Domain Analysis for Micro Economics

Microeconomics Domain Analysis

Introduction

This analysis covers Practice AP Exam #1 from Princeton Review.

Global Requirements

I have identified several microtheories that appear to be particularly important in the microeconomics AP domain. The following lists the questions from the AP practice exam

(discussed in detail below) that are addressed by each microtheory.



Consumer choice: Q4



Producer choice: Q14, Q21, Q32, Q35, Q44, Q47



Supply and demand: Q9, Q11, Q17, Q22, Q27, Q36, Q41, FR1, FR2, FR3



Perfect competition: Q6, Q7, Q10, Q26, Q30, Q42, Q56, FR1



Monopoly: Q24, Q50, Q52, FR1



Game theory: Q39, Q46

Each microtheory may be characterized by key definitions, causal rules, mathematical relationships, and underlying assumptions. They may also include one or more central graphs that serve as the primary basis for reasoning in the situation covered by the microtheory.

Question by Question Analysis

Practice AP Exam #1 from Princeton Review

Q1 . Straight definition question. “Fundamental economics questions” is a set, comprising three questions. Could be represented as a set of facts, of the form:

“What goods to produce?” ISA fundamental-economic-question

Q1 is organized as a list of such assertions, followed by multiple choices giving combinations of these assertions. Thus, we require testing the individual assertion against the defining ISA facts, and then reasoning about conjunctions of these tests. Implicitly, the multiple choices assert that the other named questions are not part of the set.

KR-R ontology: Boolean combinations 1.2, structured objects (members of a class) 1.5

Q2

. Focuses on definition. Items listed (“land”, “labor”, etc.) are standard categories of factors of production. Question asks to identify what these are examples of, and answer is

“factors of production”. This is not quite right, as these are categories, not really example factors, though they can also be treated as abstract example factors.

KR-R ontology: structured objects (members of a class) 1.5

Q3 . Focuses on definition. Shows standard supply-demand graph, asks to identify region defining “consumer surplus”. This graphical display is actually the standard way to define consumer surplus, though of course it could be expressed algebraically as well. No doubt we’ll need both kinds of representations, but for this question the diagram is most useful. Diagrammatic reasoning required to align curves and points on given graph to the standard definition version.

KR-R ontology: diagrams 1.10

Q4 . Reasoning about basic economic laws. Need to recognize that diminishing marginal utility can “explain” (i.e., is an assumption underlying) the law of demand. Could be represented as a structured object (e.g., with “assumption-for” roles), or more fundamentally, derived from the consumer-choice microtheory. In that theory, law-ofdemand is the property that demand curves are downward-sloping, and this can be derived from diminishing marginal utility in a simple qualitative model. Note that this is a qualitative model of rational decision making, which will be commonly applied in microeconomics.

KR-R ontology: structured objects (object attributes) 1.5, preferences (utility theory, rational decision making) 1.14, qualitative reasoning MW1

Microtheory: consumer choice

Q5 . Identifying a qualitative property that holds of a numeric relationship represented in tabular form. Need to recognize that the table represents a production function, and extract the data. Actually, it is the projection of a production function onto one input

(labor, measured in number of workers), as it says “holding other inputs constant”. This is important, as the justification for not applying “decreasing returns to scale” is that we need to consider all inputs for that. However, “diminishing marginal returns” is defined for one input, so that applies. We can define diminishing returns as the property that the one-input production function is concave. This question actually calls for identifying on what region (i.e., starting from what point) the diminishing returns starts, which we can do by applying the definition of concavity to the extracted function.

