Welcome back to module two, Quality and Consumers.

My name is Carlo Russo,

and I am associate professor in agricultural economics at

the Department of Economics and Law at the University of Cassino and Lazio Meridionale.

Now, let's move on to the second topic on lesson one, consumer choice.

We investigate consumer decision in a differentiated market,

which means when quality is important.

The discussion builds on standard consumer theory.

I assume that we all have had an intermediate microeconomic class at the undergrad level.

Please take a moment to answer the following question.

If you're not clear about the answer,

and the basic concepts,

please consider reviewing your micro theory before moving on.

In this section, we spoke to consumer problem in a differentiated market,

which means when quality is important.

As you know, standard micro theory models

the consumer problem as a maximization of the utility function under a budget constraint.

Yet, in this standard approach,

quality is not considered.

There are not attributes or other references to quality.

Here we place the model to incorporate quality

using the building blocks from Section one.

We know that when quality is important consumers derive utility from attributes,

and the product is just a means to obtain these attributes.

In terms of theory,

it means that the attributes,

not the product are the argument of the consumer utility function.

Another difference with the standard consumer problem is

that a consumer cannot buy attributes directly.

Attributes can be consumed only by purchasing products.

I cannot buy health,

but I can buy healthy oranges.

Of course the consumer faces the typical budget constraint.

The expenditure for the basket of goods must be affordable,

that is less or equal than available budget.

And yet the consumer faces an additional constraint.

The desired bundle of attribute must be obtained from a combination of existing product.

We call this the product constraint,

the bundle of attributes must obtainable from

a linear combination of non-negative quantities or existing goods.

Now let's have a closer look at the changes in utility function and constraint.

Let's start with the utility function.

Compare the standard approach with our quality oriented approach.

We call it the Lancaster model named after the economist who did it first.

The argument that utility function is

different product in the standard approach than the attributes in the Lancaster one.

Standard consumers like product per se,

the Lancaster consumers like what the product can do for her or him.

The product constraint drives the decision process.

We know that consumer must buy product in order to obtain attributes.

There was one, our building blocks.

We also know that product contain a variety of attributes.

It's product in a different proportion.

The idea is that consumers can mix products in a different way,

creating baskets that deliver different combination of attributes.

The consumer chooses the affordable and obtainable basket

that gives the utility maximizing attribute combination.

The product attribute matrix is a simple way to represent the product constraint.

Consider metrics such that the rows are products,

and columns are attributes.

In this example we restrict our attention to fruits,

and relevant products are apples, oranges and bananas.

Of course we can extend the number of products if we want.

Fruits have several attributes.

For simplicity we report only the average sugar content, grams per hectogram,

vitamin C micrograms, and fiber grams per hectogram.

Again we consider just three attributes,

but we could extend to as many as a business we think are relevant.

We can feel the metrics with the content of each attribute within each product.

For example a hectogram of apples has 11.8 grams of sugar on average,

same quantity of oranges has 10.6 and so on.

Now we illustrate the solution of the consumer problem in the Lancaster model.

The problem is maximize utility under two constraints, budget and product.

We use a graph to explain the properties and the solution,

and we work the optimal consumer choice that miss that.

We refer to our fruit example.

We consider a consumer who's interested in the sugar content,

and the vitamin content only.

We want to find the optimal combination of oranges and banana she can buy.

We start from step one,

defining the attribute space.

This is a graph where the x is represented by the quantity of attributes.

Here on the x axis,

we report the quantity of sugar,

how many grams for sugar,

and in y axis the quantity of vitamin

C. The graph represent any possible combination of attributes.

This is important because in this way we can define the consumer utility at any point.

Yet we know that consumer must buy product.

So the second step is placing products on this graph.

For this purpose, we use the product attribute matrix we introduced just a minute ago.

From this matrix we can see that an hectogram of oranges

has an average of 10.6 grams of sugar and

49 units of vitamin C. These coordinates identify

the point in the attribute space corresponding to a hectogram of oranges.

Similarly a hectogram of bananas has 20.4 grams of

sugar and 10 units of vitamin C.

The point with this coating is correspond to a hectogram of bananas.

We can replicate this process for any quantity,

for example two hectograms of oranges caries twice the quantity of one, as one hectogram.

This two hectogram of oranges can be found at the coordinates 21.2 and 98.

Same process for bananas.

In theory, we can run this exercise for any non-negative quantity of oranges.

If we do we obtain a line like this.

The orange line is the orange product line.

