Unit 8: Household Supply

Theory of Labour Supply

The theory of labour supply examines how households decide the number of hours to work, balancing income and leisure. This decision is influenced by wage rates, preferences, and opportunity costs.

• Budget Line: Represents all combinations of leisure and income a household can achieve, given wage rates and non-labour income.

• Opportunity Cost of Leisure: The wage rate is the opportunity cost of leisure, as each hour not worked is an hour of foregone earnings.

• Budget Constraint Equation: , where is consumption, is wage rate, is hours worked, and is asset income.

• Indifference Curves: Show combinations of leisure and income that yield the same utility. The slope of the indifference curve reflects the marginal rate of substitution (MRS) between leisure and income.

• Utility Function Example: , where is leisure and is consumption.

Example: If a worker has 24 hours in a day, a wage of C = 1 imes (24 - L) + 16$.

Comparing Employment Alternatives

Households may face different employment options, each with distinct wage rates and asset incomes. The optimal choice depends on the budget constraint and preferences.

• Budget Line Comparison: For each alternative, plot the budget line and indifference curves to determine optimal labour supply.

• Reservation Wage: The minimum wage at which a household is willing to supply labour, found where the budget line is tangent to the highest attainable indifference curve.

Example: Comparing a job with and to a job with and .

Income and Substitution Effects of a Wage Change

When the wage rate changes, two effects influence labour supply: the income effect and the substitution effect.

• Income Effect: Higher wages increase income, allowing more leisure if leisure is a normal good.

• Substitution Effect: Higher wages make leisure more expensive, encouraging more work and less leisure.

• Compensated Budget Line: Used to isolate the substitution effect by adjusting income so utility remains constant after a wage change.

Example: If wage increases from $1.25 to $2.00 per hour, the budget line rotates outward. The maximum amount of leisure is determined by the intersection with the leisure axis.

The Labour Supply Curve

The labour supply curve shows the relationship between wage rates and the quantity of labour supplied by households.

• Upward Sloping Segment: At low wages, the substitution effect dominates, so higher wages increase labour supply.

• Backward-Bending Segment: At high wages, the income effect may dominate, so higher wages reduce labour supply.

• Reservation Wage Calculation: The wage at which a household is indifferent between working and not working.

Example: For and , draw the supply curve and compute the reservation wage.

Households as Savers in Capital Markets

Households also decide how much to save and invest in capital markets, balancing current and future consumption.

• Intertemporal Budget Constraint: Shows trade-offs between present and future consumption, given interest rates.

• Utility Function Example: , where is current consumption and is future consumption.

• Optimal Saving Decision: Determined by the point where the highest indifference curve is tangent to the budget line.

Example: If the interest rate is 20%, plot the budget line and indifference curves to find optimal savings.

Applications and Practice Problems

Labour Supply and Utility Maximization

• Budget Line and Indifference Curve Diagrams: Used to illustrate optimal choices for various wage rates and asset incomes.

• Marginal Rate of Substitution (MRS): The rate at which a consumer is willing to trade leisure for income, given by the slope of the indifference curve.

• Effects of Asset Income Changes: Increasing asset income shifts the budget line upward, allowing more leisure and consumption.

Summary Table: Effects of Wage and Asset Income Changes

Key Terms and Definitions

• Budget Line: Shows all possible combinations of leisure and income for a given wage and asset income.

• Indifference Curve: Represents combinations of leisure and income yielding the same utility.

• Marginal Rate of Substitution (MRS): The rate at which a consumer is willing to substitute leisure for income.

• Reservation Wage: The lowest wage at which a household is willing to supply labour.

• Income Effect: Change in labour supply due to a change in income.

• Substitution Effect: Change in labour supply due to a change in the relative price of leisure.

Formulas and Equations

• Budget Constraint:

• Utility Function (Leisure and Consumption):

• Intertemporal Budget Constraint:

• Marginal Rate of Substitution:

Additional info:

• Some diagrams and tables referenced in the questions are not shown here but can be constructed using the equations and concepts above.

• Applications and tutorial questions provide practice in drawing budget lines, indifference curves, and analyzing changes in wages and asset income.