1 Models, maths, fundamentals

This, combined with the above outline represents approximately half a week of material

Key goals of this chunk:

Get a sense of, and be able to explain:

  1. What Microeconomics is about and why it is useful
  2. What the point of ‘models’ are
  3. Some applications of these models
  4. Some examples of microeconomic models and questions (should be largely revision)
    • Get your econ brain flowing
  5. Discuss maths revision: know which maths you need to revise (if any)
  6. Discuss ‘empirical work’ in Microeconomics, and how it connects to ‘theory’

Main reading for this chunk: this web book


Readings on ‘what is Economics’, ‘what are the purpose of Economic models’, etc.: The readings below are each optional, but you must read at least some of these*

Unfold to see these…

We will return to the issues of ‘what and why models’ throughout the module.

1.1 Empirics, maths revision

Some of the maths you need will also be simultaneously covered in your Optimisation and Econometric modules, sometimes at a higher level.

We will use some maths in this module, and now would be a good time to revise some of this on your own.

Here are some key elements.

  1. We will consider the use of microeconomics in ‘empirical identification’ of effects using data. The mixtape, Scott Cunningham pp 18-22, provides a good introduction to this

  2. So called ‘pre-calculus’ and general maths concepts including

  • The symbolic language and notation of maths, summation and product operators
  • Multivariate and univariate functions (and mappings), inverses of functions, implicit functions
    • Plotting these functions over their domain and range; the ‘level sets’ of multivariate functions
    • Specific functions including: Logarithms/exponential functions, quadratic and higher-order polynomial functions, ‘min’ and ‘max’ operators
  • Limits, Geometric series
  1. Some elements of basic calculus, including, perhaps

However, in general I’m not asking you to memorize sets of rules; I’ll give hints to remind you of these rules on any examination.

Some very simple math revision HERE, from my prior lecture. However, you will find better coverage of this at Khan Academy (free) and elsewhere.

  • Derivatives and their interpretations
    • As ‘slopes’
    • Higher-order derivatives and cross-partials, relevance for ‘minima and maxima’ (optimization)
  • Integrals and their interpretation
  • ‘Total differentiation’ of a function
  • Constrained optimization and (perhaps) the Lagrangian method (probably optional)
  • The implicit function theorem (probably optional) and ‘comparative statics’

  1. Some elements of Set theory, including open and closed sets, subsets, ordered sets, unions and intersections

  2. Basic ideas of probability and expectation

  3. The logic and construction of formal definitions and proofs

  • Proof by contradiction
  • Proof by construction

The logic of definitions and proofs may be the most important concept for this module.


Optional: I may also occasionally use matrix and vector notation, and combine this with calculus (see concepts such as the ‘gradient’ and ‘Hessian matrix’). However, these will be provided as supplements; you shouldn’t consider these to be required.

1.2 What is Economics?


Note: DR: It has changed. There are different views. Ask two economists, and you’ll probably get at least three answers.

What is Economics? Please propose a definition (from your head… give your own impression) as a comment HERE using Hypothes.is. Then unfold the box below to see some proposed definitions and ideas.

For help on using hypothes.is please see ABOVE or go to https://web.hypothes.is/.

  1. “Economics is the study of the allocation of scarce resources among alternative uses.”

  2. “Economics is the study of mankind in the ordinary business of life.” Alfred Marshall

– The first quote suggests an approach (how we do our research), the second suggests a domain (what we focus on).

Another famous quote: “Economics never tells a man how he should act; it merely shows how a man must act if he wants to attain definite ends.” - Ludwig von Mises

What is Microeconomics?

One definition, not necessarily the correct one: “The study of the (economic) choices individuals and firms make and how these choices create markets.”


Largely, using theoretical and mathematical ‘models’ that depend on strong assumptions.

Comprehension Q: Consider some examples of ‘relevant choices’ for economic study.

Students: please propose some of these as a Hypothes.is comment HERE.

