Consumer Choice and Utility (Chapter 6)

Budget Constraint

The budget constraint represents all combinations of goods a consumer can purchase given their income and the prices of those goods.

• Intercepts: The intercepts of the budget constraint are found by dividing income by the price of each good. For good X: ; for good Y: .

• Changes: If income increases, the budget constraint shifts outward. If the price of a good changes, the slope and intercepts adjust accordingly.

• Slope: The slope of the budget constraint is , representing the rate at which the consumer can trade one good for another.

Utility and Marginal Utility

Utility is a measure of satisfaction or happiness a consumer derives from consuming goods and services.

• Marginal Utility (MU): The additional utility gained from consuming one more unit of a good.

• Law of Diminishing Marginal Utility: As more units of a good are consumed, the additional satisfaction from each extra unit decreases.

Household Objective Function

The main goal of the household is to maximize total utility given their budget constraint.

Utility Maximization Rule

Consumers allocate their income so that the last dollar spent on each good yields the same marginal utility per dollar.

• Rule:

• If , the consumer should buy more of X and less of Y.

Income and Substitution Effects

When the price of a good changes, two effects occur:

• Income Effect: The change in consumption resulting from a change in real income. For normal goods, consumption increases as income rises; for inferior goods, consumption decreases.

• Substitution Effect: The change in consumption resulting from a change in relative prices, holding utility constant. Consumers substitute towards the cheaper good.

Downward Sloping Demand Curve

Demand curves slope downward due to the substitution and income effects: as price falls, consumers buy more because the good is relatively cheaper and their real income increases.

Work-Leisure Model

This model analyzes the trade-off between leisure and labor (work).

• Optimum Bundle: The combination of leisure and consumption that maximizes utility, given the wage rate.

• Labor Supplied: Labor supplied is total available time minus leisure chosen.

• Wage Changes: A higher wage increases the opportunity cost of leisure, leading to substitution and income effects.

• Effects: Substitution effect encourages more work; income effect may encourage more leisure if leisure is a normal good.

Production and Costs (Chapters 7 & 8)

Accounting vs. Economic Costs

Accounting costs are explicit costs paid out, while economic costs include both explicit and implicit (opportunity) costs.

• Economic Profit:

• Positive economic profit: firm earns more than opportunity cost; zero economic profit: firm earns exactly opportunity cost; economic loss: firm earns less than opportunity cost.

• Firm's Objective: Maximize profit.

Short-Run vs. Long-Run

The short-run is a period in which at least one input is fixed; the long-run is when all inputs can be varied.

Total Product and Marginal Product of Labor (MPL)

Total product is the total output produced. Marginal product of labor (MPL) is the additional output from hiring one more worker.

• MPL Formula:

• MPL typically rises initially (due to specialization), then falls (due to the Law of Diminishing Returns).

• Law of Diminishing Returns: As more of a variable input is added to a fixed input, the marginal product eventually decreases.

Cost Concepts and Formulas

Firms face various costs in production:

• Total Variable Cost (TVC): Costs that vary with output.

• Total Fixed Cost (TFC): Costs that do not vary with output.

• Marginal Cost (MC): The cost of producing one more unit.

• Average Variable Cost (AVC):

• Average Fixed Cost (AFC):

• Average Total Cost (ATC):

• MC is related to MPL: (where W is wage).

• Law of Diminishing Returns causes MC to rise as MPL falls.

• MC intersects AVC and ATC at their minimum points.

• AFC declines as output increases; TFC is constant.

• The distance between ATC and AVC is AFC.

• Efficient Scale: Output level where ATC is minimized.

Objective of Firms

Firms aim to maximize profit, which is the difference between total revenue and total cost.

Perfect Competition Characteristics

Perfect competition is a market structure with:

• Many buyers and sellers

• Homogeneous products

• Free entry and exit

Market Price and Demand Curve for Firms

For perfectly competitive firms, the market price is given and acts as both their demand curve and marginal revenue (MR) curve.

• MR = P:

Profit Maximization

Firms maximize profit by producing where marginal cost equals marginal revenue.

• Rule:

• At this output, profit is maximized.

• Profit on a graph: If , firm earns profit; if , firm earns loss.

Short-Run and Long-Run Decisions (Chapter 9)

Shut-Down Decision

In the short-run, a firm should shut down if price is less than average variable cost.

• Shut-Down Point: Where

Supply Curves in Perfect Competition

The individual supply curve for a perfectly competitive firm is its MC curve above AVC.

• Market Supply Curve: Sum of individual supply curves.

• Relationship:

Long-Run Average Cost (LRAC) and Returns to Scale

The LRAC curve shows the lowest possible average cost for each output level when all inputs are variable.

• Firms move from one short-run ATC curve to another as they adjust inputs.

• Economies of Scale: LRAC decreases as output increases.

• Diseconomies of Scale: LRAC increases as output increases.

• Returns to Scale: Identified from LRAC graph; different from diminishing returns (which is a short-run concept).

• Minimum Efficient Scale (MES): Lowest output at which LRAC is minimized.

Long-Run Market Adjustments

Long-run decisions are based on economic profits:

• If firms earn above normal profit, new firms enter, supply increases, price falls.

• If firms earn below normal profit, firms exit, supply decreases, price rises.

• Long-run equilibrium: Firms earn zero economic profit, operate at MES.

Long-Run Supply Curve and Industry Types

The slope of the long-run supply curve depends on industry cost structure:

• Constant Cost Industry: LR supply curve is horizontal.

• Increasing Cost Industry: LR supply curve slopes upward.

• Decreasing Cost Industry: LR supply curve slopes downward.

• Slope determined by how input prices change as industry expands.

Summary Table: Cost Concepts and Relationships

Example: Utility Maximization

Suppose a consumer has P_X = 10P_Y = 20$, $MU_X = 30$, $MU_Y = 40\frac{MU_X}{P_X} = 3$, $\frac{MU_Y}{P_Y} = 2$. The consumer should buy more of X.

Example: Shut-Down Point

If a firm's AVC at minimum is $5, the firm should shut down in the short-run.

Example: Economies of Scale

A factory increases output from 100 to 200 units and average cost falls from $10 per unit, indicating economies of scale.