grow5_solow - 5 5.1 The Solow Growth Model Models and...

Info icon This preview shows pages 1–8. Sign up to view the full content.

5 The Solow Growth Model 5.1 Models and Assumptions What is a model? A mathematical description of the economy. Why do we need a model? The world is too complex to describe it in every detail. What makes a model successful? When it is simple but e ff ective in de- scribing and predicting how the world works. A model relies on simplifying assumptions. These assumptions drive the conclusions of the model. When analyzing a model it is crucial to spell out the assumptions underlying the model. Realism may not a the property of a good assumption. 67
Image of page 1

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

5.2 Basic Assumptions of the Solow Model 1. Continuous time. 2. Single good produced with a constant technology. 3. No government or international trade. 4. All factors of production are fully employed. 5. Labor force grows at constant rate n = ˙ L L . 6. Initial values for capital, K 0 and labor, L 0 given. 68
Image of page 2
Production Function Neoclassical (Cobb-Douglas) aggregate production function: Y ( t ) = F [ K ( t ) , L ( t )] = K ( t ) α L ( t ) 1 - α To save on notation write: Y = A K α L 1 - α Constant returns to scale: F ( λ K, λ L ) = λ F ( K, L ) = λ A K α L 1 - α Inputs are essential: F (0 , 0) = F ( K, 0) = F (0 , L ) = 0 69
Image of page 3

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

Marginal productivities are positive: F K = α AK α - 1 L 1 - α > 0 F L = (1 - α ) AK α L - α > 0 Marginal productivities are decreasing, 2 F K 2 = ( α - 1) α A K α - 2 L 1 - α < 0 2 F L 2 = - α (1 - α ) A K α L - α - 1 < 0 70
Image of page 4
Per Worker Terms Define x = X L as a per worker variable. Then y = Y L = A K α L 1 - α L = A K L a L L 1 - α = A k α Per worker production function has decreasing returns to scale. 71
Image of page 5

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

Capital Accumulation Capital accumulation equation: ˙ K = sY - δ K Important additional assumptions: 1. Constant saving rate (very specific preferences: no r ) 2. Constant depreciation rate 72
Image of page 6
Dividing by K in the capital accumu equation: ˙ K K = s Y K - δ .
Image of page 7

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

Image of page 8
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