(Solved): In need of L2 part B  L1. A firm has current and future marginal productivity of capital given ...

In need of L2 part B 

L1. A firm has current and future marginal productivity of capital given by \( M P K=10,000-2 K+N \), and marginal productivity of labor given by \( M P N=50-2 N+K \). The price of capital is \( \$ 5,000 \), the real interest rate is \( 7 \% \), and capital depreciates at a \( 5 \% \) rate. The real wage rate is \( \$ 10 \). (a) (2 points) Calculate the user cost of capital. (b) (6 Points) Find the firm's optimal amount of employment and the size of the capital stock. L2. An economy has full-employment output of 7000. Government purchases are 1200. Desired consumption and desired investment are given by \[ \begin{array}{c} C^{d}=3000-2000 r+0.10 Y \\ I^{d}=1000-4000 r \end{array} \] where \( Y \) is output and \( r \) is the expected real interest rate. (a) (4 points) Find the real interest rate that clears the goods market. Assume that output equals full-employment output. (b) (3 points) Calculate the amount of saving, investment, and consumption in equilibrium. (c) (5 points) If a shock to wealth causes desired consumption to decline by 200 (so that the new equation for desired consumption is \( C^{d}=2800-2000 r+0.10 Y \) ), find the equilibrium real interest rate, saving, investment, and consumption.