KR-R ontology: tabular interpretation MW3, quantities MW2, mathematical functions

MW4 and their qualitative properties, including the concept of projection

Commonsense: question uses “gyros” as the output good, but we should recognize that nothing about the identity of the good matters for answering the question

Q6 . Properties of a competitive market. Zero profit would be a known attribute of competitive firms. Twist is that the preferred answer is expressed in terms of the definition of “opportunity cost”, and to get this we may need a deeper reasoning from definition of “economic profit”. Having no better opportunities is consistent with (and follows from) zero economic profit. The answer here says that the next best alternative also leads to exactly zero profits, which is strictly true only if doing nothing is a possible alternative. Hence, a sound derivation would require the inequality from the chosen alternative to the next best, and another fact saying the next best has to be at least zero.

KR-R ontology: structured objects (object attributes) 1.5, mathematical inequalities MW5

Microtheory: perfectly competitive market

Q7 . Properties of a competitive market. P = MC would be a basic fact associated with competitive markets. Question is phrased by comparison to monopolies, which can be confusing but is useful for ruling out other answers.

KR-R ontology: structured objects (object attributes) 1.5


Q8 . Influences on demand elasticity. Elasticity is a property of demand, and we can enumerate a set of influences on this property. One of these is that a good has many substitutes, and we would further note that a particular brand or flavor of a broader type is likely (default?) to have such substitutes.

KR-R ontology: structured objects (members of a class, object attributes) 1.5, conditionaction (causal) rules 1.8, defaults 1.13

Commonsense: Four out of five of the answer options require background knowledge to understand. (B) cigarettes are an addictive good, so demand will be inelastic (insensitive to price). (C) don’t need to know what “soda pop” is; fact that answer says “all types of” is a signal that it is a broad category of goods, so will not tend to have close substitutes as a whole. (D) “Sprite” is a brand of soda pop, which is particularly meaningful in light of

(C). In this case we will need to know that there are many brands, so likely to be close substitutes—we don’t really have to know about Sprite knock-offs in particular. (E) “Life sustaining pills” also suggests that our demand for this will not be sensitive to price.

Q9 . Influences on demand and supply. Reducing cost will be one of the known causes of supply increasing (shifting right). Change in cost will have no known effect on demand.

KR-R ontology: structured objects (object attributes) 1.5, condition-action (causal) rules

1.8

Microtheory: supply and demand

Commonsense: question uses “Frisbees” as the good, but we should recognize that nothing about the identity of the good matters for answering the question (same as “gyro” in Q5).

Q10 . Properties of a competitive market. P = MR would be a basic fact associated with competitive markets. Since MR is a constant, the average and marginal must be the same—follows from basic algebra, or some qualitative reasoning.

KR-R ontology: structured objects (object attributes) 1.5, qualitative models MW1, mathematical function properties MW4


Q11 . Influences on supply. Decrease in price of joint product will be one of the known causes of supply decreasing (shifting left). [explanation in AP prep book seems

unnecessarily indirect] Ruling out answer (A) may require more elaborate two-step reasoning, through the effect on costs of inputs.


1.8, qualitative models MW1


Commonsense: question uses “textbooks” as the good, but we should recognize that nothing about the identity of the good matters for answering the question (same as “gyro” in Q5).

Q12 . Causes of market failure. All of the listed phenomena are known causes of market failure.


1.8

Q13 . Properties of cost functions. Standard functions have known (default?) qualitative profiles, characterized as conditions on sign of first and second derivatives (i.e., monotonicity and concavity). Must extract these properties from given graph (inflection points sufficient), only profile that will match is for total cost function.

KR-R ontology: structured objects (object attributes) 1.5, qualitative models MW1, mathematical function properties MW4, diagrams 1.10, defaults 1.13

Q14 . Firm operation under different market structures. Point of this question is that profits are maximized when MR = MC, regardless of market structure.

Q14 is organized as a list of market structures, followed by multiple choices giving combinations of these market structures posing the question about MR = MC. We could answer this by verifying that it holds of each enumerated case, but it would be preferable to notice that the equality is universal. In either case, the most straightforward approach to get the overall answer would establish the conclusion for each market structure

(perhaps by universal instantiation), and then reason about conjunctions of these tests.

