1. The Baumol-Tobin Model
Here we'll build some intuition for the money demand function we've been using to characterize the money market. Suppose you earn pY in nominal income that you want to spend at constant rate over the course of the next year.One of the ways generally used to generate demand for money in a model is to posit that a cash-in-advance constraint must be satisfied ( ie. in order to spend your income on goods you need to hold cash first). Suppose wealth can be held in the form of some asset or in the form of money. For simplicity assume the asset yields return r(the real rate), and money is subject to inflation π and does not pay interest.
You have to go to the "bank" to transfer wealth from the asset to money. It is costly for you to go to the bank, and it is costly for you to hold money, so the question is how often do you go to the bank, and how much money should you hold.
For example, if you went once during the year your average money holdings would be pY/2. For N times per year, you would get pY/2N
a.) What's the opportunity cost of holding real money balances? (Hint:consider the definition of the real rate).
b.) Suppose the nominal cost of going to the bank is pF. Write down an equation for the total cost of holding money as a function of N.
c.) You'd like to minimize this cost function in order to determine how many times per year it is optimal to visit the bank. In order to do this take a derivative of your answer in (b.) with respect to N and solve for N.
d.) If nominal rates increase, do you want to visit the bank more or less often?
2. The Current Account
In 2007, the country of Ikonomia has a current account deficit of $1 billion, and a trade deficit of $800 million. Ikonomia's factors of production located in foreign countries earn $700 million. The country neither gives nor receives unilateral transfers. Ikonomia has a nonreserve financial account surplus of $750 million,and a capital account has a $100 million surplus. Ikonomia's GDP is $9 billion.
a.) What was the movement in Ikonomia's net foreign assets during 2007?
b.) Compute the official settlements balance. Based on this value, what was the change in the central bank of Ikonomia's foreign reserves?
c.) Give the amount of income foreign factors of production earned in Ikonomia during 2007.
d.) Compute NFIA.
e.) Verify that CA+FA+KA=0.
f.) Give the values of GNE, GNI, and GNDI.