What sort of models are we talking about?…

To refresh your memory… you have probably seen some of these models before in your previous economics module. You should have some familiarity with the simple models of supply and demand curves yielding an equilibrium price and quantity. You may also have seen a models of trade, between two countries or two individuals, with only two goods, where for each good one has a ‘comparative advantage’. Other models involve ‘strategic’ interactions bwtween a few ‘players’. Others involve individual ‘optimizing’ choices. Still others involve firms and governments setting ‘mechanisms’ trying to induce particular choices by others.

Consider: Are they ‘fully realistic’? No. They are models, i.e., simplifications.

A huge body of work has gone into making these models more complex and ‘general’; some of the conclusions are preserved, others are weakened or reversed. But even these more general models are simplifications.

But I don’t find it satisfactory if people respond to a meaningful criticism of a model and the way it is being applied with ‘it’s just a model, and all models are abstractions.’ Specific critiques need to be dealt with directly.

1.2.1 So why learn these models, if they are not realistic?

Consider the parable of the tortoise and the hare (Aesop)…


One might question the realism of this story:

  • Can hares really speak?
  • Is this a rabbit or a hare?
  • What other animals were racing?

Okay, the story is not so realistic. However, it conveys an important message. Is this message in any way affected by the answers to the above questions?

The same can be asked about many criticisms of simple economic models. Of course one should always consider the applicability of particular models to real-world problems, and carefully consider whether the assumptions are reasonable and relevant, and whether the departures from these assumptions will lead to any different predictions. However, in considering the general insight conveyed by the model, some criticisms can merely be distracting. At the very least, we should not reject economic models simply because they are not fully realistic, just as we do not reject Aesop’s fables because they involve talking animals. The idea of ‘Ceteris paribus’ (all other things being equal) can help us here.


Again, so why learn these models?

  • They are a starting point

  • They (sometimes) make concrete predictions you can test

  • They may be useful for building insight, clear arguments, a way of thinking

  • Discussion is framed around these models and they are seen as a ‘baseline’

  • You must understand the arguments and models to be able to effectively critique or extend them

For example, some critics of what they call ‘neoliberal economics’ can be misinformed about what it is. Their criticism can sound to us mainstream economists like someone who says ‘cars are dangerous and should be banned because they go too fast and have no mechanism for stopping’.

1.3 Economic Models

See audio/slides, from 101:25 - HERE

Economic model:

One definition:

A simple theoretical description that captures the essentials of how the economy works.

For the material we cover in this module, this definition would only work if we interpret the term ‘economy’ very broadly.


What is economic theory and what can it do?

Unlike “theory” in some other social science disciplines, economic theory is mostly based on mathematical modelling and rigorous proof that certain conclusions or results can be derived from certain assumptions. But theory alone can say little about the real world.

For example, my impression is that in Psychology a ‘theory’ can represent broad descriptions and stories summarizing and providing a framework for understanding empirical evidence.

In Economic theory we can prove theorems, essentially the logic of ‘if-then’ statements… ‘if one assumes the following preferences, the following choice is optimising’, etc. However, here the realism of the assumptions is always in question; as caricatured in this Twitter ‘meme’.

In Economics: Models = Theory = Uses Mathematics… for the most part.

Again, ‘economic theory’ and models generally do not provide evidence about the real world, they just tell us things like

if (i) people make choices exactly as specified by assumption X, (ii) their choices will be the same as if they made these according to assumption Y, (iii) and the outcomes will have the following relationship (e.g., quantity demanded sloping downward in prices), and vice-versa.

But this doesn’t tell us that people do make choices as specified by assumption X. We are simply showing the mathematical equivalence of (i), (ii), and (iii).

I discuss this further: - in my ‘writing book’ here and - here

1.3.1 Differing views about models

There are differing views on the meaning, purpose, and use of economic models.

This discussion is rather abstract but important. These concerns and issues may make more sense as we get into considering specific models in detail. So we will try to come back to this.

We will return to this in our discussions, and again when we consider the use of experiments. See the suggested readings/notes on readings.

