Maharashtra State BoardHSC Commerce 12th Board Exam
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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

Sum

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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Solution

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

∴ MPC = `("dE"_"c")/"dI" = (0.0003)(2"I") + 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"(0.0003"I"  +  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

Concept: Application of Derivatives to Economics
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 4 Applications of Derivatives
Exercise 4.4 | Q 13 | Page 113
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