Consumption II: Characteristics demand theory and revealed preference theory

 Characteristics demand theory states that consumers derive utility not from the actual contents of the basket but from the characteristics of the goods in it. This theory was developed by Kelvin Lancaster in 1966 in his working paper “A New Approach to Consumer Theory”.

This approach allows us to predict how preferences will change when we change the options or baskets presented to consumers by studying how these vary according to the change in the characteristics that make them up. With conventional theory, the introduction of a new option meant that we could not reliably predict how this would slot into the consumer’s preference map. However, by relying on a study of the characteristics rather than the goods or service involved, we can predict how changes will affect a consumer’s behaviour without needing to start once again empirically.

This allows us to calculate ‘shadow prices’ for different attributes without having a price for the good itself by associating utility to the characteristics that make up the good rather than the good itself. With these ‘shadow prices’, we can solve utility maximisation problems for baskets or options for which we do not have empirical evidence, as Lancaster demand also lends itself to building utility functions (based on the amount of each type of characteristic rather than the amount of each type of good in a particular basket).

Characteristic demand theory also helps justify the existence of brands. Luxury brands are able to charge a surprice for their products by differentiating themselves from competitors that sell similar goods. In the first diagram, if we suppose that both brands have the same characteristics and are perfect competitors, then we will choose the basket that maximises our total consumption. This means will tend to opt for the cheaper brand, which allows us to reach the highest utility curve: for a given amount of money, we are able to buy either a certain amount of brand 1 (point B) or a certain amount of brand 2 (point A). We choose A since it’s on a higher indifference curve. Point C represents a higher utility curve achieved by a drop in the price of brand 1. However, even though brand 1 got cheaper, we’ll still consume A, since it remains on a higher indifference curve.

In the second diagram, if we look at Lancaster demand, our utility functions will be based on the characteristics that each basket contains rather than on the amount of each type of good. Here, it is no longer ‘all or nothing’- we can allow for convex demand curves that represent our preference for variety in consumption: point C. This time, if the price of one brand drops, we will change our outcome: we can opt for point D.

How do we know enough to build an individual’s demand curve? Do we have to watch them endlessly as they affront each new possibility? Revealed preference theory aims to simplify the information necessary to be able to make assumptions about an agent’s choices through two basic tenants.

Revealed preference theory

Revealed preference theory is attributable to Paul Samuelson in his article “Consumption Theory in Terms of Revealed Preference”, 1948. Consumer theory depends on the existence of preferences which materialise into utility functions. These utility functions are maximised by consumers subject to a budget restraint. The issue is that it is difficult to accept that individuals really have a definite mathematical formula in mind when choosing between different options. What revealed preference theory does is work backwards to assume that we can deduce these utility functions from consumer behaviour. Analysing these choices leads us backwards to a set of preferences that influences the choices they make. It therefore allows economists to study consumer behaviour empirically.

There are two main axioms to the theory, both based on completeness and transitivity:

WARP (Weak Axiom of Revealed Preference): If A is revealed preferred to B (A RP B), then it must be so in every case. That is, if a consumer ever chooses B, then we must assume that A was previously chosen and that the budget constraint had enough ‘left over’ to allow a consumer to choose B as well.

SARP (Strong Axiom of Revealed Preference): This adds transitivity. If there are only two goods, then it is clear that WARP already defines a consumer’s choice: A over B. However, the SARP adds the idea of indirectly revealing preferences: if A is chosen over B and B over C, SARP and transitivity dictate that A is also preferred to C, so A is indirectly revealed to be preferable to C (A R* C). This drastically reduces the amount of empirical evidence necessary to define consumer preferences.

 

In the case shown in the figure below, we know that C is indirectly preferred to B (C R* B) because it allows us to reach a higher utility curve. Because C and B define a space (R*), and we know that C, B and A are contained within R*(R*{(C,B)}), then we can say that C RP A RP B, that is, by knowing from observation that C is indirectly preferred to B, we can tell that C is revealed as preferable to A (C RP A) and that A is revealed as preferable to B (A RP B).

