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.

Microeconomics: Private and Public Choice (MindTap Course List)

16th Edition

ISBN:9781305506893

Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson

Publisher:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson

Chapter14: Investment, The Capital Market, And The Wealth Of Nations

Section: Chapter Questions

Problem 10CQ

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