Chapter V. Aggregate Supply Aggregate Demand Curve Analysis
Macroeconomics1Chapter V. AS-AD
Chapter V. Aggregate Supply Aggregate Demand Curve Analysis
1. Aggregate Demand
1) Algebraic Derivation
You may remember that the equilibrium national income from the IS-LM curve is
Let’s focus on the relationship between Y and P.
If all variables are constant except for Y and P, we can get an equation showing the relationship between the two variables Y and P, such as Y = 500 + 200/P. This equation carves up the relationship between two variables, Y and P, is called the Aggregate
Demand Curve.
In the discussion of monetary policy which involves a change in money supply M and its impact on P and Y, we deliberately drop the intercept A, which is related to fiscal policies, and frequently use Y = B/P = B’ (M/P) to carve up the relationship between the three key variables, M, P, and Y (real income).
2) Graphic Derivation
We derive the AD curve by examining the impact of a changing price level on the LM curve and consequently on the AD.
When the price level falls from P1 to P2, the real money supply rises from M/P1 to M/P2. This shifts the LM curve to the right.
The equilibrium national income level rises in the IS-LM curve.
The corresponding point shifts in the AD setting. By linking the two points, we get the AD curve.
3) Shift of AD curve
∆ C0, ∆I0, ∆G0, - ∆T0 ∆IS ∆AD
∆ M ∆LM ∆AD
∆ md= ∆u ∆LM ∆AD
To countervail the Aggregate Demand Shocks and thus to eliminate any impact on the equilibrium national income, the government may control G, T, and M in counter-cyclical ways. This is called ‘the Counter-cyclical policy’ or ‘Income stabilization policy’.
2. Aggregate Supply
1) What is the aggregate supply?
AS versus YS
The aggregate output is the sum of all the supplies of goods and services in the economy. You may remember the 45 degree line of YS = Y in the Keynesian Cross Diagram. When the aggregate output YS is drawn against a particular price level, that is the aggregate supply. The only difference is that the AS is drawn again at the price level while YS is not. In a sense, AS comes from YS. Then, our next question is, what determines YS?
2) Aggregate Production Function
AS is the aggregate outputs at a particular price level. Output results through production process from inputs. The production function shows the relationship between the inputs and the outputs: production combines production factors with a certain technology. The production function summarizes all three aspects of the supply: Inputs, outputs, and technology.
(1) Functional Form
In microeconomics theories, an individual production function, say, a hamburger or i th industry, is given by
Qi = f (K,L),
where K and L are capital and labor inputs, and Q output at the firm or industry level. Technology is implied in the functional form.
The aggregate production function is obtained by summing up the production functions of all industries. The aggregate production function shows the aggregate output YS as an increasing function of capital and labor inputs.Again technology is implied in the functional form. We use notation K for the capital stock or the amount of capital, and N for labor input at the aggregate level of economy.
YS = F (K, N; T ).
Note that unlike the microeconomics which uses L for labor input, we use N for the aggregate labor inputs, which is called the ‘level of employment’ in an economy. N may be measured in total hours worked for a given period of time, which is equal to the number of workers employed times the number of hours worked by each worker. Here T stands for Technology employed in production.
(2) Derivation of the Aggregate Production Curve
Note that in the short-run, K remains fixed and T does not change. Thus the short-run aggregate production function can be expressed as an increasing function of one variable N or the level of employment of existing workers: the more workers employed for longer hours, and then more aggregate output.
Aggregate Production Curve
Let’s take a numerical example for the Short-run Aggregate Production Function:
YS = 100N – 0.3 N2
If the level of employment is given at 40 (say, million hours worked for a year), what is YS? The answer is YS = 100 x 40 – 0.3 (40)2 = 3520.
If N increases up to N = 60, then the aggregate outputs rise to a new level: 100X60 – 0.3 (60)2 = 4920.
These two points give us an aggregate production curve. It is upward sloping, and is convex upwards. In the short-run, there is a one-to-one relationship between the level of employment and the aggregate outputs: N*’ – AS* t in the short-run. An increase in the level of employment leads to a movement along the given aggregate production function.
Note that the slope of the tangent line to the Aggregate Production Curve is the Marginal Product of Labor.
The shape of the above Aggregate Production Curve is part of a so-called ‘S curve’ of the total (aggregate) production curve:
The first phase or Phase I shows the concave upward and implies that as the input of labor force or the level of employment goes up, the output increases by more than proportion due to an increase in efficiency coming from specialization and cooperation, etc. That is an increasing marginal product of labor or MPL increases in this phase.
Then there occurs a point of inflection. The curve become convex upwards and implies that as the input(labor forces or level of employment) rises, the output increases by less than proportion: This is the area where the diminishing marginal product of labor takes place. As the level of N increases by one unit, the output increases but it does so by less and less. It is called ‘Decreasing Marginal Product of Labor’. This is due to some imbalance between the size of (given) capital (equipment and facilities) and the number of workers working in and with them, and the resultant inefficiency such as congestion(too many workers collide and crowd, free-riders(some workers are not carrying their fair work load)etc.