If we think of A, B and C as infinitely complex bundles of goods, we can map out all a consumer’s choices. In theory, we can track this backwards to actually build utility functions if we have access to unlimited data. Without actually having to do this, we can aggregate consumer data to reveal general truths about a certain population’s preferences.

As we have seen throughout this Learning Path, consumer theory allows us to understand how consumer needs are met, respecting a certain budget constraint and given possible price changes. Characteristics demand theory and Revealed preference theory expands the way we study consumer theory.

https://cutt.ly/s8oKJ80

Consumption II: Laspeyres and Paasche price indices

 

Summary

This Learning Path is a bit more of a mixed bag than the previous one, finishing off our consumer choice problem, looking at the some useful implications of this in demand theory before moving on to other types of demand theories.

Price indices are used to monitor changes in prices levels over time. This is useful when separating real income from nominal income, as inflation is a drain on purchasing power. The two most basic indices are the Laspeyres index (named after Etienne Laspeyres) and the Paasche index (named after Hermann Paasche).

Both indices are very similar:

Laspeyres index:

Paasche index:

 

They work by dividing expense on a specific basket in the current period (the sum of p*q for each product in the basket considered when calculating the index) by how much the same basket would cost in the base period (period 0). The main difference is the quantities used: the Laspeyres index uses q0 quantities, whereas the Paasche index uses period n quantities.

What this translates to is that a Laspeyres index of 1 means that, as the nominator is the same as the denominator, an individual can afford the same basket of goods in the current period as he did in the base period. As the quantities are the same, this just leaves price as a variable, which must remain unchanged. This translates to the concept of compensated variation (CV): by how much do we need to increase an individual’s income in order to offset inflation? This is, at the new level of prices, how much is required to compensate the effect of the price increase? In the top diagram, we see that an increase in the price of good x1 means a move to a lower utility curve. The compensated variation is the theoretical amount of money the individual would need to maintain their level of utility, putting them back on their original utility curve.

What we can also see is that the Laspeyres index overestimates this CV: it assumes that inflation has a greater effect than it does. This can be more clearly seen in the bottom diagram. The change in price from P0 to P1 leads to a change in the quantity of X consumed from X0 to X1. The green rectangle shows the Laspeyres effect associated with this, which is greater than the CV effect. The CS effect, the dark blue trapezoid, shows the loss of consumer surplus associated with the price variation.

A Paasche index of 1 means that the consumer could have afforded the same bundle of goods in the base period as they can now. This can be translated to the concept of equivalent variation (EV): how much income would we have to take away from an individual, at the base price level, to have the same impact on their utility as the inflation between the base period and period 1? That is, if we took the individual’s utility in 2009 at that price level, how much would we have to take away from it to have the same utility as a person on the same income with 2012’s level of prices? Applying the same dynamic we applied to the Laspeyres index, we can see from the top diagram that the Paasche index underestimates the equivalent variation.

We can see this more clearly in the bottom diagram: the consumer surplus is greater than the variation effect, which is in turn greater than the Paasche effect.

If we put this all together, it may be easier to understand each of the effects and understand their downisdes:

These diagramas are simply a combination of the two we saw individually. They help us, however see the differences between both indices. The main downside to these indices is the fact that they do not take into effect substitution effects. When the price of something rises, we tend to consume less of it. Because the Laspeyres index uses base period quantities, it tends to overestimate inflation by assuming that individuals’ income expense is still distributed in the same way. The opposite is true of the Paasche index: because it uses current period quantities, it underestimates inflation.

