In the problem, we consider the impact of sensitivity of investment demand to changes in interest rates on the slope of the IS curve. Consider a competitive profit-maximizing firm with Cobb-Douglas production function Yt = AtK t L 1 t that chooses the quantity of labor and capital, taking rental rate rt and wage wt as given. Profits are defined as output net of payments to workers and capital owners. Question 2.1 Set up the problem for the profit maximizing firm. Question 2.2 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