Economics 102 Discussion Handout Week 13 Fall 2017 Introduction to Keynesian Model: Income and Expenditure The Consumption Function The consumption function is an equation which describes how a household s level of consumption varies with its disposable income. In order to fully understand the consumption function, we need to understand a few ideas about household income and how they choose to use that income. A household s disposable income is their income after net taxes Disposable Income = Y d = Income - (Tax - Transfer Payments) Out of each additional dollar a household earns, they can choose to either save or consume it. The fraction of each dollar that a household chooses to consume is referred to as the marginal propensity to consume. The fraction of each dollar that a household chooses to save is the marginal propensity to save. Marginal Propensity to Consume = MPC = Maginal Propensity to Save = MPS = ΔS ΔY D Change in consumption Change in desposable income = C Y D We can go a bit further here. Assuming that there are lump sum taxes (i.e. no tax rate), this means that out of each additional dollar you earn you must either spend or save the entire dollar. As a result, the MPC and MPS must always add up to equal 1. National Income = Y = C + S + T Y = C + S + T (assume T = 0) Y = C + S (divide both sides by Y ) 1 = MPC + MPS What happens when your disposable income is zero? You must still consume in order to survive (food, clothes, etc.). This amount that you consume when your income is zero is called autonomous consumption. With this, we are ready to derive the consumption function: Consumption Function = C = C auto + MPC Y d
The Aggregate Expenditure Model The aggregate expenditure (or income-expenditure) model is a macroeconomic model that focuses on the relationship between total spending and real GDP, assuming the price level is constant. To fully investigate this model we first need to define the aggregate expenditure function. Aggregate expenditure = AE = C + I planned + G + NX AE = C auto + MPC Y d + I planned + G + NX = AE auto + MPC Y d Remember when dealing with this formula that C here is referring to the consumption function. Also of note is a new term, I planned, which in this model refers to planned investment. Planned investment refers to the investment spending businesses intend to carry out in a given time period. In this chapter it is given, but in general (and as we will see in later chapters), it is a function if the interest rate, r. Missing in this equation is unplanned investment, which refers to unplanned changes to inventories firms make during a given time period. Actual investment spending, then, is the sum of these two: Actual Investment = I planned + I unplanned Now if we add unplanned investment to our equation for aggregate expenditure we get: AE + I unplanned = C + I planned + I unplanned + G + NX = GDP Aggregate Expenditure Model Equilibrium In the previous section we described how aggregate expenditures plus unplanned investment equals GDP. What are the implications of this for the economy? For instance, if aggregate expenditures are larger than GDP, this means that unplanned inventories must be negative in order for this formula to hold. However, if this is true, that means that there are unexpected decreases in inventories. How are firms going to respond to this? By increasing production to meet this demand for expenditures. By producing more goods though, this leads to an increase in GDP, which in turn leads to a decrease in GDP. We can summarize the logic as follows: ㆍ When AE<GDP, inventories will and GDP and total employment will ㆍ When AE>GDP, inventories will and GDP and total employment will Therefore, the only time when GDP is not changing is when aggregate expenditures are equal to GDP. This is what we call the macroeconomic equilibrium of this model:
We can illustrate these ideas graphically. If we place the function AE = Y on the graph containing the aggregate expenditures function, it represents all of the possible equilibrium points in the economy. The macroeconomic equilibrium is thus the point where the aggregate expenditures function intersects with this line, often referred to as the 45 line. Note however that the macroeconomic equilibrium here does not correspond to the economy being at full employment. In fact, it is possible for the economy to be in equilibrium, but be below full employment GDP, in which case we are in a recession, or above full employment GDP, in which case we are in a boom. In these cases, we cannot get to full employment by moving along the current aggregate expenditures line. Instead, we have to shift the aggregate expenditures function. The Multiplier and Shifting the Aggregate Expenditures Function The multiplier effect describes how changes in autonomous expenditures lead to changes in real GDP. This is best illustrated with an example: A University decides to build a new residence hall worth $100 million, provided by the government. Construction workers earn $100 million in income, and if we assume the MPC is 0.8, they spend 80 percent or $80 million dining out, going to the movies, shopping, and buying new cars. The increased spending of $80 million becomes income to the owners and employees of the restaurants, movie theatres, shopping malls, and car dealers. In turn, these people spend 80 percent of the new $80 million, or $64 million, on other goods and services. The $64 million becomes income to others in the community, and the process continues. The following Table shows the impact of the multiplier through various rounds.
The above table can be summarized as follows and introduces you to the multiplier process. In general, the multiplier can be described with the following formula: Multiplier = Y AE auto = 1 1 MPC
Practice Question 1. Use the Keynesian Model to answer this set of questions. Suppose that in the economy under consideration the consumption function can be written as C = 100 + 0.8(Y T). Furthermore, you know that taxes are autonomous and equal to $20. There are no transfers. a. Draw a graph of the consumption function with respect to real GDP. Measure consumption spending on the vertical axis and real GDP (Y) on the horizontal axis. In your graph indicate the value of consumption spending when real GDP is equal to $0, $100, $200, $300, and $400. b. Now, suppose that government spending is constant and equal to $50 at every level of real GDP. Alter your graph to show the C + G line. c. Now, suppose that investment spending is constant and equal to $20 at every level of real GDP. Alter your graph to show the C + I + G line. d. Now, suppose that (X M) is constant and equal to $20 at every level of real GDP. Alter your graph to show the C + I + G + (X M) line. [b, c, and d] Note the y-intercept of the C+ G equation is 134; the y-intercept of the C + I + G equation is 154; and the y-intercept of the C + I + G + (X M) equation is 174.