Therefore, for normal goods, if inflation exists:

L > CV > CS > EV > P

 

Video – Laspeyres index:

Video – Paasche index:

So far, we have looked at consumer theory as individuals choosing one good over another. However, newer theories examine the possibility of consumers maximising utility by choosing characteristics of particular goods (not ‘music’ over ‘reading’, but ‘progressive rock’ over ‘Dickens’- leaving open ‘crime novels’ over ‘heavy metal’). Let’s explore how this changes demand functions.

https://cutt.ly/N90I6tb

Consumption II: Marshallian and Hicksian demands

 Marshallian and Hicksian demands stem from two ways of looking at the same problem- how to obtain the utility we crave with the budget we have. Consumption duality expresses this problem as two sides of the same coin: keeping our budget fixed and maximising utility (primal demand, which leads us to Marshallian demand curves) or setting a target level of utility and minimising the cost associated with it (dual demand, which gives us Hicksian demand curves). We must also look at the Lagrangian functions where we obtain the first derivatives.

Marshallian and Hicksian demands stem from two ways of looking at the same problem- how to obtain the utility we crave with the budget we have. Consumption duality expresses this problem as two sides of the same coin: keeping our budget fixed and maximising utility (primal demand, which leads us to Marshallian demand curves) or setting a target level of utility and minimising the cost associated with it (dual demand, which gives us Hicksian demand curves). We must also look at the Lagrangian functions where we obtain the first derivatives.

Marshallian and Hicksian demand curves meet where the quantity demanded is equal for both sides of the consumer choice problem (maximising utility or minimising cost). For prices above this equilibrium point, consumer wealth is higher with Hicksian demand curves than Marshallian demand curves, because to maintain utility constant, Hicksian demand curves assume real wealth remains unchanged. Marshallian demand assumes only nominal wealth remains equal. The opposite is true for prices below this point: Marshallian demand assumes that as nominal wealth remains the same but price levels drop (negative inflation), the consumer is better off. Hicksian demand assumes real wealth is constant, so the individual is worse off. This is why Marshallian demand curves are more ‘stable’: they reflect both rent effect and substitution effect. Hicksian demand curves only show substitution effects (utility is constant, therefore rent must remain constant), which means that demand varies with price only because other options become more attractive.

Formally,

Marshallian demand (dX1) is a function of the price of X1, the price of X2 (assuming two goods) and the level of income or wealth (m):

X*=dX1(PX1, PX2, m)

Hicksian demand (hX1) is a function of the price of X1, the price of X2 (assuming two goods) and the level of utility we opt for (U):

X*=hX1(PX1,PX2,U)

For an individual problem, these are obtained from the first order conditions (maximising the first derivatives) of the Lagrangian for either a primal or dual demand problem.

Marshallian demand makes more sense when we look at goods or services that make up a large part of our expenses. Here, the income effect is very large. However, for smaller purchases, we are willing to spend more or less any amount as long as we derive the utility we expect to.

Video – Marshallian and Hicksian demand curves:

https://cutt.ly/P2s2qT6

Consumption II: Consumption duality. Substitution and income effects.

Consumption duality 

There are two ways to solve a consumer’s choice problem. That is, we can either fix a budget and obtain the maximum utility from it (primal demand) or set a level of utility we want to achieve and minimise cost (dual demand).

The way to solve either problem is very similar: we look for the Lagrangian function and obtain first order conditions, then solve the system.

When dealing with primal demand, that is, utility maximisation, our Langrangian is as follows:

Subj. to:

So that:

That is, our Lagrangian is our utility function, which depends on x1, x2 minus the restriction- our budget. The first order conditions (which we obtain from the first derivatives) give us Marshallian demand curves.

When dealing with dual demand, that is, cost minimisation, our Lagrangian system is as follows:

Subj. to:

So that:
That is, our Lagrangian is our cost function, which depends on x1, x2 minus our utility function, which must equal a constant. The first order conditions give us Hicksian demand curves.

Video – Consumption duality:

We all know that, in theory, when the price of something goes up we buy less of it. But there are two factors at play here: one is the fact that we will look for something similar but less expensive and the second is the fact that if what goes up takes up a large proportion of our budget (a mortgage), we simply have less to spend. In the next entry, we cover the dynamics of this in more detail.

