Question

1) Consumption and savings are two sides of the same coin. Given one, you can always know the other. Consider an economy whose consumption function is C = 10 + 0.8Yd. There are no taxes in this economy. Suppose initially that the interest rate is r = 0.

i) National income Y = $70. What is the economy’s total consumption C and total savings S?

ii) What is the marginal propensity to consume in this economy? The marginal propensity to save? Of all dollars earned, what fraction are saved? Is the marginal propensity to save the same as this average amount saved per dollar earned in the economy? Explain.

iii) Suppose for this question that the economy always saves exactly S = 3. Initially, the interest rate in the economy is 10%, which we will represent as r = 10. Suddenly, the interest rate jumps to r = 20. How does this increase in the interest rate impact the economy’s ability-to-consume in the future?

iv) Return to the consumption function in the setup. Notice from the initial setup that when Y = 0, S = -10. Interest r is an incentive to save. For any given Y, as r rises one point (for example, from r = 3 to r = 4), total saving S rises by $1. State total saving S as a function of both Y and r.

v) Given your answer to part d, state the consumption function, given that saving is a function of the interest rate r and national income Y, as in part d.

Answer 1

Answer:

1)

Given C=10+0.8Yd.

i) National income Y=$70.

C=10+0.8*70=10+56=66

Savings (S)=Y-C=$70-66=$4.

ii) Marginal propensity to consume(MPC) is the proportion of consumption out of the income that increases with the increase in Income. This is shown as the coefficient of Y in consumption function.

In Consumption equation C=10+0.8Yd, 0.8 is the Marginal propensity to consume.

Marginal propensity to save=1-MPC=1-0.8=0.2.

MPS shows that of all dollars earned 0.2, i.e. 20% are saved.

MPS=S/Y, it shows increase or decrease in saving with change in income,whereas APS=S/Y.. So both are not same.

iii)

With increase in the interest rate from 10% to 20%, people will get greater incentive to save and would save today to earn interest and to consume later. So, the future consumption will increase with the increase in the interest rate.

iv) Saving function S=-10+0.2Y+cr, where c=1 because with increase of r from 3 to 4 , S increases by $1.

v)

Consumption function C=Y-S=Y+10-0.2Y-cr or C=10+0.8Y-cr.