Source reading: The discussion below is largely from (Sugden 2017) “Credible worlds: the status of theoretical models in economics.” Journal of Economic Methodology (2010)

Sugden’s paper mentions two famous papers, one of which is (Nobel Laureate George) Akerlof’s “the Market for Lemons” (Akerlof 1970). It would be worth reading some of Akerlof’s paper and seeing how much you can follow; it is rather accessible. We may return to this specific model of asymmetric information later in the module, and it could certainly be relevant for your project.

If you are interested, I will set up a wiki to engage in a group discussion of these articles.


The instrumentalist view:

The Methodology of Positive Economics (Friedman 1953): the ultimate goal of theory is to “yield valid and meaningful … predictions about phenomena not yet observed.”

  • “Simplicity” – ‘the less initial knowledge needed to make a prediction’.

  • “Fruitful” – more precise predictions, for a wider range of situations


In contrast, the ‘Fictionalist’ view (Sugden 2017):

describes a fictional world that is credible or truthlike in something like the way that the events of a realistic novel are; the model connects with the real world by relations of similarity


Some considerations:

Are these models predictive? If not, are they useful?

  • There are arguments for modeling optimising behavior even if it is not predictive.

  • There is some evidence for near-optimisation in some settings, and that choices move in this direction.

  • There is also evidence of ‘predictable irrationality’ (or ’bounded rationality); this motivates behavioural economics. There is also some evidence for the following (unfold).

  1. Psychological costs/benefits relating to outcomes other than their own final consumption. People may care about
  • others’ consumption (altruism etc.),
  • about the way they make the decision
  • … and about how close they come to certain goals (see ‘reference points’ and ‘loss aversion’).

  1. People have self-control problems. They also may realize their short-term choices are not in their lt interest, and try to constrain themselves.

  2. It is mentally costly to carefully calculate the costs and benefits \(\rightarrow\) ‘rational inattention’

  • As a result, people may follow simple rules or ‘heuristics’ to make their decisions easier; e.g., ‘work every day until I’ve earned target income’.

1.3.2 The PPF: a ‘model’ and a way of seeing things

At this point we consider a simple and specific model to fix ideas, to make things less abstract. The NS text brings up the production possibility frontier; this is a common example to start with, although by itself it could be argued that ‘the insights gained are basically by assumption’ … there is not really an additional reasoning step. Perhaps a better depiction of this example is in the Curtis and Irvine open access text, sections 1.3-1.5, where they consider two individuals with distinct production possibilities, and derive the ‘aggregate’ ppf, and show the gains to trade.

Production possibility frontier

Figure 1.1: Production possibility frontier

PPF file source LINK, User:Everlong, CC-BY-SA-3.0)

Above, we see a depiction of the “production possibility frontier”. You may be familiar with this from your previous study. The PPF describes the maximum amount of one good that can be produced conditional on a certain quality of another good being produced.

According to (Nicholson and Christoper 2007)

The PPF illustrates key principles:

  1. Scarce Resources

  2. Scarcity involves opportunity cost.

  • The opportunity cost of a good is measured by the alternative uses that are foregone producing it.
  • On the PPF above the opportunity cost of more guns is less butter.
  • The opportunity cost of a choice is the foregone ‘next best’ opportunity from a choice.
  • I may just call this ‘cost’

Can you think of an example that illustrates the distinction between what is commonly thought of as the ‘cost’ and the economists’ definition of an ‘opportunity cost’?

  1. Opportunity costs are (often) increasing.

  • What this means is that as you produce more of one good, its opportunity cost (in terms of the other good foregone) increases.

  • The “law” of diminishing marginal returns.

I’m somewhat sceptical of this being a ‘law’; there are certainly increasing returns in certain regions. However, you will see it again and again as it is a fairly standard assumption.


However

I’m not sure if I would call this a ‘model’. It certainly provides a way of visualizing the trade-offs in an economy, and the way it is drawn embody certain assumptions.

This graphic has a mathematical representation which we will not cover now.

Consider: How could we make this a meaningful ‘model with assumptions’? I could imagine it as below (unfold).

