After taking Boal's section of Econ 173, students will be able to do the following.

Part 1: Mathematical Tools

A. Introduction

B. Review of basic calculus

- Find formulas for derivatives of functions using power rule, rules for logarithms and exponential functions, product rule, quotient rule, and chain rule.

- Use numerical derivatives to approximate the effect of a change in the independent variable on the dependent variable.

- Find formulas for elasticities of functions.

- Use numerical elasticities to approximate the effect of a percent change in the independent variable on the dependent variable.

- Use first-order necessary condition to find maximum or minimum of a function.

C. Introduction to multivariate calculus

- Find formulas for partial derivatives of functions of several variables.

- Use numerical derivatives to approximate the effect of changes in the independent variables on the dependent variable.

- Apply approximation rules for finding percent changes in products or ratios.

- Find formulas for partial elasticities of functions of several variables.

- Use numerical elasticities to approximate the effect of a percent changes in the independent variables on the dependent variable.

- Find formulas for marginal rates of substitution from functions of two variables.

Part 2: Consumers and Demand

A. Preferences and utility

Given a simple function of the Cobb-Douglas, Stone-Geary, or CES type,

- Find formulas for the marginal utilities.

- Determine whether a utility function satisfies the axiom of monotonicity.

- Find a formula for the marginal rate of substitution in consumption.

- Determine whether a utility function satisfies the axiom of diminishing marginal rates of substitution in consumption.

B. Budgets and choice

- Derive an equation for the budget constraint, given prices and income.

- Describe how the budget constraint changes when prices or income change.

Given a simple function of the Cobb-Douglas, Stone-Geary, or CES type,

- Compute the utility-maximizing bundle, given prices and income.

C. Individual demand functions

- Derive the demand function implied by a simple utility function.

- Determine whether a proposed demand function is homogeneous of degree zero in income and prices.

- Determine whether a proposed demand system satisfies the budget constraint.

D. Income and substitution effects

- Identify income and substitution effects of a price change from an indifference-curve graph.

- Compute the income effect of a price change, given numerical values for the partial derivative of a demand function.

E. Measuring consumer welfare

- Compute changes in consumer surplus caused by changes in prices, for a linear demand function.

- Contrast the simple cost savings, the compensating variation, and the increase in consumer surplus from a price reduction.

- Compute Laspeyres, Paasche, and Fisher indexes of the cost of living.

F. Market demand and elasticity

- Derive a formula for elasticity from a demand function.

- Recognize a constant-elasticity demand function by its form.

- Use price elasticities to compute changes in quantity demanded and revenue (spending).

- Use income elasticities to compute changes in budget shares.

Part 3: Firms and Competition

A. Production

- Find formulas for the marginal products.

- Determine whether a production function is subject to diminishing returns to individual inputs.

- Find a formula for the marginal rate of substitution in production (also called the "rate of technical subsitution").

- Determine whether a utility function satisfies the axiom of diminishing marginal rates of substitution in production.

- Given a verbal description of a fixed-proportions technology, find a mathematical formula for its production function.

- Determine whether a production function is characterized by increasing or decreasing returns to scale.

- Given output elasticities of labor and capital, and percent increases in labor, capital and output, compute the Solow residual measure of technical change.

B. Cost

- Compute the cost-minimizing input combination for a simple production function.

- Derive marginal and average cost functions from a (long-run total cost function.

- Compute the "efficient scale" of output by minimizing the average cost function.

- Given a verbal description of a fixed-proportions technology, find a mathematical formula for its cost function.

- Given a short-run variable cost function and fixed cost, derive short-run marginal cost, average variable cost, average fixed cost, and average total cost.

C. Profit maximization and supply

- Derive the firm's supply function from a short-run or long-run cost function.

- Given graphs of short-run average variable cost and average total cost, find the breakeven price and the shutdown price.

- Given a short-run variable cost function and fixed cost, find the profit-maximizing (or loss-minimizing) quantity of output.

D. Welfare analysis

- Identify Pareto improvements and potential Pareto improvements in simple examples.

- Compute changes in producer surplus caused by changes in prices, for a linear demand function.

Given linear equations for supply and demand,

- Compute the changes in consumer and producer surplus and the deadweight loss from a price ceiling or price floor.

- Compute the changes in consumer and producer surplus and the deadweight loss from a tax or subsidy.

- Compute the changes in consumer and producer surplus and the gain in social welfare from international trade.

Part 4: General equilibrium and market power

A. General Equilibrium

- Identify Pareto efficient points on a graph of a contract curve.

- Determine whether a two-good, two-person allocation is efficient, given utility functions of the two persons.

B. Monopoly

- Compute the profit-maximizing monopoly price and quantity, and calculate deadweight loss, given a linear demand curve and constant marginal cost.

- Compute the profit-maximizing monopoly price and quantity, given a constant-elasticity demand curve and constant marginal cost.

- Compute optimal prices for a price-discriminating monopolist, given market-segment elasticities and constant marginal cost.

C. Collusion, Cournot oligopoly, and monopolistic competition

- Compute equilibrium quantities and market price for a Cournot duopoly, given linear demand and constant marginal costs.

- Compute the equilibrium market price for a symmetric Cournot oligopoly, given marginal cost, demand elasticity, and the number of firms.

D. Introduction to game theory

- Find the dominant-strategy equilibrium for a simple two-player game in normal form.

- Find the Nash equilibrium in pure strategies for a simple two-player game in normal form.

Part 5: Further Topics

A. Externalities and public goods

- Compute deadweight social loss from externalities given linear demand, supply, and marginal external cost functions.

- Compute the optimal Pigou tax, given linear demand, supply, and marginal external cost functions.

- Compute the optimal Pigou subsidy, given linear demand, supply, and marginal external benefit functions.

B. Uncertainty and information*

- Compute expected income given the amount and probability of loss.

- Compute expected utility given a utility-of-wealth function and the amount and probability of loss.

- Compute the amount a consumer is willing to pay for insurance, given a utility-of-wealth function and the amount and probability of loss.

- Identify problems of adverse selection or moral hazard.

C. Input markets*

- Distinguish the elasticity of demand for labor at the firm level and at the industry level.

- Apply the Hicks-Marshall rules for input demand.

D. Labor supply*

- Compute a worker's utility-maximizing choice of hours of work, given the wage, nonlabor income, and a simple utility function of the Cobb-Douglas, Stone-Geary, or CES type.

- Identify income and substitution effects of a wage change from an indifference-curve graph.

- Compute a worker's reservation wage, given a simple utility function of the Cobb-Douglas, Stone-Geary, or CES type.

- Distinguish the elasticity of supply of labor at the worker level, at the industry level, and at the economy-wide level.

* These topics are always covered in the summer term, but are covered only as time permits in the regular term.

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