#### Question

The expenditure E_{c} of a person with income I is given by E_{c} = (0.000035) I^{2} + (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.

#### Solution

`E_c=(0.000035)I^2+(0.045)I`

`MP_c=(dE_c)/(dI)`

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

`=(0.000035)(2I)+(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)=1-(MPC)_(I=5000)`

`=1-0.395`

`=0.605`

`Now " "APC=E_c/I=((0.000035)^2+(0.045)I)/I`

`=(0.000035)I+(0.045)`

`(APC)_(I=5000)=(0.000035)(5000)+(0.045)`

`=0.175+0.045`

`=0.22`

We have

`(APS)=1-APC`

`(APS)_(I=5000)=1-(APC)_(I=5000)`

`=1-0.22`

`=0.78`

Is there an error in this question or solution?

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Solution The expenditure Ec of a person with income I is given by Ec = (0.000035) I^2 + (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. Concept: Maxima and Minima.