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## Capital stock

The next key idea on which growth models are based is that the capacity of a country to produce goods depends on the amount of capital stock in the economy. A poor country with only basic agricultural equipment and little electricity supply or infrastructure is obviously not going to be able to produce very much, because it has a low capital stock. A richer country with hi tech equipment, fast railways, high speed internet connections, large scale production plants and so on, is going to be able to produce more because it has a high capital stock. To get more growth you need to increase your productive capacity, that means increasing your capital stock.

Every year you add to your capital stock through investment, firms getting more machinery, plants etc. But because capital stock depreciates, every year you lose some of last year’s stock through depreciation. So you can express this as $K_{t+1}=K_t+I_t-\delta(K_t)$. This is saying that the capital stock you will have next year is equal to the capital stock this year plus investment (the new capital you add) minus the depreciation rate, $\delta$ multiplied by this year’s capital stock. The last part of that equation gives you the amount of capital that has been depreciated. You can rewrite the equation as $K_{t+1}=I_t+K_t(1-\delta)$, which basically says capital next year is equal to investment this year plus the amount of your existing capital stock that is left after depreciation. Usually the depreciation rate is constant.