Part 2: IS Curve

This video is the second in a set of four explaining the Hicks-Hansel model of Keynes'  theory of Aggregate Demand, specifically the IS-LM interpretation. This model is very important to short run macroeconomics and attempts to explain shifts in the aggregate demand curve. These topics are usually taught in an intermediate Macroeconomics class, and these videos are intended as a visual aid to further your understanding of the models.This video covers the investment demand curve, integrates investment into the aggregate demand curve, introduces the IS-curve and provides an overview of the factors that determine the slope and position of the IS curve. If you did not view the introductory video, you can find it here

The  I - S stands for Investment and Saving and the IS curve displays the equilibrium in the goods and service market for various interest rates.


Investment Equation
To begin we revisit the aggregate demand equation. While investment was previously considered to be exogenous, we're going to see how it relates to interest rate, so it becomes endogenous and loses the bar above the variable. 

There is, however, still a portion of investment that is unaffected by interest rate. It is represented by "I-bar" and called exogenous investment. Next we have interest rate, represented by "i". And as you see by the minus sign, investment is negatively related to the interest rate. The degree to which firms adjust investment spending relative to the interest rate is called interest sensitivity which is represented by "b". This coefficient will be anywhere between zero and one.

Investment Curve

Investment Curve
Now we'll examine this relationship graphically. Investment is on the x-axis and interest rate is on the y-axis. Typically the independent variable (in this case, investment) is put on the Y-axis, but we will be using interest rate as the independent variable when we graph the IS curve, so it's put here now for consistency.

Exogenous investment determines the initial level. Again, a higher interest rate results in lower investment spending. A high interest rate means firms reduce their investment spending to avoid high interest payments.  A low interest rate means firms can increase their capital spending and pay relatively low interest.

Slope & Position

The slope of the investment curve is determined by the interest sensitivity coefficient. A high interest sensitivity results in a more gradual slope. In this case, there is a drastic increase in investment spending in reaction to a relatively small reduction in the interest rate, because of the higher sensitivity.

The position of the curve is determined by the exogenous investment. An increase would result in an outward shift of the curve. 

Incorporated Investment into the Aggregate Demand Equation

Investment, Aggregate Demand
Now we're going to incorporate this investment function into the aggregate demand equation. Recall in the first video we separated the components into exogenous and endogenous to arrive at this formula. Investment was previously grouped with the exogenous components, but our new formula has endogenous as well as exogenous components.  The "I-bar" will go back into the exogenous group, while the interest and sensitivity coefficient move to the back of the equation.

Review: AD for aggregate demand. A-bar for exogenous demand, lower case c is the marginal propensity to consume. lower case t for tax rate, Y for income, lower case b for interest sensitivity and i for interest rate. You will notice that all of the lower case variables are rates between zero and one. 

Aggregate Demand Curve with Investment

Aggregate Demand Curve with Investment
We're going to display this function graphically, and just as before the 45 degree line where aggregate demand = income is our equilibrium criteria. Here is upward sloping demand function. Higher levels of national income lead to higher levels of aggregate demand. The y-intercept is given by exogenous demand minus interest rate * sensitivity. The intersection of the lines gives us the equilibrium level of national income.

Reduction in Interest Rate

Reduction in Interest Rate
A reduction in the interest rate results in an upward shift in the aggregate demand curve. This results in a higher equilibrium level of national income. So the interest rate went down and the equilibrium income went up.

Increase in Interest Sensitivity

An increase in interest sensitivity results in a downward shift in both aggregate demand curves. The downward shift is more pronounced for the curve with the higher interest rate (i-1). This means that the distance between the two resulting equilibrium levels of income is larger.

IS Curve

IS Curve
Now we can move on to the IS Curve, which denotes the equilibrium levels of national income for different interest rates. Just as we did in the previous slide, we will be graphing the aggregate demand curve for different interest rates in the top graph. The bottom graph also has income on it's x-axis and will show the different interest rates.

Here is the curve for interest rate #1. The equilibrium level of income is the same for both graphs. When we put interest rate #1 on our bottom graph we have the first point of our IS curve. The second aggregate demand curve has a lower interest rate, so its parallel and higher up. On the lower graph the intersection of interest rate #2 and equilibrium income #2 produce the second point of the IS curve. This could be repeated for every different interest rate in this range to produce the IS curve. Since this model only uses linear curves, we need a minimum of two points to graph the IS curve. There you have it, at any point on this IS curve the goods & services market is in equilibrium. 

Slope of IS Curve - Interest Sensitivity

Slope of IS Curve
Now we're going to discuss the determinants of the IS curve's slope. Holding other factors constant, an increase in interest sensitivity will result in a more gradually sloped IS curve. b prime will signify the new, higher level of interest sensitivity. Lets watch how this happens.  For i-1, the higher interest rate, the downward shift is more prominent and produces a low equilibrium level of national income, Y* 3. For i 2, the lower interest rate, there is a downward shift, but not as big. When we connect the points to form the second IS curve we see that it's slope is more gradual. 

Slope of IS Curve - MPC

Another determinant of the IS curve's slope is the marginal propensity to consume. As we saw in the introductory video, An increase in the MPC creates a steeper aggregate demand curve. c prime will represent the higher MPC. When we graph the steeper aggregate demand curves it becomes apparent that the second IS curve is more gradual as a result of the increased MPC.

Slope of IS Curve - Tax Rate

Slope of IS Curve - Tax Rate
The last determinant of slope is the tax rate. An increase in the tax rate reduces the slope of the aggregate demand curve. t prime will represent the higher tax rate. The flatter aggregate demand curves produce an IS curve that is steeper as a result of the increase tax rate.

Position of IS Curve - Exogenous Demand

Position of IS Curve- Exogenous Demand
Moving on to the position of the IS curve, an increase in exogenous demand results in an upward shift of the aggregate demand curve. 'A' bar prime will represent the higher level of exogenous demand. The higher aggregate demand curves produce an IS curve that is shifted outward as a result of the increase in exogenous demand.

This concludes the video on the IS curve. We covered the investment demand curve, integrated investment into the aggregate demand curve, introduced the IS curve and looked at the determinants of its slope and position.

 Please watch the third video, which explains how to find equilibrium in the money market