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Find MPC, MPS, APC and APS, if the expenditure Ec of a person with income I is given as Ec = (0.0003) I2 + (0.075) I ; When I = 1000. - Mathematics and Statistics

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प्रश्न

Find MPC, MPS, APC and APS, if the expenditure Ec of a person with income I is given as Ec = (0.0003) I2 + (0.075) I ; When I = 1000.

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उत्तर

Given, Ec = (0.0003) I2 + (0.075) I

∴ MPC = `(dE_c)/(dI) = (0.0003)(2I) + 0.075` 

∴ MPC = 0.0006 I + 0.075

I = 1000            ...[Given]

∴ MPC = 0.0006(1000) + 0.075

= 0.6 + 0.075

∴ MPC = 0.675

Since MPC + MPS = 1,

0.675 + MPS = 1

∴ MPS = 1 - 0.675

∴ MPS = 0.325

Now, APC = `E_c/I`

= `((0.0003)I^2 +  (0.075)I)/I`

= `(I(0.0003I  +  0.075))/I`

∴ APC = 0.0003 I + 0.075

I = 1000          ...[Given]

∴ APC = 0.0003(1000) + 0.075

= 0.3 + 0.075

∴ APC = 0.375

Also, APC + APS = 1

∴ 0.375 + APS = 1

∴ APS = 1 – 0.375

∴ APS = 0.625

∴ For I = 1000,

MPC = 0.675, MPS = 0.325

APC = 0.375, APS = 0.625

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