Question

The consumption function is given by c=0.02Y^2+0.6Y+50

a) express the mpc and mps in terms of Y

b) calculate MPC and MPS when y=8; interpret the values

Answer 1

Answer

The consumption function is given by,

C=0.02Y² + 0.6Y + 50.....(1)

a) MPC = 0.04 Y + 0.6 ; MPS = 0.4 - 0.04Y

MPC(marginal propensity to consume) shows the change in consumption(C) for the change in income(Y), i.e., disposable income.

MPC = dC/dY

Differentiating equation(1) with respect to 'Y', we get,

dC / dY = 2(0.02Y) + 0.6

Or, dC / dY = 0.04 Y + 0.6

MPC = 0.04 Y + 0.6

MPS(marginal propensity to save) shows the change in savings(S) for the change in income(Y) , i.e., disposable income.

Now, Y = C + S

dY = dC + dS , [ dY = change in income ; dC = change in consumption; dS = change in savings]

Or, dY / dY = (dC/ dY) + (dS / dY)

Or, 1 = MPC + MPS

MPS = 1 - MPC

Now, putting the value of MPC in the above equation, we get,

MPS = 1 - (0.04 Y + 0.6)

Or, MPS = 1 - 0.04 Y - 0.6

Or, MPS = (1 - 0.6) - 0.04Y

Or, MPS = 0.4 - 0.04Y

MPS = 0.4 - 0.04Y

So, the MPC in terms of Y is, '0.04 Y + 0.6' ; and MPS in terms of Y is, '0.4 - 0.04Y'.

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b) MPC = 0.92 ; MPS = 0.08

MPC = 0.04 Y + 0.6

Now, when Y = 8, then MPC will be,

MPC = 0.04 * (8) + 0.6

Or, MPC = 0.32 + 0.6

Or, MPC = 0.92

When Y = 8, then MPS will be,

MPS = 0.4 - 0.04 * (8)

Or, MPS = 0.4 - 0.32

Or, MPS = 0.08

Thus, when Y = 8 , the MPC is '0.92' , and MPS is '0.08'.

Now, MPC + MPS = 0.92 + 0.08 = 1

It means that the sum of MPC and MPS is always '1'. If MPS is zero, then MPC is '1', and if MPC is zero(i.e., consumption didn't rise with the rise in income), then MPS is '1'. So the values of both MPC and MPS are less than or equal to '1'.

MPC 1, and MPS 1

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