Substitution and income effects

This Learning Path is a bit more of a mixed bag than the previous one, finishing off our consumer choice problem, looking at the some useful implications of this in demand theory before moving on to other types of demand theories.

Generally, if the price of something goes down, we buy more of it. This is down to two effects:

• Income effect: because it’s less expensive, we have more purchasing power because it is a smaller drain on our personal finances.
• Substitution effect: because it offers more utility per unit of money, other alternatives become less attractive.

What Eugen Slutsky managed to do was find an equation that decomposes this effect based on Hicksian and Marshallian demand curves.

Graphically:

Mathematically, it is based on the derivatives of Marshallian and Hickisan demands:

The left hand side of the equation is the total effect- that is, the derivative of x (quantity) respect p (price). It shows us how much the total quantity of x that we consume varies when we change price. The next part is the substitution effect- how much the variation is due to us finding similar options. It is obtained from the derivative of the Hicksian demand with regards price. The right hand side is the income effect, how much changes in our purchasing power affect the amount we consume of a certain good. It is the derivative of the Marshallian demand with regards wealth (multiplied by the quantity).

Whether the SE and the IE are positive or negative when prices rise depends on the type of good:

	TE	SE	IE
+	Substitute goods	Substitute goods	Inferior goods
–	Complementary goods	Complementary goods	Normal goods

It is not always possible to tell what the total effect will be- if we are talking about inferior complementary goods, for example, the SE and the IE pull in opposite directions. The TE will depend on which effect is stronger.

Video – Income and substitution effects:

Marshall and Hicks treated substitution and rent effects differently, judging whether or not they should both be included in demand functions. Let’s see why and how this affects what we would, in theory, consume.

https://cutt.ly/L00ZAs6

Consumption II: Cost minimisation

 This Learning Path is a bit more of a mixed bag than the previous one, finishing off our consumer choice problem, looking at the some useful implications of this in demand theory before moving on to other types of demand theories.

We first pick up where we left off in our previous LP and turn the tables on our consumer choice problem in:

Consumption duality II:

Cost minimisation, the mirror image of utility maximisation,

Consumption duality, looking at both problems together before going on to…

Further analysis:

Substitution and income effects: why do we buy less of things when the price goes up?

Marhsallian and Hicksian demands: taking into account both or just one of the effects.

Price indices: keeping track of changes in price levels and the implications on demand.

Reshaping consumer theory:

Characteristics demand theory: Why do we really pick one thing over another? Just how picky are we really?

Revealed preference theory: How to guess what someone will pick without having to follow them around permanently.

Cost minimisation

Cost minimisation is a way of solving the optimisation problem regarding the utility function and the budget constraint, even though the most common way of doing this is by means of utility maximisation.

If we think about it, we don’t normally have a fixed budget for most purchases. We have a certain utility we expect to derive from them and we hope to spend as little as possible on them (but we don’t have a maximum budget).

In this case, it is utility that is fixed as a restriction, and cost that we can play around with. It’s like solving the consumer’s choice problem in a mirror image way to utility maximisation, and is associated with Hicksian demand curves.

The way we resolve this minimisation problem is very similar to utility maximisation, and is also done with a Lagrangian system, since there is a duality in consumption. In this case, we want to minimise our budget for a given utility:

Video – Cost minimisation:

https://bit.ly/3hFPhfP

Module 3 – Budget Constraint

 The Policy Question: Hybrid Car Purchase Tax Credit—Is it the Government’s Best Choice to Reduce Fuel Consumption and Carbon Emissions?

The U.S. government policy of extending tax credits toward the purchase of electric and hybrid cars can have consequence beyond decreasing carbon emissions. For instance, a consumer that purchases a hybrid car could spend less money on gas and have more money to spend on other things. This has implications for both the individual consumer and the larger economy.

Even the richest people – from Bill Gates to Oprah Winfrey – can’t afford to own everything in the world. Each of us has a budget that limits the extent of our consumption. Economists call this limit a budget constraint. In our policy example, an individual’s choice between consuming gasoline and everything else is constrained by his or her current income. Any additional money spent on gasoline is money that is not available for other goods and services and vice-versa. This is why the budget constraint is called a constraint.

