Suppose that we are in the basic Solow model without technological growthor population growth. The only difference is that people live for two periods(working age and retirement). In the working age, they work and choose howmuch to save for retirement. In the retirement age, they don't work and spendtheir savings instead.The utility of someone working in period t is given by:U = (Ct) ³ (Ct+1)¹-B1. Interpret 3. Regardless of their income, what fraction of their incomewill the agent save? (Hint: this is a Cobb-Douglas utility function. Theexponents are very much related to optimal the share of spending on thedifferent goods.)2. Suppose the income of each agent is the wage wt. How much total savingswill there be at time t if the total working-age population is Lt, as afunction of wt, B and Lt?3. Supposed that the production function is the usual one (Yt = A(Kt) a (Lt) ¹-a)and that the wage is equal to the marginal product of labor (why shouldit?). What are the total savings in the economy as a function of B, a andYt?4. Write down the 4 key ingredients of this particular growth model in theaggregate (production function, aggregate ressource constraints, aggregatebehavioral equation, law of motion). This economy is equivalent to theSolow model, with a specific value of the savings rate. What is this savingsrate?5. Under what condition is the (endogenously chosen) saving rate equal tothe golden rule rate? What happens if 3 is too high or too low?

Utility function U=ctβct+11-β Production function: Yt=A(Kt)α(Lt)(1-α)

Suppose that we are in the basic Solow model without technological growth or population growth. The only difference is that people live for two periods (working age and retirement). In the working age, they work and choose how much to save for retirement. In the retirement age, they don't work and spend their savings instead.

Suppose that we are in the basic Solow model without technological growth or population growth. The only difference is that people live for two periods (working age and retirement). In the working age, they work and choose how much to save for retirement. In the retirement age, they don't work and spend their savings instead.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Suppose that we are in the basic Solow model without technological growth
or population growth. The only difference is that people live for two periods
(working age and retirement). In the working age, they work and choose how
much to save for retirement. In the retirement age, they don't work and spend
their savings instead.
The utility of someone working in period t is given by:
U = (Ct) ³ (Ct+1)¹-B
1. Interpret 3. Regardless of their income, what fraction of their income
will the agent save? (Hint: this is a Cobb-Douglas utility function. The
exponents are very much related to optimal the share of spending on the
different goods.)
2. Suppose the income of each agent is the wage wt. How much total savings
will there be at time t if the total working-age population is Lt, as a
function of wt, B and Lt?
3. Supposed that the production function is the usual one (Yt = A(Kt) a (Lt) ¹-a)
and that the wage is equal to the marginal product of labor (why should
it?). What are the total savings in the economy as a function of B, a and
Yt?
4. Write down the 4 key ingredients of this particular growth model in the
aggregate (production function, aggregate ressource constraints, aggregate
behavioral equation, law of motion). This economy is equivalent to the
Solow model, with a specific value of the savings rate. What is this savings
rate?
5. Under what condition is the (endogenously chosen) saving rate equal to
the golden rule rate? What happens if 3 is too high or too low?

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a. Show graphically what happens in the Solow Model when population growth increases. Label your graph clearly. b. Explain clearly the impact of this increase in population growth on i. income per capita ii. the growth rate of income per capita (in transition and at the new steady state) iii. the growth rate of total GNP.
when a country adds ideas what is it doing to its productivity and GDP? Which variable in the Solow Model equation is it changing?