Introductory Macroeconomics, Hilary Term 2024

Problem Set, Week 5

1. Consider the neoclassical consumption model with log utility and no impatience on the part of the household (Jones' parameter β = 1). Suppose an individual begins with £10,000 in stocks and £30,000 of equity in her house, so financial assets are f_today= £40,000. Suppose her annual labour income is £50,000, today and in the future, and suppose the real interest rate is zero.


1. What are c_today and c_future? How much does the consumer save today?


2. Suppose a boom causes the values of all stocks to double. By how much do consumption and saving change today?


3. Alternatively, suppose house prices rise so that the individual's equity in her house rises to £50,000. Now what happens to consumption and saving today?


4. How does this exercise relate to the state of the US or the UK economy ca. 2007?


2. Suppose that the government fears the economy might be heading into a recession and cuts income taxes today in an effort to prevent this.


1. How does the Ricardian Equivalence argument apply in this case? How will consumption respond according to this argument?


2. How would your answer change if some individuals were borrowing constrained?


3. Investment and the corporate income tax
   
   
   1. Write down and explain an equation for the user cost of capital when there is a tax on corporate income.
   
   
   2. How much does the user cost of capital change if the corporate income tax is raised from 10 to 20 per cent?
   
   
   3. Suppose that an economy's steady state investment rate (I/Y) is 30% when the corporate tax rate is zero. Relying on the model set out on pp. 478/9 in Jones (4e), predict the change in the investment rate when the corporate tax is raised from 0 to 20%.
   
   
   4. Are differences in corporate tax rates a plausible explanation for the large variation in investment rates that we see across countries?