KR-R ontology: Boolean combinations 1.2, structured objects (object attributes) 1.5

Microtheories: producer choice

Q15 . Comparative advantage and absolute advantage. These concepts have standard definitions which can be expressed as inequalities on ratios. These ratios can be extracted from the production possibilities frontier (PPF), which in this question are presented in graph form.

KR-R ontology: structured objects (object attributes) 1.5, mathematical inequalities

MW5, diagrams 1.10

Commonsense: question uses “shirts” and “chairs” as the goods, but we should recognize that nothing about the identity of the goods matters for answering the question (same as

“gyro” in Q5).

Q16 . Antitrust laws. Lists five congressional acts, and asks which is not about antitrust.


Q17 . Effects of demand and supply changes on equilibrium price and quantity.

Recognize “drought” as a cause of supply decrease (shift left) and “discovery that they assist in the avoidance of cancer” as a cause of demand increase (shift right). Further qualitative reasoning that this leads to increase in price and indeterminate change in quantity.




Commonsense: question uses “pineapples” as the good, which does not matter in and of itself but may be relevant to figuring out that a drought will decrease supply and the discovered health benefit will increase demand.

Q18 . Average product and marginal product. Qualitative properties follow from definition of average and marginal applied to production function. Mentions “labor”, but holds with respect to any input of production.


Q19 . Total utility and marginal utility. Need to recognize that air is an essential consumption good with enormous value, but that we consume so much of it that the last increment has relatively small value. This is also true to some extent for the other goods

(except “spam”), but air is an extreme case. Calls for a relative judgment, possibly default attribution of properties.

KR-R ontology: structured objects (object attributes) 1.5, qualitative models MW1, mathematical function properties MW4, defaults 1.13

Commonsense: Very tricky case. Need to understand “air” as an essential good, but one so plentiful a normal market does not exist. Do not really need to understand the other choices to answer question correctly.

Q20 . Firm supply curve and market supply curve. Market supply curve defined as quantity aggregation of individual firm supply curves. Need to recognize that adding

“horizontally” means aggregating quantities, given standard depiction of curve on demand-supply graphs.

KR-R ontology: structured objects (object attributes) 1.5, mathematical function properties MW4, diagrams 1.10

Q21 . Firm operation. Use known rule that firms should shut down production if they cannot cover variable costs. Need to extract from given diagram the fact that MR (price, in this case) is below average variable cost at relevant point (in fact everywhere in this case).

KR-R ontology: structured objects (object attributes) 1.5, qualitative reasoning MW1, diagrams 1.10

Microtheory: producer choice

Q22 . Externalities. Use fact that a tax equal to the negative externality is a remedy to achieve efficiency.


Commonsense: Another tricky case. Need to understand “loud party” as representing an externality situation, with “lost sleep” the cost imposed on (external) “people living nearby”.

Q23 . Given two equilibrium price-quantity points, reason backward to consistent shifts in supply and/or demand. Question presents a graph, but this is needed only to confirm we are dealing with the standard supply-demand microtheory, with strictly sloped supply and demand. Qualitative reasoning that decrease in price and unchanged quantity can be explained only by demand decrease (shift left) and supply increase (shift right). Strictness of slope is necessary to rule out the scenarios where only one curve moves.

KR-R ontology: structured objects (object attributes) 1.5, quantities MW2, qualitative models MW1


Commonsense: question uses “solar panels” as the good, but the particular is not relevant to this question.

Q24 . Monopoly. Use basic monopoly microtheory to recognize fact of downward-sloping demand. Question calls for contrast with firm under perfect competition. This may not be necessary to consider, but if we do we have to be careful about the distinction between the market demand curve (downward sloping) and the curve facing a single competitive firm (horizontal).


Microtheory: monopoly

Q25 . Cost function definitions. Need to recognize that pizza sauce is a variable cost, and that variable costs contribute to total variable costs, as well as to marginal and total costs.