Our earlier aggregate product curve is a cut out of the above S curve from and beyond the inflection point. Why cut here? Because Phase I is important and beneficial for the producer, but it is uninteresting. All the decision to be made is trivially to keep expanding the employment (N up). When the inflection point comes, now the entrepreneur has to start thinking of a very critical question: When to stop? He has to weigh the inefficiency, which has started setting in, against other benefits, and has to make a decision to stop at the right level of N. Thus, this part of S curve is important in terms of the entrepreneur’s corporate decision making, and we are only looking at this part of the S curve of the total production curve.
(3) Shift of Aggregate Production Function
In the long-run, i) an increase in N, ii) an increase in K, and iii) the enhanced level of technology are all possible, leading to an increase in Aggregate Output. However, an increase in N leads to a movement along the Aggregate Output Curve, and the two others, such as an increase in K or/and T leads to a shift of the Aggregate Output Curve.
i) Capital Accumulation: ∆K
With more capital inputs, each level of employment will lead to a larger amount of aggregate outputs: With more capital equipment, each worker can produce more outputs.
This will send the Aggregate Production Curve outward, or upward.
Let’s take a numerical example,
Before: Y* = 100 N – 0.3 N2 (a Old production function)
N = 40 – Y* = 3520; N = 60 – Y* = 4920.
After: Y* = 250 N – 0.2 N2 (a New production function)
N = 40 – Y* = 5680; N = 60 – Y* = 8280.
Therefore, capital accumulation (∆K) leads to a upward shift of the production curve.
When the Aggregate Production Curve shifts up, at each level of N, the slope of the tangent line gets steeper: The slope is equal to the marginal product of labor, and thus the MP of labor rises.
Think about the decrease in capital, which will send the Aggregate Production Curve downward.
Capital naturally wears and tears over time and it is called ‘Depreciation’
Capital can be destroyed during a war.
ii) Technical Innovation, or Technological Advances: ∆T
With an improved production technology, each level of employment will lead to a larger amount of aggregate outputs.
Let’s take a numerical example:
Before: Y* = 100 N – 0.3 N2 ( a Old production function)
N = 40 – Y* = 3520; N = 60 – Y* = 4920.
After: Y* = 150 N – 0.2 N2 ( a New production function)
N = 40 – Y* = 5680; N = 60 – Y* = 8280.
Therefore, technological advances also lead to a upward shift of the production curve. The marginal product of labor rises, too.
iii) A Growing Number of Workers: ∆Ns
This is a rightward shift of the labor supply curve. The equilibrium nominal wage rates fall: So does the real wage rate. The equilibrium level of employment rises, which increases the aggregate outputs along the aggregate production function.
This can happen in the long run due to population growth, or open-door immigration policies. As N is on the horizontal axis, this leads to a movement along the aggregate production curve.
3) Aggregate Labor Supply and Demand Curve: Labor Market
Then, the question in order is how the level of employment or N* is determined to enter the aggregate production function. N*is determined in the labor market through the interplay of the aggregate labor supply and aggregate labor demand. Now, we note that we are introducing one more market into the picture, and that is the labor market.
The supply of labor is an increasing function of real wages, which are money wage over the price level ( w= W/P), and the demand for labor a decreasing function of real wages.
(1) Aggregate Labor Supply
The labor supply is an increasing function of real wages, which are equal to nominal wages divided by the price level;
Ns = f (W/P; other variables)
For a given level of P, as W rises, Ns rises as well.
If you put Nson the horizontal axis and W on the vertical axis, the curve should be positively sloped. And P becomes a shift parameter.
Numerical Example:
Ns = 100 + 3 (W/P).
If the nominal wage or money wage (rate per hour) is $10 per hour and the price level is equal to 1, then the real wage (rate per hour) is 10/1 = 10, and the aggregate labor supply would be 100+ 3 times 10/1 = 130.
The above is sufficient for the labor supply curve in macro. Note that the vertical axis is in the real wage W/P. The labor supply is an increasing function of real wage.
However, in the macroeconomics, we would further separate real wage W/P into nominal wage W and price level P. If we draw the aggregate labor supply curve Ns against the nominal wage W, we can see impacts of P more clearly.
How can we do that? First, hold P = 1 constant, then W/P becomes W, and draw the Ns curve of the same shape:
Note that now the vertical axis is W or nominal wage, and the horizontal axis is the level of employment or N, and finally that the Ns curve or the aggregate labor supply curve is drawn with the fixed price level of 1. Thus we should note that the price level is now the shift variable of the Ns curve.
What will happen to the Ns curve for P =1 if the price level rises from 1 to, say, 2 while the nominal wage (rate for hour) is held constant?
A Shift of the Ns curve:
In the short-run, a change in the price level shifts the Ns curve. As P rises, the Nscurve shifts up as well; As P rises, for a given level of W, the real wage of W/P falls, and thus labor supply falls.
There are other variables that shift the Ns curve.
For example, in the long-run, as population grows, the aggregate labor supply curveshifts to the right.
In summary, for the dimension of W and N, we can write the aggregate labor supply curve as:
Ns = f (W(+) : P(-) , other variables such as population, immigration, etc.)
