Remember c c mpc y t so c falls by mpc 500 y c

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ), so C falls by MPC ∗ (500) Y = C + I + G + NX , so Y falls by MPC ∗ (500) C = C + MPC (Y − T ), so C falls by MPC ∗ MPC ∗ (500) Y = C + I + G + NX , so Y falls by MPC ∗ MPC ∗ (500) This process keeps repeating. Ryan W. Herzog (GU) Aggregate Expenditures February 25, 2014 32 / 43 Short-Run Equilibrium Mathematical Solution Solving for Equilibrium Mathematically It might help to solve the model in a more general format. We are going to start with planned aggregate expenditure: PAE = C + I p + G + NX (11) Recall the consumption function: C = C + MPC (Y − T ) Assuming I, T, G, and NX are autonomous. The PAE line becomes: PAE = [C + MPC (Y − T )] + I + G + NX or PAE = [C − (MPC )T + I + G + NX ] +(MPC )Y (12) Intercept Ryan W. Herzog (GU) Aggregate Expenditures February 25, 2014 33 / 43 Short-Run Equilibrium Mathematical Solution Solving for Equilibrium To find short-run equilibrium output we set Y = PAE Y = PAE (13) Substituting for PAE: Y = [C − (MPC )T + I + G + NX ] + (MPC )Y Solving for Y: Y − (MPC )Y = [C − (MPC )T + I + G + NX ] or Y (1 − MPC ) = [C − (MPC )T + I + G + NX ] Ryan W. Herzog (GU) Aggregate Expenditures February 25, 2014 34 / 43 Short-Run Equilibrium Mathematical Solution Example Dividing both sides by (1 − MPC ): Y= 1 [C − (MPC )T + I + G + NX ] 1 − MPC (14) Assuming C = 800, T = 100, NX = 180, G = 1000, I p = 300, and MPC = 0.8. Y= 1 [800 − (0.8)100 + 300 + 1000 + 180], 1 − 0.8 Multiplier or Y = (5)(2200) = 11, 000 Ryan W. Herzog (GU) Aggregate Expenditures February 25, 2014 35 / 43 Short-Run Equilibrium Mathematical Solution Example Notice that whenever the numbers change in the brackets, output will change by a multiple of 5. Suppose investment declines by $500. Y = (5)(1700) = 8, 500 Notice that the $500 decrease in investment lowered the autonomous component by 500, which was then multiplied by 5 to find the new short-run level of output....
View Full Document

This document was uploaded on 03/18/2014 for the course ECON 202 at Gonzaga.

Ask a homework question - tutors are online