This is the set of attributes,

but those that are attainable by consuming oranges only.

If my basket is composed of oranges alone,

I can obtain any attribute combination along the product line,

but not attribute the combination outside the line.

Of course I can repeat the same exercise with bananas,

and I would take the banana product line.

That is the set of attribute combinations I can

obtain consuming a basket composed of bananas only.

Once we derive the product lines,

we can identify the feasible set.

This is the combination of attributes that are

at the same time attainable and affordable.

A combination of attributes is attainable if it satisfies the graph product constaint.

This means if it can be obtained

from a linear combination or non-negative quantity of products.

In the green area,

the one between the two product lines we have the set of attainable combination.

The combination in red area are not attainable.

For example assume that they want a combination such as zero sugar and

49 genius of vitamin C. Zero sugar means that the combination lies on the y axis.

However, I can obtain such a combination,

because even if I consume vitamin rich oranges only,

still I get a positive quantity of sugar.

This is because oranges do have sugar whatever I like it or not.

If I want vitamins,

I have to consume a little bit of sugar.

A combination of zero and 49 is simply not attainable.

The green area between the product is a set of

attainable attribute combination of others indirect and unattainable.

Now let's focus on affordability.

A combination of attributes is affordable if it satisfies the budget constraint.

If the expenditure for buying a corresponding products is at most equal to the consumer,

well the combination is affordable.

In order to represent the budget constraint in a graph,

we need to mix assumption about price and consumer wealth.

For example assume that the consumer as a person worth of two euros.

Oranges are two euros per hectogram and bananas are one euro per hectogram.

If the consumer invests her entire wealth in oranges,

she can buy at most one hectogram of oranges.

From the product attribute metrics we know that a hectogram of

orange is represented at the coordinates 10.6

grams of sugar and 49 micrograms of vitamin

C. Similarly if the consumer invests her entire wealth in bananas,

she can buy of most two hectograms of bananas.

The quantity is found at the coordinates 40.8 grams of sugar and 20

micrograms of vitamin C. We can find the budget constraint connecting the two points.

We are now able to divide an attribute space into three areas.

The red areas where the attribute combination are not attainable.

The blue area where the attribute combination are attainable,

but they are not affordable.

And finally the green area where the attribute combination are attainable and affordable.

This is our feasible site.

To find the solution of the problem,

we need to consider the consumer utility function.

We represent this function with the usual indifference curves.

As you know indifference curves in standard consumer problem represent

the set of product communication yielding the same utility therefore to the consumer.

Here the notions to see only we consider the set

of attribute combination yielding the same level of utility.

Indifferent curves you have some space work exactly as standard utility curves.

The higher the indifference curve,

the higher is utility derived.

This means that consumers utility increases in the direction of the blue area.

The best choice for the consumer is

the feasible amount of attribute that maximize his or her utility.

This is the bundle in the feasible set that

allows the consumer to reach the highest indifferent curve.

You can find it at the tangency point between

the budget constraint and indifference curve,

the one marked with the red dot.

Any higher indifferent curve represents unfeasable combination of attributes only.

We can project the point to the axis to find the optimal quantity of each attribute.

But we are interested in finding the optimal combination of products too.

We can find the quantity of oranges projected

the point onto the orange from the line parallel to the banana for that line.

Similarly we can find the quantity of bananas projecting

the point onto the banana to the line parallel to the orange product line.

The highlighted red segment represent the quantity of oranges,

and the green segment is the quantity of banana.

the optimum consumption bundle depends on three key factors,

the product attribute matrix defining the position of the product lines.

Consumers utility function defining indifference curves,

and the budget constraint,

which is price and wealth.

A change in any of these factor determines a change in the optimal bundle of product.

For example let's consider a change in prices,

and assume that we dropped the price of oranges from two to one.

Of course euros per hectogram.

This change means a shift in the budget constraint.

If the consumer uses his entire wealth to buy oranges,

now he can buy two hectograms of oranges as in the point up there.

Of course the point on the banana product line does not change,

because the price of banana has not changed.

Now we can draw a new batch of line, the red line.

With the new budget line,

the feasible set is larger and the consumer can obtain

higher utility, higher indifference curves.

So the new optimal choice is located at a tangency point of the new budget constraint,

and that indifference curve.

As you can see, the consumer now consume much more vitamin C and a bit more of sugar.

This is because the change in relative prices make oranges less expensive.

The consumer in fact buys many more oranges and fewer bananas.

As you can see as soon as we change one of the three factor,

the optimal location changes.