All other variables, except W and Ns, become shift variables. A change in these shift variables leads to a shift of the Ns curve.
Remember that an increase in the price level or P leads to the visually upward movement of the Ns curve or a decrease in Ns.
(2) Aggregate Labor Demand:
Let us examine the labor demand first:
The aggregate labor demand is a decreasing function of real wages:
Nd =g (W/P; other variables).
If we draw a curve which shows the relationship between Nd and W. It will be downward-sloping; as W goes up, the entrepreneurs demand for labor falls. The third variable P becomes a shift parameter.
By holding P = 1 constant, we can get a Nd curve corresponding to P=1.
Background-You may recall the following Microeconomics theory of labor demand:
The entrepreneur does demand labor and hires workers. If s/he is maximizing profits, at the margin or for the last worker hire, the cost is equal to the benefit. The cost of hiring the last worker in monetary terms is the money wage W, and the benefit from hiring the worker is the marginal product MP (units of output the worker produces) times the price of the output P. So at the profit maximizing level of employment, W = P x MPL.
Numerical example) It costs $10 to hire a worker because W = $10. The last worker increases the total products or outputs by 5 (5 units of outputs), and each unit of output has the price of $2 in the market. The cost of hiring the last worker is $10, and the benefit from hiring her/him is 5 times $2, being equal to $1.
We now know that at the equilibrium for the profit maximizing firm
W = P x MPL in dollar terms, or W/P = MPL in physical terms.
MPL is a decreasing function of the amount of labor inputs.
The real wage w= W/P is set by market forces, and is paid uniformly to all workers, regardless of whether there are many or few workers.
When the real w = W/P is set at a certain level in the labor market, the entrepreneur who is a price taker will hire workers in such a number that the last worker’s marginal product is equal to the real wage set in the market. The entrepreneur is making profits from hiring intra-marginal workers (all the workers except the last worker hired) as their marginal products are higher than the real wage. S/he is not marking any profit from hiring the last or marginal worker (MP = W/P)This implies that the MPL curve itself drawn against real wages is the labor demand curve.
A Shift of the Nd curve:
As P or the price level rises, the real wages(W/P) falls for a given level of W. And thus Nd rises: this is a rightward movement or upward movement of Nd curve.
where P =1, and P’ = 2 in this case.
There are other variables that shift the Nd curve:
In the long run, ∆K or an enhanced technology increases each worker’s productivity or marginal product. The MPL shifts up, and the labor demand curve shifts up (or to the right): some workers who used to be unproductive and thus unemployable become now productive due to technical innovations and become employable. There is an increase in the aggregate labor demand by the entrepreneurs.
In summary, for the dimension of W and N, we can write the aggregate labor supply curve as:
Nd = g(W (-) : P(+) , other variables such as population, immigration, etc.)
All other variables, except W and Ns, become shift variables. A change in these shift variables leads to a shift of the Nd curve.
Remember that an increase in the price level leads to the visually upward movement of both Nd and Nscurves.
(3) Labor Market Equilibrium
The interplay of the Nd and NS determines the equilibrium level of employment N* and the equilibrium level of real wages w*;
At equilibrium,
f(W/P) = g(W/P), or
f(W: P ) = g (W: P)
We can solve for the real wages or W/P at this equilibrium in the labor market.
And then, for a given price level, we can also get the nominal wages W for this equilibrium.
Graphically,
By plugging the value of W* back into the aggregate labor supply or demand function, we can get N*
In summary, As – YS – N*- w* - W for a given level of P.
(4) Responses of Nominal Wages to Changing Price Levels: Flexible or Not?
We would revisit the question of what will happen to the equilibrium real wage W/P = w when the price level rises? This depends on what will happen to nominal wage or W when the price level rises.
In the microeconomics, which belongs to the world of classical economics, there is an assumption of flexibility of nominal wage. In other words, the nominal wage W will rise in an exact proportion to the increase in P. As P rises, W rises by the same amount. Thus, W/P = w or real wage does not change. There will be no change in the level of employment N, and thereby no change in aggregate output YS or real national income Y.
The flexibility of nominal wage W ensure the separation of the world of nominal variables such as W and P, and the world of the real variables such as N, YS, and Y. There is a dichotomy between the real and the nominal variables.
However, in macroeconomics, there are different schools which have different assumptions about the degree of flexibility of nominal wage. And the different degrees of flexibility of nominal wage opens up the possibility of W not exactly following the movement of P and thus lead to a change in real wage or w =W/P, level of employment N, aggregate output YS, and real national income Y. An increase in the price level, which is a change in nominal variable, can affect the real variables.
Let’s elaborate on this point:
If W is viewed to be flexible, just as assumed in theclassical economics, and follows the movement of P, a change in P will be accompanied by an equal movement of W, leaving w unchanged.
First, the rising P shifts both the labor supply and demand curves up;
The new equilibrium occurs at E;
The new equilibrium nominal wages are proportionally higher than the previous one: In other words, the increase in W is proportional to the increase in P;
Therefore the real wages (w= W/P) do not change;
The level of employment is the same as before.