Aggregate Demand Curve

The aggregate demand curve shows the relationship between the price level and the quantity of goods and services demanded in the economy. In other words, the aggregate demand shows the quantity of goods and services that households, businesses, government, and foreign consumers demand at each price level. It is the relationship between the quantity of aggregate output and the aggregate price level, and thus, the overall quantity of goods and services demanded at any price level.

Graph of the Aggregate Demand Curve

To graph the aggregate demand curve, it is assumed that all variables other than the price level and aggregate output remain constant, especially the amount of money in the economy. In other words, assuming that the money supply is fixed, a change in the price level affects the demand for goods and services.

As can be seen in the graph, keeping everything else constant, a reduction in the general price level generates an increase in the quantity of goods and services demanded. If the price level decreases from P1 to P2, the quantity demanded increases from Y1 to Y2, and on the aggregate demand curve, we move from point B to point A. The opposite is also true: an increase in the general price level generates a reduction in the quantity of goods and services demanded.

Classical macroeconomic theory, or long-term macroeconomic theory, is based on the assumption that nominal variables do not affect real variables, but short-term microeconomic theory, not without criticism, abandons this assumption. Consequently, the aggregate demand curve shows how the price level (a nominal variable) affects the level of output (a real variable).

The Quantity Equation of Money as Aggregate Demand

The quantity equation of money is expressed as:

\[ MV = PY \]

Where:

  • M: is the money supply.
  • V: is the velocity of money, which measures how many times money is spent in a given period.
  • P: is the price level.
  • Y: is real output (real gross domestic product).

If the velocity of money V is constant, this equation establishes that the money supply determines the nominal value of output, which in turn is the product of the price level P and the amount of output Y. That is, a change in M will affect PY proportionally.

Now, let's see how the quantity equation is transformed in terms of supply and demand for real money balances:

  1. We start with the original equation: \[ MV = PY \]
  2. We divide both sides of the equation by P to isolate Y: \[ \frac{MV}{P} = Y \]
  3. Next, we rearrange the equation to express real money balances \( \frac{M}{P} \): \[ \frac{M}{P} = \frac{Y}{V} \]
  4. Expressing the Demand for Real Money Balances: In this step, we introduce the concept of demand for real money balances. We define \( (M/P)^d \) as the demand for real money balances. From the equation, we can equate the supply of real money balances \( \frac{M}{P} \) to the demand for real money balances: \[ \frac{M}{P} = (M/P)^d \] This means that the amount of money available, adjusted for the price level, is equal to the amount of money the economy wishes to hold.
  5. Introducing the Parameter \( k \): At this stage, we use the relationship that exists between the demand for real money balances and output. We say that the demand for real money balances is proportional to output Y: \[ (M/P)^d = kY \] Here, k is a parameter that indicates how much money people wish to hold per unit of monetary income. In other words, k helps us understand how output impacts the demand for money.
  6. Relationship between \( k \) and \( V \): Finally, we recall that the parameter k is related to the velocity of money V in the following way: \[ k = \frac{1}{V} \] This implies that the velocity of money is the inverse of the money demand parameter k. The assumption of constant velocity is equivalent to the assumption of constant demand for real money balances per unit of output. In summary, the higher the velocity of money, the lower k, indicating that people prefer to hold less money relative to their income.

In this form, the quantity equation establishes that the supply of real money balances \( \frac{M}{P} \) is equal to the demand for real money balances \( \left( \frac{M}{P} \right)^d \), and that demand is proportional to output Y. This can be summarized in the triple equality: \[ \frac{M}{P} = (M/P)^d = kY \]

If we assume that the velocity of money V is constant and that the money supply M is set by the central bank, then the quantity equation produces a negative relationship between the price level P and output Y. That is, if output Y increases, the price level P must decrease to maintain equality in the equation \( \frac{M}{P} = kY \).

In conclusion, the quantity equation of money not only establishes a relationship between the money supply and the price level, but when transformed in terms of supply and demand for real money balances, it helps us understand the relationship between the supply and demand for real money balances and the level of output.

The following graph shows the combination of P and Y that ensures the quantity equation, while holding the money supply (M) and the velocity of money (V) constant, is fulfilled. This curve is the aggregate demand curve, interpreted through the quantity equation.

This aggregate demand curve shows the relationship between the price level and the quantity of goods and services demanded, keeping the money supply and the velocity of money constant. The fact that the curve has a negative slope implies that with higher price levels, real money balances are lower, and consequently, fewer goods and services are demanded. Conversely, with lower price levels, real money balances increase, and more goods and services are demanded, as shown by the equation explained earlier.

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