Microeconomics Exam 1 Study Guide: Supply & Demand, Consumer Choice, and Production Theory

Exam Overview

Format and Structure

This exam covers foundational microeconomics concepts, focusing on supply and demand, consumer theory, and production/cost analysis. The exam consists of 18 multi-part questions, with an even distribution across the three main topic areas.

• Format: 18 questions (multi-part), online with proctored browser

• Tools: Calculator, blank scratch paper, written notes

• Content: Based on problem sets from chapters 2-7

• Topic Distribution: Supply/demand, consumer theory, production theory

Chapter Coverage & Focus Areas

Chapters 2-3: Supply and Demand

These chapters introduce the core model of market equilibrium, the distinction between shifts and movements, and the effects of taxes and subsidies.

• Key Concepts: Market equilibrium, shifts vs. movements, comparative statics

• Mathematical Skills: Solving for equilibrium price/quantity, calculating effects of taxes/subsidies

• Interactive Application: Forecasting Market Outcomes, Market Analysis Simulators

Chapter 4: Consumer Choice (Selective)

This chapter explores how consumers make choices to maximize utility, subject to budget constraints, using indifference curves and budget lines.

• Covered: Utility maximization, indifference curves, budget constraints

• Omitted: Compensating/equivalent variation, cost-of-living adjustments

• Mathematical Skills: MRS calculations, corner solutions, interior solutions

• Interactive Application: Consumer Choice Explorer, Calculus of Utility Maximization

Chapters 6-7: Production and Costs (Selective)

These chapters focus on how firms transform inputs into outputs, the cost structure of production, and the implications of returns to scale.

• Covered: Production functions, cost minimization, short-run vs. long-run costs

• Omitted: Productivity/technical change (Ch. 6), learning curves/multi-product costs (Ch. 7)

• Mathematical Skills: Marginal products, isoquants, returns to scale analysis

• Interactive Application: Short-Run Production and Cost Curves, Cost-Minimizing Input Mix

Core Mathematical Techniques to Master

Supply & Demand Mechanics

• Setting Equilibrium: Set $Q_d = Q_s$ to find equilibrium

• Linear Demand/Supply: $Q_d = a - bP$, $Q_s = c + dP$

• Tax Analysis: Consumer price $P_c$, producer price $P_p$, with $P_c = P_p + \text{tax}$

• Practice Strategy: Master the algebra first, then verify with graphs

Consumer Optimization via Tangency

• Key Insight: Optimal choice where indifference curve is tangent to budget line

• Tangency Condition: Slope of indifference curve = Slope of budget line

• Mathematical Setup: $\frac{MU_X}{MU_Y} = \frac{P_X}{P_Y}$ (slopes are equal)

• Two-Equation System:

  • $\frac{MU_X}{MU_Y} = \frac{P_X}{P_Y}$ (tangency condition)

  • $P_X Q_X + P_Y Q_Y = I$ (budget constraint)

Demand Curve Derivation

• Method: Fix $P_Y$ and $I$, vary $P_X$, trace out optimal $Q_X$ values

• Cobb-Douglas Demand: $Q_X = \alpha I / P_X$

• Perfect Substitutes: Corner solutions, kinked demand curves

• Income and Price Elasticities: Connect to utility function parameters

• Spending Shares: $\alpha I$ spent on $X$, $(1-\alpha)I$ spent on $Y$

Income & Substitution Effects (Graphical Method)

• Total Effect: Income Effect + Substitution Effect

• Graphical Decomposition:

  1. Original optimum at initial prices

  2. Change price, find new optimum (total effect)

  3. Separate into substitution and income components using intermediate budget line

• Signs: Substitution effect always opposes price change

• Practice Strategy: Master the three-step graphical decomposition

Production Theory and Cost Minimization

• Production Function: $Q = f(K, L)$, often $Q = K^{\alpha}L^{1-\alpha}$

• Marginal Product: $MPL = \partial Q / \partial L$, $MPK = \partial Q / \partial K$

• MRTS: $-MPL/MPK$ (slope of isoquant)

• Cost Minimization: $MPL/w = MPK/r$ (equal marginal product per dollar)

• Returns to Scale: How output changes if all inputs are increased proportionally

• Average vs. Marginal Cost: Relationship depends on whether $TC$ is increasing/decreasing

Corner Solutions vs. Interior Solutions

• Interior Test: Check if $MU_X/P_X = MU_Y/P_Y$ at positive consumption levels

• Corner Test: Compare $MU_X/P_X$ or $MU_Y/P_Y$ at boundary points ($Q_X=0$ or $Q_Y=0$)

• Perfect Substitutes: Often yield corner solutions unless prices are exactly right

