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Economics Dynamics Problems 50

Economics Dynamics Problems 50 - 34 Economic Dynamics...

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34 Economic Dynamics present at time t . If dn / dt denotes the number of atoms that degenerate per unit of time, then according to Rutherford dn dt = − λ n λ > 0 (2.9) where λ is the decay constant of the substance concerned and n is a continuous function of time. This is a first-order linear homogeneous differential equation and is identical in form to the exponential population growth specified in example 2.6 above. We shall return to this example later when we consider its solution and how the solution is used for calculating the half-life of a radioactive substance and how this is used to authenticate paintings and such items as the Turin shroud. Example 2.8 In this example we consider a continuous form of the Harrod–Domar growth model. In this model savings, S , is assumed to be proportional to income, Y ; investment, I , i.e., the change in the capital stock, is proportional to the change in income over time; and in equilibrium investment is equal to savings. If s denotes
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