Q25 is organized as a list of cost concepts, followed by multiple choices giving combinations of these costs. Thus, we must reason about conjunctions of these tests.

KR-R ontology: Boolean combinations 1.2, structured objects (object attributes) 1.5, mathematical function properties MW4

Commonsense: refers to “pizza” (output good) and “pizza sauce” (input good). Essential observation is that the sauce constitutes a variable input in pizza production.

Q26 . Lerner index. Need mathematical definition of the index (a simple formula), and fact that under perfect competition, P = MC.

KR-R ontology: structured objects (object attributes) 1.5, mathematical function properties MW4


Q27 . Price determination in factor market. Increase in price of output good (tubas) leads to increase in quantity supplied, which in turn leads to increase in demand for factor

(tuba-maker labor), which in turn raises equilibrium prices (wages). Alternatively, could reason more directly in terms of the marginal revenue product (MRP) of tuba-maker labor.




Commonsense: question uses “tubas” as the good, but essential observation is that this is output, whereas “wages for tuba makers” is price of input factor. Incorrect answers mention related concepts, like “tuba-maker training school” and “tuba lessons”, and further understanding of how they relate would be necessary for ruling these out.

Q28 . Inferior goods. Basic definition is that demand goes down when income goes up.

KR-R ontology: structured objects (object attributes) 1.5, qualitative reasoning MW1

Commonsense: question uses “popsicles” as the good, but nothing particular about popsicles is necessary to recognize inferiority of good.

Q29 . Price discrimination. Under perfect price discrimination, the monopolist extracts all consumer surplus by definition, so the conclusion follows immediately. The question refers more vaguely to “when the opportunity for price discrimination arises”, which suggests more partial forms (e.g., 3d-degree). Although price discrimination is intuitively

(and perhaps usually) associated with reduced consumer surplus, I do not believe it is true in general. So deriving from first principles seems unpromising.

KR-R ontology: structured objects (object attributes) 1.5, vagueness 1.12.2, defaults 1.13

Q30 . Unemployment in a competitive labor market. It is a basic property of competitive markets that producers can supply any quantity at the market price. Applied to labor markets, this means that any laborer can find employment at the market wage.

KR-R ontology: structured objects (object attributes) 1.5, condition-action rules 1.8


Q31 . Identifying a qualitative property that holds of a numeric relationship represented in tabular form. Need to recognize that the table represents a total cost (TC) function, and extract the data. Further need to construct marginal cost and variable cost functions from given information. From extracted marginal cost function, can verify that it falls then rises.


MW4 and their qualitative properties

Commonsense: question uses “basketballs” as the output good, but we should recognize that nothing about the identity of the good matters for answering the question

Q32 . Shape of the production possibilities frontier (PPF). Straight-line PPF (question implicitly assumes two output goods) means that the marginal rate of transformation is a constant. The intuitive explanation given is that curvature in the PPF can arise when input resources are specialized, and so producing relatively more of a good means relying on less specialized resources. I am not aware of a technical definition of “specialized resources” (vague, possibly associated with curved PPF by default?). A single input with constant returns would be sufficient for straight-line PPF, but multiple inputs with linear marginal product would not be.

KR-R ontology: structured objects (object attributes) 1.5, vagueness 1.12.2, defaults 1.13


Q33 . Oligopoly. Basic definition in terms of representative features of an oligopoly market. Characterization in terms of “a small number of firms (3–5)” requires handling vague specification.

KR-R ontology: structured objects (object attributes) 1.5, vagueness 1.12.2

Q34 . Public goods. Basic definition in terms of associated features.

Q34 is organized as a list of phenomena, followed by multiple choices giving combinations of these phenomena as associated with public goods. Thus, we require testing the individual associations, and then reasoning about the conjunctions.


Q35 . Maximizing profit. Total product function given in tabular form. Total revenue is output price times total product, and total cost derivable from information in question

(wage times number of worker-hours). Profit is difference, and question calls for amount of labor input maximizing profit.

