Example of 4 sector model Let’s say we start with a linear model with a consumption function (or “schedule”): C = (Y – T) Let’s use a 4 sector model of AE with: I = 80 G = 60 T = 40 NX = 30

Example of 4 sector model Firstly graph the consumption function. If we plug in 40 for T, we get (0.75*40 = 30): C = Y – 30 C = Y We know the vertical intercept (Y=0): C = (0) = 70 C Y 70 Slope is 0.75 C= Y 0

Example of a 4 sector model From the C function, we know our MPC is a fact we will use later. Now we need to derive our AE curve. We use the 4 sector AE equation: AE = C + I + G + NX Plugging in the facts above, we get AE = Y C IGNX

Example of a 4 sector model Adding all those together, we get: AE = Y Just like we did with the C function, we can graph this AE function: C, AE Y 70 AE= Y C= Y 0 240

Example of a 4 sector model Now we need to find the equilibrium of this model. This occurs where goods demand, AE, is equal to goods supply, Y. –Note that AE is a function of income, Y, and we are also requiring that in equilibrium goods supply, Y, is equal to AE. We are using Y in two different senses, as income and as output. But remember from the first lecture, we can calculate GDP either from income or from production and get the same value. We are looking for an income level, Y*, that produces an AE level equal to Y*.

Example of a 4 sector model Using our equation for AE, we get: AE = Y* Y* = AE = Y* 0.25Y* = 240 Y* = 960 AE Y 240 AE = Y deg line

Example of a 4 sector model Since our MPC = 0.75, we know that the multiplier for autonomous expenditure is: Multiplier = 1/(1-MPC) = 1/(1-0.75) = 4 So a $1 change in I or G or NX would lead to a $4 change in equilibrium GDP, Y*.