1.3 The Income-Expenditure Model
What is a model?
A model is a toy. It is a simple simulation of some aspect of the real world. We use models because the real world is too complex to understand in all of its detail. We use models because we hope that a simplification will help us understand something important about the world. An architect's model, made of cardboard, is a lot simpler than a real building, but it is enough like the real thing that it helps the architect understand some important things about how the building will look and work, and identify problems in the design.
In social science, we often build models by using mathematical equations. Learning to use a model requires getting used to some math, and it's tempting to feel that once you've figured out the math you're done learning the model. You're not! That's like saying an architect is finished using a model when all the bits of cardboard are stuck together. You're only done learning a model when you can relate it back to the real world that the model is supposed to portray, just as the architect uses what the model shows to modify the design of the real building.
We're making a model of the entire national economy, or macroeconomy. We base it on the following idea: if total output exceeds what people want to buy, there will be stuff left over -- which means that inventories of unsold goods will rise. On the other hand if people want to buy more than is produced during some period, what will happen is that previously-accumulated inventories of goods will fall.
Think about a shoe store. It has a certain amount of inventory that it wants to keep on hand at all times so as to be able to normal customer demand. If customers buy shoes at a slower rate than it gets new shipments from the manufacturers, inventory will rise. If on the other hand customers buy shoes at a more rapid pace than it gets shipments from the factory, inventory falls. Think about the entire economy this way and you understand how we think output adjusts to demand.
Equilibrium just means a position of stability. If inventories are rising, we are not in equilibrium because too many goods are being made, and sooner or later factories are going to have to cut production because the current level of output is not sustainable. If inventories are falling, we are not in equilibrium because too few goods are being made, and sooner or later factories are going to have to increase production. In other words macro equilibrium is when total output is equal to total desired expenditures. We believe that the national economy will move toward such a macro equilibrium on its own.
When we set up our macro framework, we said that
So let's distinguish between "planned investment," or Ip, and total investment, which is Ip plus unintended inventory changes. So while
In other words, since we said
Aggregate Supply and Aggregate Demand
Let's repeat our macro equilibrium condition
In the income-expenditure model, total output responds to the demand for it. In other word, aggregate supply is driven by aggregate demand. ( Not all models work like this.) That means that to figure out what the equilibrium level of output is, we have to figure out how much demand there is. That means that we have to know what determines the levels of C, Ip, and G.
In this particular model, the answers for the last two are easy. We will assume they are fixed and unchanging. We will assume that businesses make plans about how much capital equipment they want to acquire, and do not change those plans. We will assume that G is set through some political process. We will similarly assume that T is fixed. In fancier language, G, Ip, and T are "exogenous" to this model.
That leaves C, which is at the center of this model. What determines how much consumers spend? Well, their income, Y. But we've just said that Y is partly determined by C, since C is an element of demand. So C affects Y and Y affects C. How exactly? Read on.
The Consumption Function
How much do consumers wish to spend? We focus on the relationship between income Y (remember this is also the same thing as aggregate output) and consumption C. The actual consumption households undertake depends on their disposable income, because they don't have any choice about paying taxes. So consumption and savings will be functions of disposable income, or (Y-T).
Since whatever is not consumed must be saved, as soon as we specify a consumption function we have necessarily specified a savings function. "Function" just means that one thing depends on another thing or things.
To keep things simple, we are going to specify consumption as a linear (straight line) function:
This "b" has a special name: the Marginal Propensity to Consume (MPC). In economic terms, it tells the additional amount of aggregate consumption that the members of the economy will desire to undertake, for each additional dollar of income they receive.
The MPC is always positive (since when people earn more, they will consume more).
The MPC is also less than 1. That is we assume that some part of each extra dollar earned is saved. That gets us to the next point, We know from our savings identity that in all circumstances
Aggregate Expenditure and Equilibrium -- a numerical example
We now have C, Ip, and G. That means we have all the information we need about the planned level of total (aggregate) expenditure in the economy. Here is a numerical example, with a graph.
To begin with, let's specify the consumption function as:
We can also graph G and Ip as functions of Y.
which makes for a boring graph because they are constants and won't change if Y changes -- hence they appear as horizontal lines. That's because, remember, they are exogneous to the model rather than being determined within the model. Finally we can put them all together:
including aggregate expenditure, which is just C + Ip + G, or the three components added up. Finally, we put the level of output on the graph, as a dotted line. Since output always equals income, it's just a simple line from the origin.
Here is how to solve for Y. Start with our equilibrium condition
We can also check that we have the reight level of Y by seeing if
Now let's show all this on one of our flow diagrams.
so you can see that everything adds up. Notice the fiscal deficit, and the fact that government has to borrow from the flow of savings, via the financial sector. There is no reason here to seek a balanced budget in which G = T. (Don't confuse macro equilibrium with a balanced budget.)
If you like algebra, here's a generalized
solution for the income-expenditure model.
Changes in the numerical example
Starting with the model from the previous section