To make this more clearly a ‘model with assumptions’, let’s assume an economy with

  1. Two possible goods: food and clothing

  2. A single input into the production process for either good labour (L)

  3. The economy has a fixed supply of labour \(\bar{L}\).

  4. The production function for food is \(F_f(L)\) and the production function for clothing is \(F_c(L)\), with both ‘strictly and continuously increasing in their argument’. All firms have these same production functions (this implies there are no spillovers/externalities between firms, and no complementarities between producing each good)

  5. Both production functions exhibit diminishing returns to scale (we leave off the maths for how to precisely define this for now)

These assumptions in the fold above could be considered a ‘model’ of an economy. Note that not everything has been specified. E.g., we might ask: i. How many firms are there? ii. How do the firms compete in output and input markets? iii. What exactly are these production functions? There are also clearly unrealistic elements, e.g.: i. Only two goods, ii. Only one input, iii. No complementarities in production

Still, the assumptions given will yield a PPF with the shape above: the ‘feasible production set’ of the economy will have a particular shape. It’s ‘maximal elements’ constitute the ‘frontier’ of this set, which will be:

  • downward-sloping, because each unit of the input (\(L\)) used to produce clothing cannot be used to produce food, and

  • concave (increasing opportunity costs), because of the diminishing returns to scale for each good … as more labour is diverted to clothing away from food, it becomes less and less relatively productive.

This seems to convey an insight that 1. teaches us a way of thinking and 2. seems likely to carry over into more ‘realistic’ models. At the very least, it suggests that, under any economic system, there may be tradeoffs between how much of each good or service can be consumed. E.g., policymakers may need to consider ‘should we have more health care or more non-health consumption’, rather than simply saying ‘we should provide the best health care that money can buy to everyone.’

One might at this point raise the ‘paradox of analysis’: we have stated a set of ‘assumptions’ and then noted what logically follows. But actually, the ‘results’ and the assumptions are basically logically equivalent. So have we simply defined the answer we wanted to get, i.e., circular reasoning? This is a deeply philosophical issue.

The ‘increasing opportunity costs’ insight seems more fragile, more dependent on a fairly strong assumption. How do we know that there are diminishing returns to scale for each good? There are plausible reasons why it may be the opposite… returns to specialisation as an economy, etc.

Furthermore, the model at this level of simplicity cannot speak to a number of questions. E.g., without a sense of the market structure (how many firms and how do they compete), we do not know whether we will attain the PPF– the economy may end up producing at the inferior point ‘C’, for example.

A ‘simpler’ model is not necessarily better, nor necessarily worse.

For comprehension: Be sure you can draw the PPF; consider its slope and what it means

“Supply and demand functions”, the “Marshallian cross”, “equilibrium effects”

Perhaps the most famous model from micro-economics is what is often called ‘supply and demand’, the ‘Marshallian cross’.

I try to avoid the terms ‘supply’ or ‘demand’ because it confuses whether we are referring to:

  1. Supply curves and demand curves (or functions) or
  2. Quantities exchanged (in equilibrium quantity demanded will equal quantity supplied in each market.

Is this helpful in explaining the real world?

Does it make better predictions than other approaches might do in terms of… (for example)?

  • The impact of taxes on prices and quantities exchanged?
  • The response of oil prices to events like the Coronavirus pandemic?
  • Whether a tradesperson would find it profitable to increase his or her price when she seems to be getting more orders than she can handle?

Of course the simple model predicts that she should raise her prices in this situation… so there should never be a ‘shortage’ unless prices are restrained. However, when I tried to hire a plumber in Exeter in 2017 I was repeatedly told ‘everyone is too busy’, not ‘rates are very high these days’. What could explain this?


Models applied in the context of “returns to university education”

We may ask a question something like:

Is it worth the cost and time for the typical US high-school student to enroll in university (‘college’)?

In the US private university tuitions run at over £40,000 per year (for a four-year course!) There is constant popular (and academic) discussion of this. See some links below the fold.


Note: the above are popular accounts, not academic Economic peer-reviewed publications.