The budget constraint is governed by income on the one hand, how much money a consumer has available to spend on consumption, and the prices of the goods the consumer purchases on the other.

Exploring the Policy Question

What are some of the budget implications for a consumer who owns a hybrid car? What purchase decisions might this consumer make given his or her savings on gas, and how does this, in turn, affect the goals of the tax subsidy policy?

3.1 Description of the Budget Constraint

LO1: Define a budget constraint, conceptually, mathematically, and graphically.

3.2 The Slope of the Budget Line

LO2: Interpret the slope of the budget line.

3.3 Changes in Prices and Income

LO3: Illustrate how changes in prices and income alter the budget constraint and budget line.

3.4 Coupons, Vouchers, and Taxes

LO4: Illustrate how coupons, vouchers, and taxes alter the budget constraint and budget line.

3.5 Policy Example: The Hybrid Car Subsidy and Consumers’ Budgets

3.1 Description of the Budget Constraint

LO1: Define a budget constraint, conceptually, mathematically, and graphically.

The budget constraint is the set of all the bundles a consumer can afford given that consumer’s income. We assume that the consumer has a budget – an amount of money available to spend on bundles. For now, we do not worry about where this money or income comes from, we just assume a consumer has a budget.

So what can a consumer afford? Answering this depends on the prices of the goods in question. Suppose you go to the campus store to purchase energy bars and vitamin water. If you have $5 to spend, energy bars cost fifty cents each, and vitamin water costs $1 a bottle, then you could buy 10 bars, and no vitamin water, no bars and 5 bottles of vitamin water, 4 bars and 2 vitamin waters and so on.

This table shows the possible combinations of energy bars and vitamin water the student can buy for exactly $5:

Energy Bars	Bottles of Vitamin Water
10	0
8	1
6	2
4	3
2	4
0	5

It is also true that you could spend less than $5 and have money left over. So we have to consider all possible bundles −including consuming none at all.

Note that we are focusing on bundles of two goods so that we maintain tractability (as explained in module 1), but it is simple to think beyond two goods by defining one of the goods as “money spent on everything else.”

Mathematically, the total amount the consumer spends on two goods, A and B, is:

(3.1) , $P_{A}A+P_{B}B$

where $P_A$  is the price of good A and $P_B$ is the price of good B. If the money the consumer has to spend on the two goods, his income, is given as I, then the budget constraint is:

(3.2)$P_{A}A+P_{B}B\le I$

Note the inequality: This equation states that the consumer cannot spend more than his income but can spend less. We can simplify this assumption by restricting the consumer to spending all of his income on the two goods. This will allow us to focus on the frontier of the budget constraint. As we shall see in Module 4, this assumption is consistent with the more-is-better assumption – if you can consume more (if your income allows it) you should because you will make yourself better off. With this assumption in place, we can write the budget constraint as:

(3.3)$P_{A}A+P_{B}B=I$

Graphically, we can represent this budget constraint as in Figure 3.1. We call this the budget line: The line that indicates the possible bundles the consumer can buy when spending all his income.

Figure 3.1 The budget line is the graph of the budget constraint equation (3.3).

LO2: Interpret the slope of the budget line

From the graph of the budget constraint in section 3.1, we can see that the budget line slopes downward and has a constant slope along its entire length. This makes intuitive sense: If you buy more of one good, you are going to have to buy less of the other good. The rate at which you can trade one for the other is determined by the prices of the two goods, and they don’t change.

We can see these details in Figure 3.2

Figure 3.2 Intercepts and slope for the budget line

We can find the slope of the budget line easily by rearranging equation (3.3) so that we isolate B on one side. Note that in our graph, B is the good on the vertical axis, so we will rearrange our equation to look like a standard function with B as the dependent variable:

(3.4) $B=\frac{I}{P_B}-\frac{P_A}{P_B}A$

Now, we have our budget line represented in point-slope form where:

The first part, $\frac{I}{P_B}$, is the vertical intercept.

