{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Economics Dynamics Problems 122

Economics Dynamics Problems 122 - t = a t − 1 bY t − 1...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
106 Economic Dynamics Figure 3.12. Example 3.6 A bank is offering a savings account paying 7% interest per annum, compounded quarterly. What is the effective interest rate? re = 1 + 0 . 07 4 4 1 = 0 . 072 or 7.2%. If we assume that m is a continuous variable, then given an interest rate of say, 7%, we can graph the relationship between re and m . A higher market interest rate leads to a curve wholly above that of the lower interest rate, as shown in figure 3.12. Returning to the compounding result, if an amount is compounded at an annual interest rate r , then at time t we have the relationship Y t = (1 + r ) Y t 1 . If we generalise this further and assume an additional deposit (or withdrawal) in each period, a t , then the resulting recursive equation is Y t = (1 + r ) Y t 1 + a t 1 Or more generally, we have the recursive equation Y
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: t = a t − 1 + bY t − 1 Many problems reduce to this kind of relationship. ±or example, population of a species at time t may be proportional to its size in the previous period, but predation may take place each period. Or, human populations may grow proportionally but immigration and emigration occurs in each period. Solving the recursive equation can be achieved by iteration. Let the initial values be Y and a , respectively, then Y 1 = a + bY Y 2 = a 1 + bY 1 = a 1 + b ( a + bY ) = a 1 + ba + b 2 Y Y 3 = a 2 + bY 2 = a 2 + b ( a 1 + ba + b 2 Y ) = a 2 + ba 1 + b 2 a + b 3 Y Y 4 = a 3 + bY 3 = a 3 + b ( a 2 + ba 1 + b 2 a + b 3 Y ) = a 3 + ba 2 + b 2 a 1 + b 3 a + b 4 Y...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern