Macro 101: The goods market

The first part of the IS-LM model

This place does not exist; the image was created using Stable Diffusion with the prompt “people walking by stalls in New York, long shot, 4k, golden hour”

Understanding what are the consequences of our choices is key to deciding consciously according to our values. To do so, we will devise a first basic model that could help us address real-world cases. This article will deal with the first part of the IS-LM model, while the following will analyse the so-called money market. The theoretical framework set out will be used to interpret the recent European energy crisis resulting from the Russian illegal invasion of Ukraine.

First, let us make clear what a model is. Models are stylized representations of reality, in which different variables affect each other according to mathematical relationships. We do need models not only in economics but also in various fields since they help simplify reality. Nevertheless, one has always to bear in mind that there are no unique causal relationships between variables, so it is crucial to acknowledge the limits of a model and interpret reality accordingly.

The variables used in a model may be either exogenous or endogenous:

-An exogenous variable is a figure whose value does not depend on its relationship with other variables within the model. An exogenous variable is known as a priori; it is indispensable for computing the other variables (ex: if the variable consumption depends on taxes, but the model does not provide a theory for a change in the level of taxation, taxes are a given value established a priori and therefore exogenous, while consumption will depend on taxes).

-An endogenous variable is a figure determined by the value of other variables within the model.

The first part of the IS-LM model: the goods market

We will first devise a model to study the dynamics of a national economy that does not interact with any other country (closed economy case). However, we will later relax this assumption since it is not realistic. In a closed economy, aggregate demand is equal to the goods produced within the economy (Goods produced are consumed within the country). Therefore aggregate demand is given by:

Z is aggregate demand, C is consumption, I is investment, G is government spending, and X and IM are exports and imports. However, since we consider a closed economy in which there is no interaction between countries, both X and M are 0. Se can ignore them:

Let’s look at these elements one by one:

• The aggregate demand (Z) for goods and services is the total value of goods and services demanded by the population. Thus, it is the sum of C, I, and G. At equilibrium Z is equal to Y (that corresponds to the incomes distributed in the economy) since the domestic demand is equal to the domestic supply.
• C is the demand for products and services for private consumption. In our model, two components determine consumption: autonomous consumption (c0) and propensity to consume (c1), such that c0>0 and 0<c1<1.

Why do we split the demand into two components? Because part of the consumption is rigid and consists of staple goods like bread, sugar, etc(this is captured by the fixed parameter c0). On the other hand, there are products that people may buy proportionally to their income (think of luxury goods, vacations, etc.). Therefore, C is :

Where Y is aggregate output (at equilibrium is equal to income and Z; to understand why: What is GDP?), which corresponds to the overall sum of the incomes in the economy, and T corresponds to the taxes. (Y-T) is also called disposable income. According to the formula mentioned above, a change in consumption may be caused either by a change in disposable income, a change in c0, or a change in c1.

• Investments are considered exogenous.
• G is the public spending. T and G stand respectively for taxes and government spending. They describe the fiscal policy pursued by the domestic government and are considered exogenous.

Plotting the aggregate demand

Recall the aggregate demand function:

The aggregate demand function is equal to:

The following graph represents the equation:

Remarkably, the aggregate demand is directly proportional to the income produced in the economy. Parameter c1 determines the slope of the line(as c1 grows, the line gets steeper), and c0, I, and G determine the intersection of the line with the vertical axis (An increase in autonomous consumption would translate into a shift upwards of the ZZ line). So the demand is directly proportional to the income Y.

However, the determination of the aggregate demand must be consistent with the fact that, at equilibrium, it must be equal to production, which corresponds to overall income. Therefore, given G, c0, c1, and T, the visual representation of equilibrium output is the following:

The equation of the demand becomes:

Substituting the second equation into the first:

So Y is defined by the equation

(Notice that c1 is a number between zero and one, so the demand multiplier is always bigger than one)

The equilibrium demand (and output) is the product of the demand multiplier and the level of autonomous spending. Autonomous spending is the share of output not influenced by the output itself. On the other hand, the final consumption depends partly on the output such that a change in income entails both a variation in consumption and a further change in income (a change in autonomous spending entails both a direct and an indirect effect on output). The intuition is the following: suppose a $10 increase in public spending G. The increase in G will cause an immediate increase in demand by $10 that will entail an increase in production and change in income. The variation in income will entail an increase in demand smaller than the original $10 change etc. This adjustment process will lead to a new equilibrium such that the overall change in output is greater than the initial $10 increase. The demand multiplier captures exactly this adjustment process. Graphically, the result is the following:

Notably, the final increase in Y is larger than the original change in G. In this case, the difference between the new equilibrium and the initial equilibrium is:

Since c1 is between zero and one, the demand multiplier is larger than one. So, the final change in output is more than the original change in G.

However, it is worth mentioning that this model does not consider the quality of the public expenditure; actually, the allocation of public spending does matter and may affect income. The following article will face the second part of the model, allowing us to analyze real-world problems.

Hey! I am a student passionate about what I am doing. English is not my mother tongue, and one of the reasons why I am writing in a foreign language is to get better at it; feel free to make me aware of any mistakes. Any suggestion or comment on the topics dealt with is appreciated as well!

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