e. Suppose that (a) through (d) are all true for this economy and you also know that full employment output in this economy (Yfe) is equal to $800. Given this information, what do you predict is happening to inventories if the full employment level of output is produced? f. What is the equilibrium level of output for this economy? To answer this question, we first need to see what the equilibrium level of real GDP is for this economy. In equilibrium we know that Ye is equal to aggregate expenditure or Ye = AE Ye = C + I + G + (X M) Ye = 100 + 0.8(Y T) + 20 + 50 + 20.2Ye = 100 0.8(20) + 90.2Ye = 190 16.2Ye = 174 Ye = 870 But, Yfe is equal to $800: if this economy tries to produce at the full employment level, the level of aggregate production ($800) will be less than the level of aggregate expenditure (AE = 100 + 0.8(800 20) + 20 + 50 + 20 or AE = 814). Since production is less than aggregate expenditure we know that inventories will decrease and this will act as a signal to producers to increase their production toward the equilibrium level of output.
g. Suppose that government spending is decreased from its initial level to $40. Holding everything else constant, what will be the change in the equilibrium level of output given this spending change? You can answer this question in two ways: 1) use the multiplier or 2) plug in the new number and recalculate the equilibrium level of output. 1. (change in real GDP) = [1/(1 b)] (change in government expenditure) (change in real GDP) = [1/(1-0.8)] (-10) (change in real GDP) = 5 (-10) = -$50 So real GDP decreases from $870 to $820 2. Y = 100 + 0.8(Y 20) + 20 + 40 + 20 0.2Y = 164 Y = $820 The change in real GDP = Y - Y = $820 - $870 = -$50 h. Suppose that government spending is increased from its initial level by $20. Holding everything else constant, what will be the change in the equilibrium level of output given this spending change? You can answer this question in two ways: 1) use the multiplier or 2) plug in the new number and recalculate the equilibrium level of output. 1. (change in real GDP) = [1/(1 b)] (change in government expenditure) (change in real GDP) = [1/(1-0.8)] (20) (change in real GDP) = 5 (20) = $100 So real GDP increases from $870 to $970 2. Y = 100 + 0.8(Y 20) + 20 + 70 + 20 0.2Y = 194 Y = $970 The change in real GDP = Y - Y = $970 - $870 = $100
[Out of Class] 2. Use the following graph and the Keynesian Model to answer this question. Assume that the aggregate price level is fixed in this problem. a. Given the above graph, what is the interpretation of the slope of the planned aggregate expenditure? The slope of the aggregate demand curve is the MPC (marginal propensity to consume). b. Given the above graph, what is the equilibrium level of output (Y1, Y2 or Y3)? The equilibrium of output is Y1. c. Suppose that the level of aggregate output or production is less than the level of planned aggregate expenditure. Which level of output (Y1, Y2 or Y3) in the above graph best describes this situation? How will inventories adjust for this economy to return back to the equilibrium level of real GDP? Y2 is the best representation among the labelled points for an output where aggregate expenditure is greater than aggregate production. Because at Y2, the level of output produced is lower than the level of planned aggregate expenditure. When the level of production is below the equilibrium level of output, the change in inventories will be negative telling us that unplanned inventory reductions are occurring in this economy. This unplanned fall in inventories will act as a signal to firms to increase their level of production toward the equilibrium level of real GDP.
d. Suppose you are told that the full employment level of production is equal to Y2. Given this information and the above graph, how would you describe the current state of this economy? In your answer make sure you describe the current state of unemployment and that you also contrast and compare the unemployment rate at Y1 and Y2. When the full employment of output is less than the equilibrium level, then we say the economy is in a boom. The unemployment rate aty1 is smaller than the unemployment rate at Y2. When this economy operates at Y1 where Y1 is greater than Yfull employment (Y2), then we know that this economy's unemployment rate is lower than its natural rate of unemployment. e. Suppose you know that people in this economy decide to start saving more aggressively for each additional dollar of income that they earn (note: they will still save at a constant rate, but it would be a different constant rate). Would this change in behavior alter the equilibrium level of real GDP you found in (b)? Draw a graph that illustrates the initial situation and then the new situation given this change in saving behavior. Explain in words what you have depicted in your graph. We are told that people are now saving more of each additional dollar of income: this implies that the MPC is decreasing from its initial level and that the MPS is increasing relative to its initial level. The change in the MPC will alter the slope of the AE curve (it will flatten) and the new equilibrium level of real GDP will be less than the initial equilibrium level of Y1.
f. Assume that the changes in (e) are still in effect in this economy. Suppose the government now decides to increase its spending and, in particular, to increase its spending on improving elderly welfare (assume that this does not change the new saving behavior). How does this policy change affect the planned aggregate expenditure and the level of output in equilibrium relative to the equilibrium you found in (b)? We know that the change in saving behavior alters the slope of the planned AE (see yellow line). With the change in the government spending program this will cause the planned AE line to shift up (the orange line). However, we don t know whether the equilibrium level of output would be higher or lower than Y1. It depends on how much the planned AE line shifts up with the change in government spending.