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When capital stock exceeds the golden rule reducing

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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....
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