• Recognition Pattern: If $MRS$ ≠ price ratio at interior point, check corners

Returns to Scale Analysis

• Mathematical Test: For $Q = f(K, L)$, check $f(tK, tL)$ vs. $tQ$

• Cobb-Douglas Rule: $Q = K^{\alpha}L^{\beta}$ has returns to scale = $\alpha + \beta$

  • $\alpha + \beta > 1$: Increasing returns to scale

  • $\alpha + \beta = 1$: Constant returns to scale

  • $\alpha + \beta < 1$: Decreasing returns to scale

• Cost Curve Implications: Returns to scale determine long-run average cost shape

Problem-Solving Strategies

For Supply & Demand Questions

1. Always start with a graph – even for algebraic problems

2. Identify the shift: Demand shifters vs. supply shifters

3. Predict direction first: Price up/down? Quantity up/down?

4. Then calculate: Use algebra to find exact values

5. Check reasonableness: Does your answer make economic sense?

For Consumer/Cost Questions

1. Identify the production function: Cobb-Douglas $Q = K^{\alpha}L^{\beta}$ is most common

2. Calculate marginal products: $MPL = \partial Q/\partial L$, $MPK = \partial Q/\partial K$

3. Check returns to scale: For Cobb-Douglas, sum the exponents ($\alpha + \beta$)

4. Apply cost minimization: Set $MPL/w = MPK/r$ for optimal input mix

5. Connect to cost curves: Use relationships between $TC$, $AC$, $MC$

6. Short-run vs. long-run: Remember which inputs are fixed vs. variable

Graphing Essentials

Must-Know Graph Types

• Supply & Demand: Market equilibrium, shifts, tax wedges

• Indifference Curves: Different shapes for different preferences

• Budget Lines: Slope = $-P_X/P_Y$, shifts with income changes

• Production Functions: Isoquants, expansion paths

• Cost Curves: U-shaped $AC/MC$, relationship between short-run and long-run

Common Graphing Mistakes to Avoid

• Confusing shifts with movements along curves

• Wrong direction for income/substitution effect arrows

• Forgetting that $MC$ passes through minimum of $AC$

Useful Appendices for Mathematical Review

• Appendix 4A: Utility and Indifference Curves – calculus approach

• Appendix 6C: Cobb-Douglas Production Functions – specific forms

• Appendix 7A: Minimum of the Average Cost Curve – proves why $MC = AC$ at minimum

Final Exam Preparation Tips

The Night Before

• Review your whiteboard notes: Focus on derivations

• Do one final practice problem from each major area

• Organize your open-book materials: Tab important formulas and graphs

• Get good sleep: Mathematical reasoning requires a clear mind

Day of Exam

• Bring scratch paper and multiple pens/pencils

• Start with problems you’re most confident about

• For multi-part questions: Answer what you can, partial credit is available

During the Exam

• Read each question completely before starting to solve

• Draw graphs when helpful: Visual aid for your own understanding

• Check units and reasonableness: Does a negative price make sense?

• Use the calculator effectively: Don’t make arithmetic errors on easy parts

Success Indicators

• Set up and solve two-equation systems for consumer optimization (tangency + budget)

• Derive demand curves from utility maximization without looking at notes

• Perform complete income and substitution effect analysis graphically

• Calculate returns to scale from production function exponents and interpret economically

• Solve tax incidence problems showing consumer price, producer price, and deadweight loss

• Explain why tangency represents optimal choice using both math and economics

• Work fluidly between different utility function types (Cobb-Douglas, perfect substitutes, etc.)

• Connect mathematical slopes (MRS, budget line) to economic trade-offs

Key Formulas and Equations

• Budget Constraint: $P_X Q_X + P_Y Q_Y = I$

• Marginal Rate of Substitution (MRS): $MRS = \frac{MU_X}{MU_Y}$

• Cost Minimization: $\frac{MPL}{w} = \frac{MPK}{r}$

• Returns to Scale (Cobb-Douglas): $Q = K^{\alpha}L^{\beta}$, returns to scale = $\alpha + \beta$

• Elasticity as Derivative: $\varepsilon = (\partial Q/\partial P)\cdot(P/Q)$

Sample Table: Returns to Scale Classification

Sum of Exponents ($\alpha + \beta$)	Returns to Scale	Implication
> 1	Increasing	Output increases more than inputs
= 1	Constant	Output increases proportionally with inputs
< 1	Decreasing	Output increases less than inputs

Additional info:

• Some omitted topics (e.g., compensating variation, cost-of-living adjustments) are advanced and not required for this exam.

• Interactive tools and appendices are recommended for deeper understanding and practice.