KR-R ontology: tabular interpretation MW3, quantities MW2, optimization MW6


Commonsense: Good is called “silverware” but the particulars are irrelevant.

Q36 . Price ceiling. Basic definition is that it is a price set below the equilibrium price

(otherwise it would be irrelevant).

KR-R ontology: structured objects (object attributes) 1.5, mathematical inequalities MW5


Q37 . Income elasticity of demand. Apply formula defining this concept to the data given in the question.

KR-R ontology: structured objects (object attributes) 1.5, quantities MW2, mathematical function properties MW4

Commonsense: Good is called “vitamins” but the particulars are irrelevant.

Q38 . Identifying a qualitative property that holds of a numeric relationship represented in tabular form. Need to recognize that the table represents a two-input production function, and extract the data. To assess marginal returns we would need to construct all the oneinput functions holding the other input constant at all levels. There are only a few relevant data points to assess returns to scale, and these are consistent with constant returns.


MW4 and their qualitative properties, including the concept of projection

Commonsense: question uses “trees” as the output good, and “workers” and “shovels” as inputs, but we should recognize that nothing about the identity of the goods matter for answering the question

Q39 . Game theory. Need to read diagram into a normal-form game description.

Determining nonexistence of a dominant-strategy equilibrium will be straightforward.

KR-R ontology: structured objects (object attributes) 1.5, diagrams 1.10

Microtheory: game theory

Q40 . Monopolistic competition. Zero profit would be a known attribute of monopolistically competitive firms.


Q41 . Influences on demand. Expected future increase in income will be one of the known causes of demand increasing (shifting right). Default assumption that good is not inferior.


1.8, defaults 1.13


Commonsense: question uses “orange juice” as the good, but nothing about the identity of the good matters for answering the question (same as “gyro” in Q5). Ruling out incorrect answers would require recognizing that “oranges” and “orange pickers” are inputs in orange juice production, and that “Tang” is (to some) a consumption substitute.

Q42 . Marginal product and marginal revenue product. Using the formulas for MP and

MRP (“labor” part is not crucial, except for realizing that “wage” is the input price), equating, and simplifying, we get the sufficient condition P = MR. This would be a basic fact associated with competitive markets, which are characterized by price-taking firms.



Q43 . Constant (increasing/decreasing) cost industry. Given the fact that this industry uses a small fraction of the input good, we would not expect any input price changes as the industry scales. Qualitative model would connect input prices with overall scaling properties. No effect here would have to be a default assumption, since we are not given enough information to make a definitive assertion.


1.8, qualitative models MW1, defaults 1.13

Commonsense: question uses “plastic army figures” as the output good, and “plastic” as input, but nothing implicit in the identity of the goods matter for answering the question.

Q44 . Maximizing profit. General rule (see Q14) is to operate where MR = MC. We need to find this intersection point on the given graph, and report the associated quantity.



Q45 . Concentration ratio, monopoly. Apply definition of concentration ratio (a simple formula) to case where a single firm has 100% market share—the definition of monopoly. Note that standard term is n -firm concentration ratio, but for case of monopoly the result will be the same for any n > 0.


Q46 . Nash equilibrium. Select correct definition.


Microtheory: game theory

Q47 . Allocative efficiency. Applying definition calls for a condition that leads to producing optimal level of outputs. From producer choice microtheory we see that P =

MC is a criterion for choosing output level. Determining that this leads to allocative efficiency requires deeper reasoning, including understanding that P represents consumers’ relative marginal values in equilibrium (under default assumptions).


1.8, defaults 1.13


Q48 . Necessary preconditions for price discrimination. Market power (monopoly) and preventing resale would be specified as conditions for price discrimination to be applicable. Separating different elasticities is definitional, so to “be able” to do this is a precondition.

Q48 is organized as a list of conditions, followed by multiple choices giving combinations of these. Thus, we must reason about conjunctions of these conditions.