For some fairly recent academic references, see (e.g.) (Carneiro 2011), papers cited wihin this, and papers citing it. Link to paper

Consider:

  1. How would you frame the above question, as an economist, in terms of things that can be defined and measured?


  1. What does the answer to the question depend on, from an economics perspective?

This involves microeconomic concepts such as (unfold)

  • Returns to labour inputs in (competitive?) markets; human capital

  • The role of skilled labor in the production function

  • Asymmetric information over employee ‘type’ and ‘signaling’

  • Intertemporal substitution of consumption and ‘discount rates’

Even framing the question requires microeconomics.

Consider: Social vs private returns. Is there a case for ‘market failure’ in the provision of education?


  1. How would you measure this empirically? (some thoughts in the fold)

Empirical ‘identification’ is very difficult. Suppose you simply compared the incomes of those who did and didn’t go to university. These is a well known ‘endogeneity’ or ‘omitted variable bias’ problem here. It seems reasonable to think:

“…compared to those who did not go to university, those who went to university would have tended to earn more (and perhaps to be more socially productive) even if they had not gone to university.” So how can we identify the actual effect of university on their outcomes.

We have a set of other approaches that arguably allow us to answer this ‘causal question’… see further discussions on ‘causal inference’, causal econometrics, and in ‘empirical labor economics’.

These approaches generally involve either:

  1. Very careful ‘control strategies’ to try to compare observably similar people who did or did not attend university or

  2. Something approximately equivalent to a ‘natural experiment’ (‘instrumental variables’, lottery assignments, ‘regression discontinuities’, etc.)


How to evaluate, asses, and test models?

Unsurprisingly, there are a variety of opinions as to how to asses the value of a model. Some considerations include their ‘elegance’ (which is a bit vague), their ‘insightfulness’, ‘how many predictions are generated from the fewest assumptions’, the ‘simplicity’ of the model, and other somewhat-difficult to asses concerns.

As models are simplifications, it is not always clear what it would mean to ‘test their validity’ in terms of the real world.

We might consider two broad approaches:

  1. Testing Assumptions: Examining the validity of assumptions upon which models are based. (Is it reasonable to assume that people are rational, that firms maximize profits etc.?)

  2. Testing Predictions (of the models): Can the model accurately predict real-world events (in the context which it purports to?) If the model predicts events well, then the theory is useful even if the assumption may not appear to be valid.

DR: But if the assumptions are substantially wrong, it may predict well in one particular case but not in general.


Consider: Should we ever ‘test assumptions’? (Unfold)

Some authors (e.g., the undergraduate textbook (Nicholson and Christoper 2007)) are somewhat dismissive of the idea of testing assumptions.

However, there are many cases in which the predictions of the models are very hard to test; e.g., the impact of a radical change in government policy or the merger of the two largest firms. On the other hand, in many cases the key assumptions entering into models, such as ‘constant relative risk aversion’ or ‘geometric discounting’ can be very credibly tested. We can use existing micro data on thousands of household decisions, as well as experiments, to measure ‘how close’ behavior is to the assumption.


There is also substantial debate over what it means, and whether/when it is valuable to ‘test an Economic model in the laboratory’. See the discussion by Sugden and Sitzia, 2011; “Implementing theoretical models in the laboratory, and what this can and cannot achieve.”

1.4 Aside: Empirical work/econometrics

I want you to have a sense of what this is, and how it connects to economic theory. This is relevant background for the present module, and extremely important for your later research/dissertation work (and it may give some perspective for other modules like Econometrics). I give a supplement on this which I highly recommend reading in supplement 10.4 ‘Empirical research’.

References

Akerlof, George A. 1970. “The Market for" Lemons": Quality Uncertainty and the Market Mechanism.” The Quarterly Journal of Economics, 488–500. https://doi.org/10.2307/1879431.

Carneiro, P. 2011. “Estimating Marginal Returns to Education.” The American Economic …. https://doi.org/10.1257/aer.101.6.2754.

Friedman, Milton. 1953. “The Methodology of Positive Economics.” The Philosophy of Economics: An Anthology 2: 180–213.

Nicholson, Walter, and Snyder Christoper. 2007. Intermediate Microeconomics: And Its Applications/by Walter Nicholson. POS 339.23 N52 2007.

Sugden, Robert. 2017. “Credible Worlds : The Status of Theoretical Models in Economics.”