ps5 - Economics 202 Principles of Macroeconomics Name...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Economics 202 Name: _______________ Principles of Macroeconomics Professor Melick Problem Set #5 Due Monday February 18, 2008 This problem set is meant to provide you with a solid understanding of the Solow growth model as presented in Chapter 6 of Abel and Bernanke (2005). The first part of this problem set develops the equations that characterize steady state equilibrium while the second part deepens your understanding of the model through an Excel example. The last section sheds some light on the optimal or “Golden Rule” steady state equilibrium. I. Theory - Simple Solow model We start in the simplest possible setting – there is no government and the economy is closed. In this case, the two main building blocks of the Solow model are the equilibrium condition d d d d d d t t t t t t t t S I or Y C I or Y C I = - = = + and the capital accumulation identity K K I d K t t t t + + - 1 The first equation tells us that the economy is in equilibrium in period t if desired savings is equal to desired investment. The capital accumulation identity simply states that next year’s capital stock must be equal to this year’s capital stock plus any investment over this year minus depreciation over the year. As discussed in class, the equilibrium solution for the model must be done in per worker terms, so we define the following variables t t t t t t Y K y k N N = = 1. If we assume that the labor force ( ) t N grows at rate n and that savings ( ) t S is just a constant fraction s of income ( ) t Y , use the space below to show that t t I S = implies that ( ) ( ) t t t k d k n y s - + + = + 1 1 1 .
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
The economy reaches a steady state when capital per worker and output per worker are constant, that is when y y y t t = = + 1 and k k k t t = = + 1 . We denote steady state equilibrium values as * y and * k . 2. Use the space below and your answer to question 1 to show that the steady-state equilibrium condition in the Solow model is written as ( ) * * k d n y s + = To make any numerical, as opposed to graphical, headway we must assume a functional form for the production function. As you might imagine, we turn to our old friend the Cobb-Douglas function α α - = 1 t t t N K A Y . 3. In the space below, put the production function into per worker terms, showing that it can be written as ( ) α t t k A y = . 4. In the space below, use the per worker production function to substitute for per worker output in ( ) * * k d n y s + = to show that the equilibrium, steady state, capital per worker can be written as α - + = 1 1 * d n s A k .
Image of page 2
5. Given the expression for steady state capital per worker, use the space below to show that steady state output per worker can be written as α α - + = 1 * d n s A A y . II. Spreadsheet Example - Simple Solow model We can gain more intuition about the Solow model by constructing a spreadsheet version of the model and demonstrating most of the points made in Chapter 6. First we will need to supply values for the parameters of the model ( s n d A , , , , α ). NOTE: Throughout, we will use data for 2006 , since
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the 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