Q49 . Economies of scope. Question provides defining situation, noting representative features, which we need to recognize.


Commonsense: mentions “Internet companies” and some examples (AOL, Amazon), and describes situation. In this case, we do not really need to understand any of this because last question describes the situation presented to “such companies” directly in the more abstract economic terms.

Q50 . Analogy between monopoly and monopsony. This is basically asking us to solve

marginal revenue : demand :: marginal factor cost : ?? where the LHS is in the context of monopoly, and the RHS is in the context of monopsony. The demand curve determines marginal revenue in the same sense that factor supply determines marginal factor cost, which could be represented in both case by causal rules. (The explanation given in the guidebook is too superficial.) Actually the monopoly/monopsony contexts may not be essential. The fact that the correct answer instantiates the factor with “labor” is also inessential (possibly confusing).


1.8, analogy MW7


Q51 . Free rider problem. How to avoid the free rider problem, which arises when attempting to fund public goods by voluntary contributions. Question could be answered by recognizing that correct answer is the only one that directly addresses public goods.

Would also help to know that a tax is a contribution that is patently not voluntary.


1.8

Q52 . monopoly. Qualitative reasoning could determine that downward-sloping demand

(need to lower prices to sell more) entails that MR is below demand. Need to translate this description in terms of a curve being below another into a statement about functions.



Q53 . Opportunity cost. What we need to give up to get a 7 th carrot can be extracted (with a little arithmetic) directly from the production possibilities frontier (PPF), which in this question is presented in graph form.


Commonsense: question uses “carrots” and “tomatoes” as the goods, but we should recognize that nothing about the identity of the goods matters for answering the question

(same as “gyro” in Q5).

Q54 . Influence on demand in factor market. Aggregate factor demand is the sum of demand over firms, so increasing firms will increase (shift-right) this demand.




Q55 . Barriers to entry. Listed concepts would all be known examples of phenomena causing barriers to entry. Economies of scale may be an indirect example, requiring deeper representing and reasoning about the entry decision.


1.8

Q56 . Price determination under perfect competition. That prices are determined by the market (rather than set by a firm) would be explicitly represented. Wrong answers can be ruled out through technical reasoning with the perfect competition microtheory.


1.8


Q57 . Complements and cross-price elasticity. The definition of gross complements is that when the price of one goes up demand for the other goes down. Simple mathematical reasoning concludes that this is entailed by negative cross-price elasticity (using the defining formula). The reasoning is qualitative in that only signs matter. The “gross” qualifier is a subtlety left out at this (AP) level, as income effects are neglected (for this purpose) by default.

KR-R ontology: structured objects (object attributes) 1.5, mathematical function properties MW4, qualitative models MW1, defaults 1.13

Q58 . Positive externalities. The situation where “benefits go beyond those that [the decision maker] enjoys himself” is definitional for a positive externality. The prescription for subsidies would be directly associated.


Commonsense: question uses “education” as the good, but the particular is not relevant to this question. In this case, the question wording provides direct clues (quoted above) that the issue is positive externalities.

Q59 . Negative externalities. Need to understand that the presence of negative externalities tends to cause more of the good produced than would be socially desirable.

Imposing production limits would address that directly.


1.8

Q60 . Determination of demand in factor (labor) market. Need to understand that question refers to an individual firm’s demand, which is determined by factor productivity and price of the output good. The latter is determined by demand for the output. Does not seem to correct to say that the labor demand is “derived from” just output demand, as factor productivity is essential as well.


1.8


Free Response Questions

FR1 . Comparison between equilibria under perfect competition and monopoly. Calls for drawing standard diagrams of these two situations, and explaining the welfare loss under monopoly. Given constant marginal cost, supply curve under perfect competition is a straight horizontal line. For monopoly, add MR curve to the picture, recognizing that it intersects MC at a lower quantity. Efficiency loss can then be characterized on graph as difference between total surplus at the two points.


