1. Draw the function Y = F(K,L ¯) in terms of Y and K, for some fixed L. On the same graph, plot the cost function for renting a certain amount of capital at a rental price of R, i.e. RK. For a profit maximizing firm, illustrate graphically how much capital they would choose to employ.
2. Consider a production economy as per class/Mankiw Ch.3 as follows:
• Y = F ( K ¯ , L ¯ )?
• Y =c(Y -T ¯)+I(r)+G?
• w=MPL,R=MPK
Suppose an earthquake destroys a chunk of the capital stock. What happens to Y ,R, w, C, I?
3. Consider a variation on the consumption function given in 2. Rather, suppose C = c(r)(Y - T ¯). That is, my consumption habits depend upon the interest rate. Justify this extension to the model, and contrast what happens to this model to what happens in (2) following a positive shock to investment demand caused by firms wanting to expand their operations.
4. Consider a variation on the consumption function given in 2. Rather, suppose C = c(1 - t)Y , where t is the percentage tax rate on income, which means the total tax revenue is T = tY . Is the equilibrium in this model any different than the equilibrium in 2, for the same level of government spending?
5. Is a credit card money? Why or why not?
6. Suppose a (very small) country has a central bank who has issued 100m of money, where nominal output is 350m annually. How frequently is the average piece of money used?
7. Give two realistic occurrences that might drive changes in the velocity of money.