The second part,$-\frac{P_A}{P_B}$ , is the slope coefficient on A.

Note that the slope of the budget line is simply the ratio of the prices, also known as the price ratio. This is the rate at which you can trade one good for the other in the marketplace. To see this, let’s return to the campus store with $5 to spend on energy bars and vitamin water.

Suppose you originally decided to buy 5 bottles of vitamin water and placed them in a basket. After some thought, you decided to trade 1 bottle for 2 energy bars. Now you have 4 bottles of vitamin water and 2 energy bars in the basket. If you want even more bars, the same trade off is available: 2 more bars can be had if you give up one bottle of vitamin water, and so on.

The slope of the budget line is also called the economic rate of substitution (ERS).

The slope of the budget line also represents the opportunity cost of consuming more of good A because it describes how much of good B the consumer has to give up to consume one more unit of good A. The opportunity cost of something is the value of the next-best alternative given up in order to do get it. For example, if you decide to buy one more bottle of vitamin water, you have to give up two energy bars. Note that opportunity cost is not limited to the consumption of material goods. For example, the opportunity cost of an hour’s nap might be the hour of studying microeconomics that did not happen because of it.

Changes in Prices and Income

LO3: Illustrate how changes in prices and income alter the budget constraint and budget line.

From our mathematical description of the budget line, we can easily see how changes in prices and income affect the budget line and a consumer’s choice set —the set of all the bundles available to her at current prices and income. Let’s go back to equation (3.3):

(3.3)$P_{A}A+P_{B}B=I$

We know from the previous Figure 3.3 that the vertical intercept for equation (3.3) is $\frac{I}{P_B}$ and the horizontal intercept is $\frac{I}{P_A}$.

Now consider an increase in the price of good A. Notice in Figure 3.3 that this increase does not affect the vertical intercept, only the horizontal intercept. As $P_A$  increases,$\frac{I}{P_A}$  decreases, moving closer to the origin. This change makes the budget line ‘steeper’ or more negatively sloped as we can see from the slope coefficient: $-\frac{P_A}{P_B}$. As $P_A$  increases, this ratio increases in absolute value, so the slope becomes more negative or steeper. What this means intuitively is that the trade-off or opportunity cost has risen. Now, the consumer has to give up more of good B to consume one more unit of good A.

Figure 3.3 Changing the price of one good changes the slope of the budget line.

Next, consider a change in income. Suppose the consumer gets an additional amount of money to spend, so I increases. I affects both intercept terms positively, so as I increases both $\frac{I}{P_B}$  and $\frac{I}{P_A}$ increase or move away from the origin. But I does not affect the slope: $-\frac{P_A}{P_B}$. Thus the shift in the budget line is a parallel shift outward – the consumer with the additional income can afford more of both.

4 Coupons, Taxes, and Vouchers

LO4: Illustrate how coupons, vouchers and taxes alter the budget constraint and budget line.

Budget constraints can change due to changes in prices and income, but let’s now consider other common features of the real-world market that can affect the budget constraint. We start with coupons or other methods firms use to give discounts to consumers.

Consider a coupon or a sale that gives consumers a discount on the price of one item in our budget constraint problem. A coupon that entitles the bearer to a percentage off in price is essentially a reduction in price and has precisely the same effect. For example, a 20% off coupon on a good that normally costs $10 is the same as reducing the price to $8.

More complicated is a coupon that gives a percentage off the entire purchase. In this case, the percentage is taken from the price of both items A and B in our budget constraint problem. In this case, the price ratio, or the slope of the budget constraint, does not change.

For example, if the price of A is regularly $10 and the price of B is regularly $20 then with 20% off the entire purchase, the new prices are $8 and $16 respectively. Intuitively, we can see that this is equivalent to increasing the income, and achieves the same result: by expanding the budget set, the consumer can now afford bundles with more of both goods.

