competitive Labor Market

1) Wage = Marginal Product of Labor

2) Wage adjusts flexibly so as to make 1 true and clear labor market