Question: By taking the first-order condition with respect to capital, derive the demand for capital as a function of the rental rate. In what follows, it

By taking the first-order condition with respect to capital, derive the demand for capital as a function of the rental rate. In what follows, it will also be useful to use this equation in logarithms. Recall that the rental rate is closely related to the real interest rate due to a no-arbitrage argument. Here, we will simply assume that the rental rate rt is equal to the real interest rate. We will further assume that at the end of every period, all capital depreciates, so that when firms demand particular amount of capital Kt , this capital must be created using new investment It (so that Kt = It). We now want to study the impact of this capital demand (or investment demand) on the IS curve

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