Product	Regular Price	New Price with 20% discount on entire purchase
A	$10	$8
B	$20	$16

Another common discount is on a maximum number of items. For example, you might see an advertisement for 20% off up to three units of good A. This discount lowers the opportunity cost of A in terms of B for the first three units, but reverts back to the original opportunity cost thereafter. Figure 3.4 illustrates this.

Figure 3.4 The effect of a 20% discount on the first A̅ units of A.

Taxes have the same effects as coupons but in the opposite direction. An ad valorem tax is a tax based on the value of a good, such as a percentage sales tax. In terms of the budget constraint, an ad valorem tax on a specific good is equivalent to an increase in price, as shown in Figure 3.5. A general sales tax on all goods has the effect of a parallel shift of the budget line inward. Note also that income taxes are, in this case, functionally equivalent to a general sales tax, they cause a parallel shift inward of the budget line.

Figure 3.5 An ad valorem tax changes the slope and horizontal intercept of the budget line.

Vouchers that entitle the bearer to a certain quantity of a good (either value or quantity) are slightly more complicated. Let’s return to your purchase of vitamin water and energy bars. Suppose you have a voucher for 2 free energy bars.

You have $5

The price of 1 energy bar is $0.50

The price of 1 bottle of vitamin water is $1.

How would we now draw your budget line?

One place to start is to consider the simple bundle that contains2 energy bars and 2 bottles of vitamin water. Note that giving up 1 or 2 bars does not allow the student to consume any more vitamin water. The opportunity cost of these 2 bars is 0, and so the budget line in this part has a 0 slope. After using the voucher, if the student wants more than 2 bars the opportunity cost is the same as before – .05 a bottle of vitamin water – and so the budget line from this point on is the same as before. The new budget line with the voucher has a kink.

5 Policy Example: The Hybrid Car Subsidy and Consumers’ Budgets

For several modules, we have considered the policy of a hybrid car tax credit. In Module 1, we thought about various driving preferences of a typical consumer. In Module 2, we translated these preferences into a type of utility function and corresponding indifference curve. Now, let’s think about the appropriate budget line for our policy example.

To start, let’s use the same two axes as we used for the indifference curve map as shown in Figure 3.6. In other words, let’s place ‘miles driven’ on the horizontal axis and $, which is all the money spent on other consumption on the vertical axis. For now, we won’t specify the precise level of income..

Now we can ask, what is the price of ‘other consumption?’ Since we are talking about money left over after paying for miles driven, the price for other consumption is simply 1. This is because we are talking about money itself and the price of a dollar is a dollar. So, the intercept on this axis is simply the value of I.

But what is the price of a mile driven? This question is more complicated and includes the cost of maintenance and depreciation. However, because we are focused on the effect of increasing the miles per gallon of gas, let’s concentrate on only the cost as it relates to the purchase of gasoline. In this case, the cost of driving a mile is the price of gasoline divided by the car’s miles per gallon (MPG). Since we are again interested not in an individual but a group, we can use the average price of a gallon of regular gas divided by the average MPG of cars driven in the United States as a reasonable approximation of the cost of a mile driven in a non-hybrid cr. Now we have the ‘price’ of driving a mile; dividing income by this price gives us the intercept on the ‘miles driven’ axis.

Figure 3.6 A consumer’s budget constraint for the hybrid car policy

Now that we have a budget constraint for our electric and hybrid car subsidy policy example, we can see the effect of the policy on the constraint. Doubling the MPG from 20, say, to 40, dramatically reduces the price of driving a mile . This reduction causes the ‘miles driven’ intercept to move upwards and the entire budget constraint to move outward. Note that now the typical consumer can afford to consume bundles with more of both miles driven and everything else – bundles that were unavailable to them prior to the policy.

Equation (3.4) summarizes the budget constraint for miles driven and other goods.

(3.4) Income = (PMiles Driven)(Miles Driven) + Dollars Spent on Other Consumption

https://bit.ly/3gDBvcN