Intermediate microeconomics: choose a model before optimizing
A tangency calculation is not a universal choice rule. Specify preferences, feasibility and what the utility representation means before optimizing. Select a graphical first pass or a formal proof route, then test the assumptions by changing the preference model.
Course topic: Intermediate Microeconomics
Study route and exercise: University Reading List editorial project. How we curate · Sources checked:
Scope and responsibility
An academic undergraduate route through consumer choice within intermediate microeconomics. The chosen records are Osborne–Rubinstein’s expanded second edition (She, 2023), Varian–Melitz tenth edition and Pindyck–Rubinfeld global ninth edition (selected 2017 print). The guide’s goods, budgets and behaviour are invented. It is not a recommendation about a person’s finances, a demand estimate or a welfare claim about an actual policy. A utility number represents an ordering in the stated model, not a measured amount of happiness.
Choose your starting point
I need a free formal route
Use Osborne–Rubinstein if you can follow definitions and sustained proofs. Elementary mathematical notation can still demand substantial reasoning; almost no calculus does not mean no preparation.
I want diagrams and a gradual intermediate course
Choose Varian–Melitz for the budget–preferences–choice sequence, especially when the tenth edition is assigned. Match named topics to your copy rather than relying on a different regional format’s page numbers.
I want a broad applied companion
Use Pindyck–Rubinfeld selectively when applications and comparisons of consumer, firm and market decisions are central to your course. Do not read a second full survey just to repeat the same vocabulary.
Compare the three books
Models in Microeconomic Theory: Expanded Second Edition (She)
Martin J. Osborne; Ariel Rubinstein · Edition: 2 (expanded, She version) · 2023
Free precise-model route
- Choose it when
- You want definitions, assumptions, results and proofs made explicit.
- Use another route when
- You first need a diagram-led introduction or a large routine-calculus exercise bank.
- Selected reading
- Expanded second edition: Preferences and utility; Choice; Consumer preferences; Demand. Later producer/equilibrium chapters are a continuation.
- Limits and trade-offs
- The selected She paperback is 9781805111214,2023. The publisher’s Chinese translation is of the first edition, not this expanded second edition. Authorized reading and its BY-NC-ND reuse conditions are distinct.
Try before choosing
From the preference/choice route, define the feasible set and show why the complementary-goods optimum lies on x=2y without differentiating at the kink.
Check your work: An argument excludes both an undersupplied component and an affordable improvement. Merely drawing a kink on a budget line is not a proof that no other feasible bundle is better.
Intermediate Microeconomics: A Modern Approach
Hal R. Varian; Marc Melitz · Edition: 10 · 2024
Graphical and algebraic intermediate spine
- Choose it when
- You know principles and want a connected route from constraints to choices and demand.
- Use another route when
- You need a free complete text or an advanced graduate theorem reference.
- Selected reading
- Tenth-edition opening topics: Budget Constraint, Preferences, Utility and Choice, then Demand.
- Limits and trade-offs
- The selected US paperback and international/digital products have separate identifiers and release dates. A publisher TOC for another tenth-edition format is useful orientation, not proof of identical pagination or question numbers.
Try before choosing
For the supplied complements case, sketch a feasible budget set and at least two indifference contours; mark the kink and calculate its coordinates.
Check your work: The budget is 2x+3y≤24 and the kink is x=2y. Use the inequalities and an improving direction, not an undefined marginal rate at the kink.
Microeconomics
Robert Pindyck; Daniel L. Rubinfeld · Edition: 9 · 2017
Broad applied alternative
- Choose it when
- You want consumer theory connected to demand and worked applied settings.
- Use another route when
- You only need a concise formal choice model or assume historical application figures are current evidence.
- Selected reading
- Global ninth edition: consumer behaviour, individual/market demand and production/cost discussions; use the consumer sequence first.
- Limits and trade-offs
- Pearson’s exact selected paperback ISBN 9781292213316 is listed as 2017. Newer storefront headers and separate access SKUs do not establish a new publication year for that print record or free platform access.
Try before choosing
After the consumer-behaviour route, explain which change in the follow-up concerns preferences and which concerns prices; keep the budget and objective separate.
Check your work: With u=x+2y compare utility per unit of budget before claiming an interior optimum. If the ratios tie, report the whole optimal set.
Check your preparation
How much mathematics is needed?
Use algebra, inequalities, graphs and fractions for these cases. A principles course helps interpret the question. The formal free route needs comfort with sets, functions and proofs; optional calculus is not a substitute for checking assumptions.
Does a first-order condition always find the answer?
No. Nondifferentiable preferences and boundary choices need separate reasoning. Even a stationary point in a smooth problem needs a feasibility and optimality argument.
Can I compare two utility numbers as happiness?
An increasing transformation can preserve all choices while changing numerical levels. Explain the ordering being represented; do not compare cardinal magnitudes across different preference specifications.
Six steps with a concrete output
Outputs marked ready: 0 / 6
These are your own study marks, not an assessment. They are not sent to this site.
-
Separate model components
Selected reading: Osborne–Rubinstein Preferences/Choice or the chosen survey’s constraint/preference route.
Make this: Write the goods, nonnegative quantities, prices, budget and utility representation as distinct items.
Check your work: The feasible set is not a preference relation, and an objective function does not establish a real demand curve without further assumptions/evidence.
