Question

On the planet Zorp, consumers consume mechanically based on the following consumption function ? = ?0 + 0.6? − 500?, where C is consumption, C0 is a constant, Y is consumers’ income (equivalent to GDP), and i is the interest rate written in decimal terms (i.e. a 5% interest rate gives i=0.05). Investors invest based on the following function: ? = ?0 − 1000?, where I is investment and I0 is a constant. There is no government in Zorp, so G=0. For the purposes of this question, you may assume that the Aggregate Supply curve is horizontal, so that GDP is entirely demand-driven.

a) Explain the economics behind the positive coefficient on Y in the consumption function and the negative coefficient on the interest rate in both the consumption and investment functions.

b) Let ?0 = 300 and ?0 = 175. Calculate GDP, consumption, investment, and savings in Zorp if the interest rate is 5% (i=0.05)?

c) Consumers decide to become more thrifty and increase their savings by 100 units and so decrease their consumption such that now ?0 = 200 (but all other parameters of the consumption and investment functions remain the same and the interest rate remains at i=0.05). What are the new GDP, consumption, investment, and savings in Zorp? By how much did savings actually increase?

d) Keynes referred to a phenomenon called “the Paradox of Thrift”, whereby attempts by individuals to save may turn out to be counterproductive. Explain why this paradox occurs given your answer to part (c) of this question.

e) To combat the recession caused by the decline in consumption described in part (c) of this question, the central bank reduces the interest rate to i=0.04. What are GDP, consumption, investment, and savings now?

f) In the consumption function, higher interest rates make consumers consume less because it encourages them to save. In the investment function, higher interest rates make investors invest less because investment becomes less attractive. But we were told that savings equal investment. Explain how it is possible for high interest rates to encourage savings and deter investment, even though savings are equal to investment (a seeming contradiction).

Answer 1

a) the positive coefficient on Y in the consumption function means that consumption is positively related to income. the coefficient being 0.6, means every $1 increase in income/ disposable income (income is same as disposable income here as government sector does not exist) leads to $0.6 increase in consumption.

The negative coefficient on interest rate in the consumption function means an increase in the interest rate results in less consumption as savings increase at a higher interest rate. Also if an individual has to borrow money from the market for consumption purpose, he will borrow less for consumption purpose when interest rate is high.

The negative coefficient on interest rate in the investment function means that investment and interest rate are negatively related. This is because at high interest rates some projects which were profitable now become non profitable due to increased cost. Such project will not be undertaken leading to reduction in investment at a high interest rate.

b)

C-Co +0.6Y-500i 300 +0.6Y -500 i

I 10-10001 175-1000i

Y = C + 1 = 300 + 0.6y-500i + 175-1000i = 475-0.6Y-1500i

0.4Y = 475-1500i

Y = 1187.5-3750i

At 1 = 0.05, y 1187.5-3750(0.05) 1187.5-187.5 1000

C 300 + 0.6Y-5001 300 + 0.6(1000)-500 (0.05) 300 + 600-25 = 875

I = 175-1000i-175-1000(0.05) 175-50 = 125

Savings S = Y-C-1000-875 125

c)
Co 200
,

C Co + 0.6Y-5001-200 + 0.6Y-500 i

I 10-10001 175-1000i

Y = C + 1 200 + 0.6y-500i + 175-1000i = 375-0.6Y-1500i

0.4Y = 375-1500i

Y = 937.5-3750i

At 1 = 0.05, y = 937.5-3750(0.05) 937.5-187.5 750

I = 175-1000i-175-1000(0.05) 175-50 = 125

125

Savings S = Y-C = 750-625 : :

So savings has not increased it remains same at 125.

d) Savings by individual is done for growth of his wealth. But it can be counter productive. At macro level if all individuals save, it results in fall in GDP.

An increase in savings results in fall in autonomous consumption which further results in fall in GDP (Y). It can be seen that GDP falls from $1000 to $750 i.e by $250. Fall in GDP leads to further fall in consumption . thus increase in savings at macroeconomic level leads to fall in GDP or income. This is known as paradox of thrift.

e)

C Co + 0.6Y-5001-200 + 0.6Y-500 i

I 10-10001 175-1000i

Y = 937.5-3750i

135

f) At high interest rate, savings increase in the beginning, due to which consumption falls and therefore GDP falls ( as seen in case c). Fall in GDP results in fall in savings. Savings will fall to such a level that it is always equal to investment.

To summarise, rise in interest rate leads to fall in investment

Rise in interest rate also leads to rise in savings. However this results in fall in GDP leading to fall in savings. So that S = I always in equilibrium