Government debt and wealth in the Global South

5 Government borrowing to shift spending over time: Consumption

Unit 10 of The Economy 1.0 and Unit 9 of Economy, Society, and Public Policy cover the same model. If you are not familiar with constrained choice models and indifference curves, read Sections 3.2–3.6 of The Economy 2.0: Microeconomics before reading this section.

As discussed in Section 1, the fundamental issue faced by the government of a country when contracting debt is not that different from that faced by a household or an individual. The issue here is dealing with changing income and/or spending needs in time. (For example, the DRC (Zaire) faced volatile copper prices in the 1970s, which resulted in high fiscal revenues in some periods and fiscal collapse in others.) To understand the lending and borrowing problem, we use the intertemporal choice model from Unit 9 of The Economy 2.0: Microeconomics.

endowment

The facts about an individual that may affect their income, such as the physical wealth a person has, either land, housing, or a portfolio of shares (stocks). Also includes level and quality of schooling, special training, the computer languages in which the individual can work, work experience in internships, citizenship, whether the individual has a visa (or green card) allowing employment in a particular labour market, the nationality and gender of the individual, and even the person’s race or social class background.

Figure 6 shows the basic problem faced by an LMI country that chooses how much to consume in the present (\(C_\text{p}\)), and how much to consume in the future (\(C_\text{f}\)). Point A represents the country’s initial combination (‘endowment’) of present and future income. The country has (or expects to have) more income in the future than the present. Follow the steps to understand how access to credit affects this country’s consumption decisions.

indifference curve

A curve of the points which indicate the combina­tions of goods that provide a given level of utility to the individual.

diminishing marginal utility

A property of some utility functions according to which each additional unit of a given variable results in a smaller increment to total utility than did the previous additional unit.

marginal rate of substitution (MRS)

The trade-off that a person is willing to make between two goods. At any point, this is the slope of the indifference curve. See also: marginal rate of transformation.

discount rate

A measure of the person’s impatience: how much the person values an additional unit of consumption now relative to an additional unit of consumption later. It is the slope of the person’s indifference curve for consumption now and consumption later, minus one. Also known as: subjective discount rate.

marginal rate of transformation (MRT)

The quantity of some good that must be sacrificed to acquire one additional unit of another good. At any point, it is the slope of the feasible frontier. See also: marginal rate of substitution.

impatience

Any preference to move consumption from the future to the present. This preference may be derived either from pure impatience or diminishing marginal returns to consumption.

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https://books.core-econ.org/insights/government-debt-and-wealth/05-government-borrowing-to-shift-spending-over-time.html#figure-6

Figure 6 A country’s intertemporal decision problem, with and without access to credit.

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The country’s endowment

Point A represents the country’s consumption under ‘autarky’ (a word that means the absence of trade or self-sufficiency). In autarky, the country’s present consumption is \(C_\text{p}^\text{A}\) and its future consumption is \(C_\text{f}^\text{A}\).

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Community indifference curves: the country’s preferences

Curve \(\text{CIC}^\text{A}\) is the community indifference curve that passes through point A and represents the utility or welfare level that this country will achieve if it consumes its endowment (that is, what it has initially). The country’s community indifference curves have a negative slope because the country’s citizens may be willing to sacrifice consumption at one point in time if they are compensated with sufficiently increased consumption in the future. The community indifference curves are concave because of diminishing marginal utility from consumption: each additional unit of consumption increases total utility by a smaller amount.

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The marginal rate of substitution

The slope of the indifference curve, called the marginal rate of substitution (MRS), is steep at A, meaning that the country is willing to trade a large amount of future consumption for one unit of present consumption. In other words, the marginal utility of consumption in the present is very high because it is so scarce, while the marginal consumption of income in the future is very low because of its abundance. If someone were to offer the country a way of moving resources from the future to the present it would be willing to sacrifice quite a lot of future resources for a lesser increase in the present. In simple terms, it needs the money today far more than it will need it tomorrow. Another way of saying this is that it ‘discounts’ (or places less value on) future consumption against present consumption. We use the Greek letter \(\rho\) to represent the discount rate, defined as the slope of the indifference curve minus one. So, the marginal rate of substitution will be \(1+\rho\). (To learn more about the discount rate, read Section 9.4 of The Economy 2.0: Microeconomics.)

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The budget constraint and marginal rate of transformation

If the country has access to credit, it will face a budget constraint that represents the cost it faces (in future income) of increasing present consumption levels. For example, if the country gets a loan to increase its present consumption, whoever lends the money will demand that in the future the loan is fully serviced. This means that the loan must be repaid, along with the interest (at an agreed interest rate, \(i\) ). Hence the fall in future consumption is \(1+i\) times the increase in present consumption. This is the slope of the budget constraint and is called the marginal rate of transformation (MRT) faced, in this case, by the country. The MRT reflects the fact that access to credit allows the country to ‘transform’ future income into present consumption.

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Access to credit can make countries better off

Once the country has the possibility of using these credit options it can access more combinations of present and future consumption: any point below and up to the budget constraint. The country will now be able to move to point B, which corresponds to a higher level of utility, represented by the indifference curve \(\text{CIC}^\text{B}\). It will borrow the amount \(C_\text{p}^\text{B}-C_\text{p}^\text{A}\) and, in the future, pay \((1+i)(C_\text{p}^\text{B}-C_\text{p}^\text{A})\). In this way the country is doing the best it can given its constraints: \(\text{CIC}^\text{B}\) is the highest feasible indifference curve. At point B, the marginal rate of substitution equals the marginal rate of transformation, that is, \(\rho=i\).

One feature of intertemporal consumption decisions is ‘impatience’. In the case of countries and governments, impatience plays a very important role. Impatience has two sources:

Read Unit 9 of The Economy 2.0: Microeconomics to learn more about intrinsic impatience and situational impatience.

• Intrinsic impatience: decision-makers know that they might not be alive in the future so they place a higher value on present consumption (known as ‘prudence’), or decision-makers experience greater satisfaction from present consumption than the same consumption in the future (known as ‘myopia’).
• Situational impatience: this refers to when individuals are more oriented to the present because they have less now and more later.

Whatever the reason, ‘impatience’ usually skews consumption towards the present, reduces savings, or increases debt. There may be good reasons to be impatient when facing an emergency or a social urgency, but impatience can also get out of hand. For example, the individual may be facing some urgency or short-term enthusiasm for present consumption that, when time passes, will go away. Sometimes whole countries and governments go through these periods of increased impatience and later regret it.

Question 7 Choose the correct answer(s)

Consider an intertemporal choice problem where an agent has an initial endowment (point A) that is skewed towards the future and needs to take a loan. Assume that the agent can borrow or lend as much as they want at the interest rate \(i\), but that the interest rate changes according to market conditions. The agent takes the loan and consumes the amount they planned in the first period (point B) but then is surprised by an increase in the interest rate (point C). Which figure correctly represents this situation?

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• Figure a
• Figure b
• Figure c
• Figure d

• Figure a is incorrect because the agent must reduce future consumption, not present consumption, in response to a higher interest rate.
• In Figure b, the agent chooses to consume at point B. In the future, the interest rate is higher than expected and so is the service of the debt. Hence future consumption has to be sacrificed, and the new point is C.
• Figure c cannot be correct because the budget constraint rotates around the endowment point, not the initial vertical axis value.
• Figure d is incorrect because the budget constraint rotates around the endowment point, not the consumption level after the loan.