-
Explain the optimum before solving
Selected reading: The consumer-choice sections of the chosen spine.
Make this: Show why spare units of the nonlimiting complement cannot improve the minimum and why the optimum uses the full positive-price budget.
Check your work: Use an improving feasible change to rule out a candidate; do not assume every monotone-looking formula is strictly increasing in each component.
-
Compute and verify
Selected reading: The same sections; use your own algebra before checking.
Make this: Solve x=2y with the budget and verify nonnegativity, spending and utility.
Check your work: Keep the exact fractions 48/7 and 24/7 rather than rounding before testing the constraint.
-
Change one price
Selected reading: The demand discussion after consumer choice.
Make this: Keep the complements preference and income, change px from 2 to 1 while py stays 3, and recompute.
Check your work: The new bundle is(48/5,24/5). State that this is a result of the stipulated model, not an estimated response of actual buyers.
-
Change the preference model
Selected reading: The follow-up and the chosen book’s substitutes/corner discussions.
Make this: Solve the linear-utility case, then the equal-ratio price variant, showing all maximizers when there is a tie.
Check your work: A corner and an interval of optima are both possible under explicit conditions. An interior-only recipe misses these distinctions.
-
Write a defensible comparison
Selected reading: Revisit utility representation and demand.
Make this: Explain what the examples establish about optimization methods, and list what would be required to use a model empirically.
Check your work: Do not interpret numerical utility differences across preference models as welfare changes; identify the assumptions changed in each comparison.
Worked exercise
Original example: complementary goods and a kink
An invented consumer chooses x,y≥0 with budget 2x+3y≤24 and utility u(x,y)=min{x,2y}. Find all utility-maximizing bundles. Then keep preferences and income but change the price of x from 2 to 1, with the price of y still 3.
Assumptions
Quantities are divisible, the stated prices/income are exact, and these preferences completely define the paper problem. No borrowing, saving or other goods are introduced. Utility represents preference ranking, not measured happiness; no real consumer behaviour was observed.
- To achieve utility at least v requires x≥v and y≥v/2, costing at least 2v+3v/2=(7/2)v. The budget therefore bounds v≤48/7.
- The bundle x=48/7,y=24/7 attains that bound and spends 24. Because the minimum cost for that utility already exhausts the budget with positive prices, no different bundle can add surplus components for free: the optimum is unique.
- With px=1, the minimum cost for utility v becomes v+3v/2=(5/2)v. Thus v≤48/5, attained uniquely at x=48/5,y=24/5.
Answer and interpretation
The original unique optimum is(48/7,24/7). After the price change it is(48/5,24/5). A smooth tangency condition is unnecessary and undefined at the kink; a cost bound plus an attaining bundle gives a complete optimality argument.
Test the result
Original spending is 2(48/7)+3(24/7)=24; new spending is 48/5+3(24/5)=24. Check x=2y in both. A positive-price budget rules out adding an unneeded component at the optimum.
Change an assumption
Replace complements by substitutes: corner or tie
Return to the original prices(2, 3) and income 24, but replace preferences by u(x,y)=x+2y. Find the optimal bundle. Then keep this new preference and change the price of y to 4. Identify every optimum in that second variant. Do not compare utility levels with the old min function as if they shared a happiness scale.
- At prices(2, 3), utility per budget unit is 1/2 for x and 2/3 for y. Moving spending from x to y strictly improves utility, so the unique optimum is x=0,y=8, with utility 16 in this new representation.
- At prices(2, 4), both ratios are 1/2. On the budget line 2x+4y=24, utility x+2y=12 is constant. Every bundle x=12−2y with 0≤y≤6 is optimal.
- Both the preference change and the later price change are explicit. The original kink bundle need not remain optimal, and choosing one endpoint in the tie case does not establish uniqueness.
Answer and interpretation
The substitutes case first yields the corner(0,8). In the equal-ratio variant, a whole line segment maximizes utility, including(12,0) and(0,6). The same optimization framework can produce unique corners, unique kinks or nonunique solutions.
Test the result
Use the bound x+2y≤(2/3)(2x+3y)≤16 in the first variant, with equality only when x=0 and the budget binds. In the tie variant, utility is exactly half of spending. These global checks do not depend on trying a finite list of bundles.
Common mistakes
A kink is not a failed derivative
Use inequalities and an attaining bundle when differentiability is absent.
A chosen optimum may not be unique
Check whether the objective is constant along a feasible segment.
Ordinal numbers are not measured happiness
Different utility representations can encode the same ranking; different preference models require even more care in comparing values.
Before moving on
- State the feasible set separately from preferences.
- Prove the kink and corner results and describe the full tie set.
- Explain why none of these invented inputs estimates actual demand or a policy effect.
Sources and edition checks
Sources checked:
- Open Book Publishers: expanded second edition, formats and contents
The publisher verifies the expanded 2023 She edition, exact format identifiers, elementary-but-proof-based audience and named consumer chapters.
- Norton: selected tenth-edition print product
The selected print product is distinguished from separate digital products and regional release dates.
- Norton: tenth-edition international contents and format distinction
The official international tenth-edition map supports the named early sequence. Later numbering anomalies on its public TOC are not imported.
- Pearson: ninth-edition global print identity and contents
The current product page still identifies the selected global ninth-edition paperback as 2017 despite newer digital/header dates.
These are proposed study activities, not official course assignments or a claim that every book has been read cover to cover.