Consider the consumption savings problem faced by an individual living in T = 100 periods with...

 

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Consider the consumption savings problem faced by an individual living in T = 100 periods with per period endowment y = 7+. consisting of a permanent and transitory component. B¹u(ci) s.t. max {ca+10 T 1-0 =0 c+a+1(1+r)a + y Vt at+1 ≥-B₁ ao = 0 a) Assume CRRA utility. Solve for {co as precisely as possible. b) Plot the time path of optimal consumption and savings/borrowing {et, at+1}o for a non-constant se- quence of e, of your choice. c) Does a one unit increase in y have the same effect as a one unit increase in e, on c? Why or why not? Argue your answer with mathematics and then explain the economies. Consider the consumption savings problem faced by an individual living in T = 100 periods with per period endowment y = 7+. consisting of a permanent and transitory component. B¹u(ci) s.t. max {ca+10 T 1-0 =0 c+a+1(1+r)a + y Vt at+1 ≥-B₁ ao = 0 a) Assume CRRA utility. Solve for {co as precisely as possible. b) Plot the time path of optimal consumption and savings/borrowing {et, at+1}o for a non-constant se- quence of e, of your choice. c) Does a one unit increase in y have the same effect as a one unit increase in e, on c? Why or why not? Argue your answer with mathematics and then explain the economies.

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a Assuming CRRA utility the individuals problem can be written as Maximize t uct subject to at1 1rat yt ct where uc c1 11 is the CRRA utility function ... View the full answer