Question

4.According to the life-cycle hypothesis, explain the pattern of saving for an individual over his/her lifetime? What impact does this behaviour have on the saving rate?

5. Give an example of a country with a low savings rate. Are the implications positive or negative? Explain

While a higher capital stock implies higher output, this does not mean a higher capital stock is desirable. To sustain a high capital stock, a lot of output will have to be devoted to investment, leaving less available for consumption.

Golden Rule: The capital stock per-worker that maximizes consumption per-worker. In the Solow Growth Model with no population growth and technological progress, this occurs where

δ =MPK

Recall, at steady state, investment is equal to total depreciation because savings is equal to investment.

Steady state: * *)( k ksf δ = Total savings = total investment: * *)( i ksf = * * ki δ =⇒



A country that is saving too much, has a steady state capital stock that is above k*G, a country that is saving too little has a steady state capital stock that is below k*G. Notice that only one savings rate s will ensure that the economy achieves the golden rule capital stock at steady state. On the graph, this savings rate will ensure the savings function crosses at point A on the graph.

The golden rule can be interpreted in terms of marginal product of capital and depreciation. A one-unit increase in k raises output by MPK; this is the added benefit of increasing k. It also implies that an extra δ units of output must be set aside to maintain the capitallabor ratio at its new higher level; this is the additional cost of increasing k. The level that maximizes consumption will be where the added benefit (MPK) equals the additional cost ( δ ).

• If MPK > δ, then increase in k will increase output by more than the implied increase in depreciation, so consumption rises because there is more output leftover for consumption. The extra benefit (MPK) associated with an increase in k outweighs the cost ( δ ), so we should increase k. • If MPK < δ, then increase in k will increase output by less than the implied increase in depreciation, so consumption falls because there is less output leftover for consumption. The extra cost ( δ ) associated with an increase in k outweighs the benefit (MPK), so we should decrease k.

In the model with population growth and technological progress, the modified golden rule is:

)( δ ++= gnMPK

The interpretation in terms of marginal product is somewhat more difficult, but the general idea is the same as in the simple model. Notice that when there is no population growth (n = 0) or technological progress (g = 0), this modified golden rule collapses to the simple one at the top of the handout

Answer 1

Answer to question 4 and 5.

4. a. The life cycle hypothesis (LCH) was propounded by Ando and Modigliani in the 1950’s. The hypothesis essentially posits that consumption function that was introduced by Keynes relating to the changes of consumption of individual and society is a function of initial endowment of wealth along with the life time income. Thus the consumption function of LCH is,

C= αW+βY; where, W- wealth, Y- Income

Where α is the marginal propensity to consume from the wealth and β is the mpc from the income flow.

The hypothesis states that individuals optimize the decision of consumption based on life time consumption smoothing function. That is, in the initial years or the young who have just joined job sector, save and as they retire from work, the dissaving period starts. Thus the their might be short run fluctuations in consumption, but in long run the consumption is smothered over say T years or whole life time years. If R is the working years and T is the total year with W wealth, then consumption smoothing would mean,

C= (W+RY)/T spread over T years.

Thus, Wealth and consideration of future value of income is considered in LCH. In a life time, one at very young age dissaves, then at the working age saves and finally after retirement till death, dissaves. This would also mean an inter period borrowing of resources for an individual itself, where the periods of low income is controlled by borrowing as if from savings or the future prospective resources to smooth out the entire life time consumption.

b. Hence the life cycle hypothesis incorporates the consideration of demography in the savings and consumption decisions. Whereby a country in case is endowed with more working age group people, would means a higher rate of savings due to the LCH position that in the initial and working years people save. On the other hand if the population is more towards senior citizens would mean an economy that mostly dissaves and the saving rate is expected to be low.

5.

Guinea, Zimbabwe and Lebanon are countries among many that faces very low savings rate which are often in negatives. However the LCH may not be the only reason behind the low rate of savings in these nations. For instance government services and also political situation along with aggregate price level plays crucial role in determining the savings rate. Marginal propensity to consume can also determine the rate of savings in the economy. However, in case a country is facing a low savings rate would mean it is dissaving or is borrowing from the future resources. And this would mean that the future savings (and flow of income) needs to be high to pay off the borrowed sum in future period and also to sustain a smooth consumption function over the entire life time. This also means that the consumption is also high in the country, currently, and requires to be supported by high savings in the future. The figure below shows the phases of savings and dissavings over a life time.