Introduction

Economics is a social science. What does this mean?

(All definitions are from Oxford dictionary.) social science: The scientific study of the structure and functions of society

This means that issues in the social sciences concern society. Even if we often get lost in technical problems, ultimately, the question we are trying to answer has to do with “the structure and functions of society”.

One can only assume that the term science belongs there.

science: The state or fact of knowing

That’s not very helpful. It could apply to anything: business studies, woodworking, engineering, literature, ... I don’t think that this is what people had in mind when they added the word science to the field. scientific method: a method of procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses

Essentially, this has meant an endless cycle of

1. observation (sometimes initially just anecdotic)

2. explanation with a theory (made up of assumptions)

3. testing the theory using data and statistical techniques

4. modifying the theory to better fit the observations

5. retesting with new data

6. ...

This means that the social sciences call for a rigorous approach. Scientific procedures must be followed. Hence, they must be learned. We often spend a lot of time doing this. Alas, sometimes more than remembering its conclusions and thus, its usefulness.

But rigor is demanding. Otherwise, we would not need an MA. We must deal with that as best we can. Some social scientists spend most of their time on improving the techniques, while keeping in view its utility in the social sciences. Others only apply them. Some do a bit of both. There are excesses at both ends. Some answer useless questions using sophisticated techniques; others pretend to have found the answers to burning and all-encompassing questions without any attempt at rigorous analysis.

So much for economics as a social science. What about economics itself?

economics: The science relating to the production and distribution of material wealth

How indeed do we study “the production and distribution of material wealth”?

Scientifically.

This means that you must learn the scientific techniques, but ultimately answer some question in economics. Techniques must be learned in order to conduct empirical analysis (econometrics) and theoretical ones. This course fits with the latter.

In the economics MA, it is common to subdivide the theoretical analyses into two subfields: microeconomics and macroeconomics. We are no exception. The subdivision is historical and somewhat artificial. We are here to study microeconomic theory.

This course is thus intended to provide you with the tools to conduct microeconomic theoretical analyzes and be able to understand them.

But what is a theory? Admittedly, this gets a little more complicated.

Here’s one view: theory: A scheme or system of ideas or statements held as an explanation or account of a group of facts or phenomena; a hypothesis that has been confirmed or established by observation or experiment, and is propounded or accepted as accounting for the known facts

Here’s another theory: In loose or general sense: A hypothesis proposed as an explanation; hence, a mere hypothesis, speculation, conjecture

Both are from the Oxford Dict. In economics, it seems that rarely is a theory ever completely “established”. There is always some going back and forth between theory and empirical testing. In any case, what matters for us is that a theory is made up of a collection of hypotheses, from which we derive conclusions.

hypothesis: A supposition or conjecture put forth to account for known facts; esp. in the sciences, a provisional supposition from which to draw conclusions that shall be in accordance with known facts, and which serves as a starting-point for further investigation by which it may be proved or disproved and the true theory arrived at.

Note that we use logic to go from the hypotheses to the conclusions. That’s why a course in microeconomic theory is heavy with mathematics. It’s not because we like math per se; remember, we are here to study “the production and distribution of material wealth”. It’s because it’s a relatively sure and efficient way to go from some hypotheses to some conclusions. (But remember the possible excesses mentioned above. It happens.)

In any case, a theory is only as strong as its basis, i.e. its hypotheses. That is where it gains, or looses, its appeal. This is why we must spend a lot of time on developing and understanding them. Economic theory is full of recurrent hypotheses that an MA student ought to master. (Some more controversial than others.) Since we are here to study “the production and distribution of material wealth”, a natural place to start is with production decisions.

We would like to know how people decide to produce what they produce. To answer this, we need to develop theories about what people want to consume, about what people want to produce, and how those wants interact.

This course begins with theories about what people want to produce. Three classes are devoted to it. It will be followed by another three classes on theories about what people want to consume, which will be taken up by my colleague Marcel Mrette. Those initial classes will be somewhat intensive in their discussions of hypotheses and techniques. They are therefore not so much geared towards conclusions in the social sciences.

We will then move on with theories on interactions. Those sections build on the previous and will be more result oriented.

Production:

We begin by studying the supply side of the economy. This the process by which goods and services being consumed are produced. We view this side as composed of productive units conveniently referred to as firms. The term firm is meant to include anything from large corporations to household or individual productive units. It thus applies equally well to industrial economics and development economics.A full consideration of a firm’s decisions should account for its labor organization, its ownership structure, its managerial structure, as much as what it can actually produce. We begin by considering only the latter. The firm is thus modeled as a black box which produces outputs with inputs. This is not to say that organization, ownership and management are less important. Quite the contrary. But it will help us move faster to a minimally useful model to study markets.

In order to analyze what people want to produce, we begin, as would be expected, by specifying how producers can produce goods and services. That’s the subject of chapter 1 titled Technology.

We use those properties of production technology to understand the behavior of a profit maximizing firm in chapter 2. This enables us to derive the properties of a profit function in chapter 3.

Alternatively, the properties of a production technology can also be used to understand the cost minimizing behaviour of a firm (chapter 4). This in turn leads us to derive the properties of a cost function (chapter 5).

Finally, in chapter 6, we look at how one can derive the properties of a given technology indirectly by looking at the cost function. This is referred to as the principle of duality of the production process. It means that one can derive the cost function of a firm starting from its technology, or do the converse, i.e. derive the technology from the cost function. This is extremely useful for empirical work because technology is much more difficult to observe than costs.

Chapter 1

The technology

NB It would be counterproductive to try to go through all the details of each sections of Varian’s book in class. Students are expected to read each section carefully and is responsible for it. My presentation will only cover a selection of the main points.

