Sorry, this is a little long, hope somebody could give me some help. Thanks in advance.
Consider the exchange rate of the dollar for the euro. Suppose that the liquidity function L(i) is the same
in both the United States and Europe. The United states and Europe are initially in long-run equilibrium.
The money supply in the United States is $1,000, and its real GDP is 10,000 units. The price level in the United States in this long-run equilibrium is $1 per unit of output. The money supply in Europe is 500 euros, and its real GDP is 5,000 units. At time T, the United States permanently (and unexpectedly) increases its money supply to $1,500. At time T, interest rates in the United States fall from 5% to 2%.
1. What is the exchange rate prior to time T?
2. What is the expected future spot rate at time T (after permanent increase in the money supply)?
3. What are the interest rates in Europe before and after time T?
4. What is the expected rate of depreciation/appreciation of the dollar immediate following time T?
5. What is the exchange rate immediately after the permanent increase in the money supply in the United States at
time T?
Sorry, international macro is not my area. I too am lost on this one.
To answer these questions, we need to analyze the impact of the permanent increase in the money supply in the United States on various economic variables. Let's go through each question step by step:
1. What is the exchange rate prior to time T?
The exchange rate prior to time T can be determined using the purchasing power parity (PPP) theory. According to PPP, the exchange rate should equalize the price levels in different countries. In this case, the price level in the United States is $1 per unit of output, while the price level in Europe is 1 euro per unit of output. Thus, the exchange rate prior to time T would be 1 dollar = 1 euro.
2. What is the expected future spot rate at time T (after the permanent increase in the money supply)?
To determine the expected future spot rate at time T, we need to consider the impact of the permanent increase in the money supply in the United States on the exchange rate. An increase in the money supply leads to a decrease in interest rates and an increase in inflation. As a result, the value of the dollar depreciates relative to the euro. However, the exact magnitude of this depreciation depends on other factors as well, such as the relative levels of inflation and interest rates between the United States and Europe. Without additional information, it is difficult to determine the exact future spot rate at time T.
3. What are the interest rates in Europe before and after time T?
The question does not provide any information about the interest rates in Europe before or after time T. Therefore, we cannot determine the interest rates in Europe based on the given information.
4. What is the expected rate of depreciation/appreciation of the dollar immediately following time T?
Given that the money supply in the United States permanently increases at time T and interest rates fall, it is expected that the value of the dollar will depreciate immediately following time T. The decrease in interest rates makes the dollar less attractive for foreign investors, reducing the demand for dollars and leading to a depreciation of the currency.
5. What is the exchange rate immediately after the permanent increase in the money supply in the United States at time T?
The exact exchange rate immediately after the permanent increase in the money supply in the United States at time T depends on various factors, such as the magnitude of the increase in the money supply, the reaction of the foreign exchange market, and other economic variables. Without additional information, it is challenging to determine the exact exchange rate at that specific moment.
In summary, while we can make some general observations about the impact of the permanent increase in the money supply on exchange rates and interest rates, determining specific values requires more information and analysis.