Worth: Mankiw Economics 5e CHAPTER 7 Economic Growth I 185 figure 7-3 atIon Depreciation Depreciation A constant frac out every year. Depreciation is therefore proportional to the capital stock per worker, k To incorporate depreciation into the model, we assume that a certain fraction 8 of the capital stock wears out each year. Here 8(the lowercase Greek letter delta) is called the depreciation rate. For example, if capital lasts an average of 25 years, then the depreciation rate is 4 percent per year(6=0.04). The amount of capital that depreciates each year is ok. Figure 7-3 shows how the amount of de- preciation depends on the capital stock. We can express the impact of investment and depreciation on the capital stock with this equatio Change in Capital Stock= Investment- Depre where Ak is the change in the capital stock between one year and the next. Be- cause investment i equals sf(k), we can write this △k=f(k)-8k Figure 7-4 graphs the terms of this equation--investment and depreciation--for different levels of the capital stock k. The higher the capital stock, the greater the amounts of output and investment. Yet the higher the capital stock, the greater lso the amount of depreciation As Figure 7-4 shows, there is a single capital stock k* at which the amount of ivestment equals the amount of depreciation. If the economy ever finds itself at this level of the capital stock, the capital stock will not change because the two forces acting on it--investment and depreciation- just balance. That is, at k', Ak=0, so the capital stock k and output f(k) are steady over time(rather than growing or shrinking). We therefore call k' the steady-state level of capital The steady state is significant for two reasons. As we have just seen, an econ- my at the steady state will stay there. In addition, and just as important, an econ- omy not at the steady state will go there. That is, regardless of the level of capital User JoENA: Job EFFo1423:6264_cho7: Pg 185: 26802#/eps at 100s ed,Feb13,20029:484MUser JOEWA:Job EFF01423:6264_ch07:Pg 185:26802#/eps at 100% *26802* Wed, Feb 13, 2002 9:48 AM To incorporate depreciation into the model, we assume that a certain fraction d of the capital stock wears out each year. Here d (the lowercase Greek letter delta) is called the depreciation rate. For example, if capital lasts an average of 25 years, then the depreciation rate is 4 percent per year (d = 0.04).The amount of capital that depreciates each year is d k. Figure 7-3 shows how the amount of de￾preciation depends on the capital stock. We can express the impact of investment and depreciation on the capital stock with this equation: Change in Capital Stock = Investment − Depreciation Dk = i − d k, where Dk is the change in the capital stock between one year and the next. Be￾cause investment i equals sf(k), we can write this as Dk = sf(k) − d k. Figure 7-4 graphs the terms of this equation—investment and depreciation—for different levels of the capital stock k.The higher the capital stock, the greater the amounts of output and investment.Yet the higher the capital stock, the greater also the amount of depreciation. As Figure 7-4 shows, there is a single capital stock k* at which the amount of investment equals the amount of depreciation. If the economy ever finds itself at this level of the capital stock, the capital stock will not change because the two forces acting on it—investment and depreciation—just balance. That is, at k*, Dk = 0, so the capital stock k and output f(k) are steady over time (rather than growing or shrinking).We therefore call k* the steady-state level of capital. The steady state is significant for two reasons.As we have just seen, an econ￾omy at the steady state will stay there. In addition, and just as important, an econ￾omy not at the steady state will go there.That is, regardless of the level of capital CHAPTER 7 Economic Growth I | 185 figure 7-3 Depreciation per worker, dk Depreciation, dk Capital per worker, k Depreciation A constant frac￾tion d of the capital stock wears out every year. Depreciation is therefore proportional to the capital stock