In this chapter, we present

1. Different ways to represent production possibilities.

2. The usual properties that those production possibilities should have.

The manner in which an individual or a firm can produce (final or intermediate) goods depends on the available technology. A technology describes how inputs can be combined to produce outputs. This is sometimes done in a very crude manner, or in very fine details.

For instance, one may assume that one type of output is produced with one type of input in a linear manner.

Alternatively, one may want to specify many outputs produced with many different types of inputs, used at different points in time, some in the form of flows, others in the form of stocks, etc.

You have previously seen that a technology can be summarized neatly by a production function. It constitutes a quite natural an intuitive way to do it. But depending on the setting, there are other ways to describe a technology which may be more general or useful. This chapter sets out to describe the most important among them.

1.1 Specification of technology

Consider an economy with n commodities. A production plan (equivalently: production vector, input-output vector) is a list of net outputs represented by vector y in R^{n}. y_{i} < 0 if it is a net input, and conversely for a net output. Note that this description is quite general. For instance, it allows for the production of any number of outputs by the firm, and some outputs may also be used as inputs. It takes electricity to produce electricity; it takes cars to produce cars... Example: Suppose that n = 5. Then y = (−5, 2, −6, 3, 0) means that 2 and 3 units of goods 2 and 4 resp are produced, while 5 and 6 units of goods 1 and 3, resp, are used. Good 5 is neither produced, nor used as an input in this production vector.

There are different ways to describe a production technology:

1. Production possibilities set (or simply production set): The set of all technologically feasible production plans. Denoted Y. It’s a list of feasible production plans for the firm. If y is feasible, then it is in Y. If y ∉ Y, then y is not feasible.

2. Input requirement set: If the firm produces only one output y, we can write:

(1.1) V (y) = {x in R_{+}^{n} : (y, −x) is inY }

It says that with input vector x, it is possible to produce at least y units of outputs.

3. Isoquant:

(1.2) Q(y) = {x in R_{+}^{n} : x is in V (y) and x is not in V (y′) for y′ > y}

Those are all the input vectors that can produce output level y, but no more.

4. Production function:

It describes a single-output technology.

(1.3) f(x) = {y in R : y is the maximum output associated with −x in Y }

5. Transformation function: It is the n-dimensional analog of the production function. (See full description in the book.)

Present examples of Cobb-Douglas and Leontief technologies directly from book.

Let us now present and discuss some of the most commonly assumed properties of a production set. Their relevance will depend on the context of the problem being analyzed. As will be seen, some of them are mutually exclusive.

Here is a list of the properties of a production set to be discussed:

monotonicity (= free disposal)

convexity

closedness

nonemptyness

constant returns to scale (also increasing, decreasing)

homogeneity (also homotheticity)

The production technology usually assumes monotonicity, i.e. 1 (monotonicity) If x is in V (y) and x′ ≥ x, then x′ is in V (y). This assumption simply allows for free disposal of inputs. It enlarges the input requirement set.

Give intuition with figure 1.3 from book.

1.2 Convex technologies

Profit Maximization

In this course, we generally assume that firms maximize profits. Is that reasonable?

To answer that, we should first think about what is a firm:

Simply put, it acquires inputs in order to produce outputs. Inputs are paid for. Outputs generate revenues. Profits is the difference between the two.

So why would one bother to create a firm? because higher profits for the owners of the firm allows them to consume more goods and services. Hence owners will naturally try to maximize profits.

Maximization of profits turns out to be also borne out by empirical observations.

If the managers of a firm do not seek to maximize profits, (nonsatiated) firm owners will likely seek to replace them.

If owners themselves do not seek to maximize profits, chances are an outside (nonsatiated) entrepreneur will seek to acquire the firm at an attractive price for present owners.

As a result, we generally make the assumption that firms seek to maximize profits. This way, we ignore all the important contractual relationships that are important to a firm. It is a simplifying assumption that can lead us to many interesting and relevant results, though it is obviously leaves out many important features of a firm.

A rigorous approach therefore makes a clear distinction between a firm’s objective, which is to maximize profits, and its constraints, which are of two general types: technological constraints and market constraints.

Profit maximization simply means maximizing the difference between revenues and costs. Revenues depend on both output prices and quantities; costs depend on both input quantities and prices.

To start with, it will be assumed that firms face the price-taking constraint, which is usually taken as a competitive firm. Hence, a firm chooses its production plan taking as given a schedule of input and output prices.

2.1 Profit maximization

(Continued in handwritten notes.)

Duality

Here is a taste of the main results that we will get from this chapter:

• If we start with a cost function, we can derive a corresponding production technology. In other words, we do the reverse from before, which was to derive a cost function associated with a production technology.

• Moreover, if the underlying production technology is convex (i.e. the production function is quasiconcave), then the derived production function will be identical to the underlying one.

• If the underlying production function is not quasiconcave, the derived production function is a “concavication” of it.

• If you are given a function that has all the properties of a cost function, it will generate a production function for which it is the cost function.

Usefulness:

• Some results are easier to show with the cost function or profit functions than directly from the production function. EG The demo that firms prefer fluctuating prices than the stabilized expected value used the convexity property of the profit function. It would be much more difficult to derive that result directly from the production technology.

• With costs or profit functions, we do not need to solve the max problem of a firm. Analysis is thus simplified. Note that the cost and profit function have already solved the profit max problem.

• Knowing that the three properties of homogeneity, monotonicity, and curvature (convexity for profit fctn, concavity for cost fctn) exhaust the properties of those fctns, any proposition about firm behavior that cannot be traced back to one of those properties imply that they do not follow from profit max behavior of the firm.

• There are also some important advantages for econometric work. (Con’t in handwritten notes.)