Comparative Statics in a Long-Run Model

In levels, the key equations are 

Y = F(K,L)

C = C(Y-T)

Y = C + I + G + NX

or equivalently,

Y-C-G  =  S  =  I + NX

The following variables are exogenous, determined outside the model:

  • K = exogenous capital stock
  • L = exogenous amount of labor
  • T = taxes net of transfers and net of interest payments by the government (= taxes - transfers - interest payments by the government)
  • G = government purchases

Each problem will specify any way in which these exogenous variables change.  

In addition, please assume:

  • technology is unchanging as well as exogenous
  • NX = 0 in a closed economy. This also implies ΔNX=0. Assume a closed economy from here on. 

The problems will not spell these assumptions out. Just assume NX = 0 and that technology is unchanging.

The endogenous variables are:

  • Y = GDP
  • C = consumption
  • I = investment
  • S = national saving

In change form, using "·" to signify multiplication, the key equations are:

ΔY = MPK · ΔK + MPL · ΔL

ΔC = MPC · (ΔY - ΔT)

ΔY - ΔC -ΔG  =  ΔS =  ΔI + ΔNX

Remember to assume ΔNX=0 because the economy is closed. In a closed economy, the last equation becomes:

ΔY - ΔC -ΔG = ΔS = ΔI

There are three local parameters (slopes) in these change-form equations:

  • MPK = marginal product of capital
  • MPL = marginal product of labor
  • MPC = marginal propensity to consume

The problems always specify these local parameters. In the problems, always solve the equations in this order:

  1. ΔY = MPK · ΔK + MPL · ΔL
  2. ΔC = MPC · (ΔY - ΔT)
  3. ΔY - ΔC -ΔG  =  ΔS  =  ΔI

The numbers below are for toy economies; they may not be particularly realistic. Your job is to fill in ΔY, ΔC, ΔS and ΔI. If you want to print out the exercise and the answer, the files for the pictures below are here (1 is questions, 2 is answers).