1.8, mathematical function properties MW4, diagrams 1.10

Microtheories: supply and demand, perfect competition, monopoly

Commonsense: question uses “gloves” as the good, but the particular is not relevant to this question.

FR2 . Demand shifts and price floor in a factor (labor) market. Need to depict graphically an increase in demand for labor (cf. logic of Q27). Minimum wage is defined as a price floor on labor, which has to be above equilibrium price to be effective (cf. Q36). Standard reasoning about price floors leads to conclusion that quantity demanded decreases, which translates to more unemployment. Need to show unemployment as difference between previous quantity and new (those directly put out of employment), as well as the difference between new quantity and the quantity who would want to work at minimum wage (overall unemployment).


1.8, diagrams 1.10


FR3 . Positive externalities. The situation where “many other people benefit, in addition to [the decision maker]” is definitional for a positive externality (cf. Q58). In this question, we also need an explicit representation for the external (social) benefit, producible in graph form as an addition to the standard supply-demand graph. Several standard prescriptions would be directly associated. We need to pick one, and show how it will affect demand or supply (depends on which remedy) and the resulting affect on equilibrium price and quantity. The end result must be to increase quantity.


1.8, qualitative models MW1, diagrams 1.10


Commonsense: question uses “flu shots” as the good, but the particular is not relevant to this question. In this case, the question wording provides direct clues that the issue is positive externalities.

Extensions Needed to the KR Ontology

1.

Include qualitative modeling/reasoning as distinct from qualitative physics (or just generalize the qualitative physics category) [ MW1 ]

2.

Include quantities and reasoning about quantities not necessarily physical quantities (similar to #1) [ MW2 ]

3.

Reasoning about tables -- or will we just assume these are re-expressed as relations/functions? [ MW3 ]

4.

Mathematical reasoning: relations/functions and projections, properties of functions (e.g., monotonicity/convexity) [ MW4 ]

5.

Mathematical inequalities [ MW5 ]

6.

Optimization [ MW6 ]

7.

Analogy [ MW7 ]

Histogram of KR Requirements

The following counts the number of multiple-choice questions labeled with each KR-R ontology category.

60

50

40

30

20

10

0

1.

5 m embe r

1.

5 at tri bu te

1.

8 ru les

1.

10

d iag ra m

1.

12

.2

va gu en ess

1.

13

d ef au lts

1.

14

p ref

MW

1 qu al ita tive

MW

2 qu an tit ies

MW

3 ta bu la r

MW

4 fu nc tio ns

MW

5 in eq ua lit ies

6 op

MW tim iza tio n

MW

7 an al og y

Summary of Analysis

Many questions in the microeconomics domain call for reasoning about mathematical functions, and in particular about qualitative properties of these functions. I would expect that many of the microtheories would focus on this level of description. We also require the ability to move back and forth between analytic and geometric descriptions of the functions and relations, that is, between properties of functions and properties of their depiction on a graph. This is required for interpreting questions (many include graphs), understanding text (e.g., shifting a curve to the right corresponds to a positive monotone transform of the function), and producing graphs for the free-form questions.

I identified “commonsense” issues arising in 21 out of 60 multiple-choice questions

(35%). Most were fairly simple, using labels for goods that don’t really matter. A few were relatively tricky (especially Q8, Q19, Q22), requiring some understanding of the background knowledge in order to make the necessary connections to microeconomic principles. A few more were in the middle, for example requiring some background to rule out incorrect answers if not to verify the correct one.

Domain Analysis for Micro Economics

Microeconomics Domain Analysis

Introduction

Global Requirements

Question by Question Analysis

Extensions Needed to the KR Ontology

Histogram of KR Requirements

Summary of Analysis

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Domain Analysis for Micro Economics

Microeconomics Domain Analysis

Introduction

Global Requirements

Question by Question Analysis

Extensions Needed to the KR Ontology

Histogram of KR Requirements

Summary of Analysis

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