4) The neoclassical consumption model, a retirement perspective: Consider the special case solved in the text where β=1 and utility takes the log form. Suppose the real interest rate is 5 percent. Let’s give this consumer a financial profile that might look like that of a middle-aged college professor contemplating retirement: suppose initial assets are ftoday =$50,000 and the path for labor income is ytoday  = $100,000 and yfuture = $10,000.

1.       What is the individual’s human wealth? Total wealth?

2.       According to the neoclassical model, how much does the college professor consume today and in the future? How much does the college professor save today?

3.       If current labor income rises by $20,000 by how much will saving change?

5) The neoclassical consumption model with log utility and β≠1: With log utility, the solution to the neoclassical consumption model is given implicitly by the two equations on page 408, the Euler equation and the intertemporal budget constraint:

                            Cfuture/Ctoday =β(1+R)      {Euler equation}

                           Ctoday + Cfuture /1+R =W      {IBC}

There, we solved these two equations for C(today) and C(future) in the special case where β=1. This exercise consider the case where βdiffers from 1.

1.       Solve these two equation for C(today) and C(future) where β≠1

2.       Verify that the solution matches what we obtained in the text when β=1

In text, when β=1     C(today)= 0.5W and C(future)= 0.5{(1+R)W}

3.When β<1, is C(today) higher or lower than β=1? Why?

6) Suppose the user cost of capital in an economy with no corporate income tax is 10 percent.

1.       What is the user cost if the corporate tax rises to 20 percent? 30 percent?

2.       Suppose an economy’s steady state investment rate i/y is 30 percent when the corporate tax rate is 0. What happens to this investment rate if the corporate tax rate rises to 20 percent? 30percent?

3.       Are differences in corporate tax rates across countries a plausible explanation for the large variation in investment rates that we see in the data?

MPK=R+d-{∆pk/∆pk}     User cost of capital without tax rate

MPK=[R+d-{∆pk/∆pk}]/ 1−τ     User cost of capital with tax rate