ln3-revised - Econ 102 Winter 2012 Lecture Note 3 The Solow...

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

View Full Document Right Arrow Icon
Econ 102 Winter 2012 Lecture Note 3 The Solow Growth Model (with no growth) The Solow model is a simple model of economic growth, with one good that is produced by a Cobb-Douglas production technology. The good is used for either consumption ( C ) or investment ( I ): Y = C + I ; there is no government and no trade with other countries. Investment is converted to capital ( K ), but not immedi- ately. We will assume that the markets for consumption, capital and labor are all perfectly competitive (firms are price takers). In addition, we assume that everyone works - there is no difference between L t and the population at time t . One of the key assumptions we make is that the savings rate of the country is given fraction s and not chosen. This means a fraction s of output will be devoted to investment in each period. In addition, capital depreciates at a constant rate δ . This means that capital, if left alone, disappears at a rate δ . In order to sustain the same amount of capital, the economy needs to replenish its capital stock ( K t ) with new investment. The Solow Model, Mathematically The above assumptions are consistent with an economy described by these equations: Y t = F ( K t ,L t ) = AK α t L 1 - α t (1) I t = sY t (2) K t +1 = K t + I t - δK t (3) (1) Output is produced by a Cobb-Douglas production function (2) Investment is a constant fraction of output (3) Capital depreciates at rate δ and accumulates with investment The values for A , α , δ , and s are all given in this model. Variables and parameters that are given from outside the model are called exogenous (Greek for “given from outside”), while variables like Y t , K t and I t , which are determined within the model, are called endogenous . 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
Per-capita Version In order to simplify our analysis, we can set up a per capita version of the model. Since F ( K,L ) is constant returns to scale, Y t = F ( K t ,L t ) = Y t L t = F ( K t /L t , 1) Whenever we use lower-case variables, we will mean per-capita. So Y t is total output while y t will stand for per-capita output. Mathematically, y t Y t L t , k t K t L t , i t = I t L t , etc. For our production function, this means: y t = F ( k t , 1) = Ak α t (1) 1 - α Since this looks a bit weird, we’ll use a lower-case f ( k t ) to mean F ( k t , 1) y t = f ( k t ) = Ak α t In order to discuss growth, first we examine what happens in the model over time. Our capital accumulation equation tells us that capital in the next period comes from capital in the current period, plus investment, minus depreciation. k
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 8

ln3-revised - Econ 102 Winter 2012 Lecture Note 3 The Solow...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online