# note4_n3 - Econ303 A Simple Model of GDP Determination We...

• Notes
• 5

This preview shows pages 1–3. Sign up to view the full content.

Econ303 A Simple Model of GDP Determination 1 We make the following assumptions Assumption 1 All countries use the same technology, Y = F ( K, L ) . Assumption 2 The supplies of labor and capital are exogenously given. Let L s denote the supply of labor and K s the supply of capital. Then L s = ¯ L and K s = ¯ K . Both ¯ L and ¯ K are some numbers. Firms in a competitive market maximize profits. Their optimal demand for capital and labor are K d and L d , which is determined by marginal conditions : MP K = ˆ r MP L = w At the equilibrium on the labor and capital markets, demands equal supplies. These are called market clearing conditions L d = L s K d = K s Definition 1 A competitive equilibrium consists of two sets of numbers: quantities ( Y, K d , L d , K s , L s ) and prices r, w ) . They satisfies the following requirements: 1. Given prices r, w ) , quantities ( Y, K d , L d ) maximize firms profits; 2. r, w ) are prices that clear markets. In another word, the equilibrium is determined by both marginal conditions and market clearing conditions. Mathematically, ( Y, L d , K d , L s , K s , w, ˆ r ) satisfies the following sets of equations MP K ( K = K d , L = L d ) = ˆ r MP L ( K = K d , L = L d ) = w L d = L s = ¯ L K d = K s = ¯ K Y = F ( ¯ K, ¯ L ) Below is how we find a competitive equilibrium for an economy: 1. The equilibrium quantities are given by the exogenous supplies of factors. (We use market clearing condition here.) At equilibrium K d = K s = ¯ K , L d = L s = ¯ L and Y = F ( ¯ K, ¯ L ).

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

Econ303 A Simple Model of GDP Determination 2 2. The equilibrium prices are given by the marginal conditions. The rental rate of capital equals the marginal product of capital and the wage rate equals the marginal product of labor. Both marginal product are evaluated at the equilibrium capital and labor. That is, ˆ r = MP K ( ¯ K, ¯ L ) , w = MP L ( ¯ K, ¯ L ) . Point: In this simple model, GDP, wage rate and rental rate of capital in an economy are determined by the total amount of labor and capital supplied. example Suppose that the production function is Y = K 0 . 5 L 0 . 5 and the labor supply in this economy is L s = 0 . 5 and capital supply K s = 0 . 5. How do we find the equilibrium for this economy? The marginal product of capital, MP K = 0 . 5 K - 0 . 5 L 0 . 5 and the marginal product of labor, MP L = 0 . 5 K 0 . 5 L - 0 . 5 . Both are functions of capital and labor input.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern