Question

The expenditure E_c of a person with income I is given by E_c = (0.000035)I² +
(0.045)I. Find marginal propensity to consume (MPC) and marginal propensity to save (MPS) when I = 5000. Also find A(average) PC and A(average) PS.

Answer 1

E_c = (0.000035)I² + (0.045)I

MP_c = `(dE_C)/(dI)`

         = `d/(dI) [(0.000035)"I"^2 + (0.045)"I"]`

         = `(0.000035)(2"I") + (0.045)`

         = (0.00007)I + 0.045

∴ (MPC)_{I = 5000} = (0.00007) (5000) + 0.045 = 0.395

We know, MPS = 1 - MPC
∴ (MPS)_{I = 5000} = I - (MPC)_{t = 5000} 

                         = 1 - 0.395
                         = 0.605
Now, APC = `E_c/I = [(0.000035)I^2 + (0.045)I]/I`

                              = (0.000035)I + (0.045)

∴ (APC)_{t - 5000}  = (0.000035) (5000) + 0.045
                         = 0.175 + 0.045
                         = 0.22

We have, (APS) = 1 - (APC)_{t = 5000}
                          = 1 - 0.22
                          = 0.78