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15: SECTION THE CONSUMPTION FUNCTION THE CONSUMPTION FUNCTION Three things to do with income (Y) 1. 2. 3. Spend it (Consumption = C) Save it (Saving = S) Pay taxes (Taxes = T) Y=C+S+T DISPOSABLE INCOME: Yd = Income available after paying taxes Yd = Y - T = C + S There are only two things to do with disposable income 1. 2. Spend it (consumption = C) Save it (saving = S) Yd = C + S CONSUMPTION FUNCTION Expresses consumption spending as a function of disposable income Holding all other variables constant Other variables also influence the level of consumption Wealth Expected future income Expected inflation rates Level of interest rates WEALTH VERSUS INCOME WEALTH (OR NET WORTH): Value of what you own minus what you owe INCOME: Amount you earn in a given time period Wealth is what you have saved over your lifetime An old person could be extremely wealthy and have almost no income CONSUMPTION FUNCTION FOR A HOUSEHOLD Consumption spending increases as income increases C = f(Y) Or C = f(Yd) The relationship between consumption and income is close to linear Slope of function decreases as income increases. CONSUMPTION FUNCTION FOR THE U.S. ECONOMY Consumption spending (C) increases as GDP increases. C = f(GDP) = f(Y) Or C = f(Yd) where aggregate income (Y) = GDP CONSUMPTION FUNCTION FOR THE U.S. ECONOMY Historically, the relationship has been almost exactly linear. Frequently, we express C as a function of Y, rather than Y d PLOTTING THE CONSUMPTION FUNCTION Example: C = 6 + .7 Yd Plot C on the vertical axis Plot Y or Yd on the horizontal axis Example: C = 6 + .7 Yd Intercept = 6 = Value of C when Yd = 0 = Autonomous consumption Slope = .7 = (Change in C) / (Change in Yd) = Marginal Propensity to Consume An easy way to plot the consumption function is to select some values of Y and find the corresponding values of C. Plot these points and draw a line through them. PLOTTING THE CONSUMPTION FUNCTION Example: Value of Y Value of C C = 6 + .7 Yd 0 6 10 13 20 20 30 27 40 34 Plot the points (C, Y): (6, 0); (13, 10); (20, 20), etc. These points fall on a straight line INTERCEPT The intercept on the vertical axis is C = 6 This represents AUTONOMOUS CONSUMPTION AUTONOMOUS SPENDING Any spending that does not depend on the level of income or GDP Consumption Investment Government Foreign spending AUTONOMOUS CONSUMPTION Consumption spending that does not depend on the level of income (or GDP) Represented by the intercept in the consumption function = 6 SLOPE If Y increases by 10, C increases by 7 Slope = (Change in C)/(Change in Y) = 7/10 = .7 = MARGINAL PROPENSITY TO CONSUME MARGINAL PROPENSITY TO CONSUME Amount that C increases when Yd increases by 1 unit MARGINAL PROPENSITY TO CONSUME (MPC) The fraction of an increase in income that is spent by consumers Represented by the slope of the consumption function MPC = (Change in C) / (Change in Yd) = C/ Yd INDUCED = CONSUMPTION the increase in consumption spending caused (or induced) by an increase in income Suppose MPC = .7 Example: C = 6 + .7 Yd If income increases by $10,000, consumption will increase by $7,000 Yd = 10,000 C = 7,000 MPC = 7000/ 10,000 = .7 PARALLEL SHIFTS IN THE CONSUMPTION FUNCTION A change in the intercept causes the consumption function to shift parallel to itself with no change in the slope. Factors causing the consumption function to shift upward 1. 2. 3. 4. rate Increases in wealth Decreases in interest rates Increases in expected future income Increases in future expectations of the inflation Example: C = 6 + .7 Yd C = 10 + .7 Yd CHANGING FUNCTION THE SLOPE OF THE CONSUMPTION A change in the slope causes the consumption function to become steeper or flatter (with no change in the intercept). Example: C = 6 + .7 Yd C = 6 + .8 Yd The MPC takes a value between 0 and 1. 0 < MPC < 1 MARGINAL PROPENSITY TO CONSUME VERSUS THE AVERAGE PROPENSITY TO CONSUME APC = Total consumption spending/ Total income APC = C/ Yd MPC = C / Yd The APC tells us the proportion of our entire disposable income that has been spent on consumption. The MPC tells us the proportion of any increase in our disposable income that will be spent on consumption IF THE CONSUMPTION FUNCTION IS A STRAIGHT LINE, THE APC DECREASES AS Yd INCREASES. Example: C = 6 + .7 Yd C 13 20 27 34 Y 10 20 30 40 APC 1.3 1.0 0.9 .85 DRAW A 45 DEGREE LINE ON THE GRAPH WITH THE CONSUMPTION FUNCTION The 45 degree line is the locus of all points such that the value on the vertical axis equals the value on the horizontal axis. The line representing the consumption function shows the amount of desired consumption spending associated with any level of disposable income. Suppose a point on the consumption function lies ABOVE the 45 degree line. Then C > Yd. This means that consumption exceeds income. Suppose C exceeds disposable income This tends to occur when income is low. These families dissave. Suppose a point on the consumption function lies BELOW the 45 degree line. Then C < Yd. Thus, income exceeds consumption. This tends to occur when income is high. Suppose a point on the consumption function lies ON the 45 degree line. Then C = Yd This means that income equals consumption. These families just BREAK EVEN. SUPPOSE C > YD. APC = C/Yd > 1. WHEN Yd IS SMALL, APC > 1 People borrow or deplete past savings Person is DISSAVING. SUPPOSE C = Yd. BREAK EVEN POINT. APC = C/Yd = 1 Person spends all his disposable income Savings = 0 SUPPOSE C < Yd When income is high, disposable income exceeds consumption spending; (that is, C < Yd) APC = C/Yd < 1 Savings > 0 IF THE CONSUMPTION FUNCTION IS A STRAIGHT LINE, THE MPC IS CONSTANT C = 6 + .7 Yd C 6 13 20 27 34 Y 0 10 20 30 40 APC 1.3 1.0 0.9 .85 C/ Y = 7/10 = .7 C/ Y = 7/10 = .7 C/ Y = 7/10 = .7 C/ Y = 7/10 = .7

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