Question

Linear equations for the consumption schedules take the general form C = a + bY and savings schedules take the general form S = –a + (1 – b)Y, where C, S, and Y are consumption, saving, and national income, respectively.

a. Use the following data to determine numerical values for a and b in the consumption and saving equations:

National Income (Y)	Consumption (C)
$0.00	$100.00
200.00	290.00
400.00	480.00
600.00	670.00
800.00	860.00

C = $ _____ + _____

S = $ _____ + _____

b. Suppose that the amount of saving that occurs at each level of national income falls by $20 but that the values of b and (1 - b) remain unchanged. Restate the saving and consumption equations for the new numerical values, and cite a factor that might have caused the change.

C = $ _____ + _____

S = $ _____ + _____

Answer 1

(a)

C = a + bY

Where, a is the autonomous consumption, i.e., the consumption level at national income level of zero.

b is the slope of consumption function. Slope of consumption fucntion measures the change in consumption due to change in national income.

We can see that every $200 increase in national income (Y) leads to increase in consumption (C) by $190

=> change in Y = $200

=> chnage in C = $190

Slope of consumption function = b = (change in C / change in Y)

=> b = ($190 / $200)

=> b = 0.95

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the value of 'a' would be $100.

because when Y = $0, then C is $100

C= a + bY

=> C = $100 + 0.95Y

S = -a + (1-b)Y

=> S = -$100 + (1-0.95)Y

=> S = -$100 + 0.05Y

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(b)

Amount of saving that occurs at each level of national income falls by$20, but the value of b and (1-b) remains unchanged.

New saving function:

S = -$100 + 0.05Y - $20

=> S = -$120 + 0.05Y

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New consumption function:

Y = C + S

=> C = Y - S

=> C = Y - (-$120 + 0.05Y)

=> C = Y + $120 - 0.05Y

=> C = $120 + 0.95Y