Unformatted text preview: demand for goods in the Solow model comes from consumption and investment. Output per worker is divided between consumption per worker and investment per worker: y = c + i, which is the per worker version of the national accounts identity (assuming a closed economy). The model assumes that people save a fraction s of their income and consume a fraction (1 – s). Therefore, c = (1 – s)y This means that in terms of the national accounts identity, y = (1 – s)y + i Rearrange to obtain: i = sy This shows that investment equals saving. Thus, the rate of saving s is also the fraction of output devoted to investment. Two forces influence the capital stock: investment, which refers to the expenditure on new plant and equipment, and depreciation, which refers to the wearing out of old capital. We can express investment per worker as a function of the capital stock per worker: i = sf(k) We assume that a certain fraction δ of the capital stock wears out each year. δ is the depreciation rate. The amount of capital that depreciates every year is δk. Change in capital stock (Δk) = investment (i) – depreciation (δk), where Δk is the change in capital stock from one year to the next. Because investment = sf(k), we can write it as: Δk = sf(k) – δk The higher is capital stock, the greater the amounts of output an investment, and depreciation. There is a single capital stock k* at which the amount of investment equals depreciation. At k*, Δk = 0. We therefore call k* the steady state level of capital. An economy at the steady state will stay there, and an economy not at the steady state will go there. The steady state represents the long run equilibrium of the economy. To find the function for output per worker, take the production function, ex. Y = K0.5L05, and solve for y. In that case you would get y = √k. Page 21 of 52 Jessica Gahtan Prof: Mokhles Hossain Macroeconomics ECON2000 Fall 2013 To find the steady state, remember that in the steady state new investment is equal to depreciation, meaning that sf(k*) = δk*. If you have s, δ, and y, you can find the steady state level of capital per worker k*. Assume the economy is in a steady state....
View
Full Document
 Fall '10
 Henriques
 Economics, Macroeconomics

Click to edit the document details