Consider the intertemporal model, where c is consumption, y is the marginal rate of time preference, P is the price level, y is real income, B denotes domestic bonds, and denotes foreign bonds (the other variables are the domestic nominal interest rate i, the foreign nominal interest rate i and the exchange rate s). The Lagrangian Z is as follows: 1 ww Z= u(c) + u(c) +[Py -PC -B-SJ]+[P ^ +1 [² + 1} +1 + (1 + i )B² +(1+i)P] (a) Write 1+ y +1' +1' +1 down the first-order conditions for c,c.B, and J. (b) Using the first-order conditions, derive the 'interest rate parity relationship' that links domestic and foreign interest rates. Comment concisely. (c) Consider the 'law of one price conditions' that link the domestic price to the exchange rate and the foreign price level (denoted P" ): P = s P and P =SPUsing the interest rate parity relationship in part (b), and these law of one price conditions, derive the +1 +1 +1 relationship between foreign and domestic real interest rates. Show your work, and explain. 2. Consider the intertemporal model, where c is consumption, y is the marginal rate of time preference, P is the price level, y is real income, B denotes domestic bonds, and J denotes foreign bonds (the other variables are the domestic nominal interest rate i, the foreign nominal interest rate i*, and the exchange rate s). The Lagrangian Z is as follows: Z = u(c+)+ + 1 1+Y u(C++1) + [Pt yt Ptt - Bt - St Jt] +++ [Pt+1 +1 + (1 + i) B + (1 + i) St+1]t - Pt+1 C++1] (a) Write down the first-order conditions for C, C+1, B₁, and J₁. (b) Using the first-order conditions, derive the 'interest rate parity relationship' that links domestic and foreign interest rates. Comment concisely. (c) Consider the 'law of one price conditions' that link the domestic price to the exchange rate and the foreign price level (denoted P*): Pt=st P and Pt+1 = St+1 P+1 Using the interest rate parity relationship in part (b), and these law of one price conditions, derive the relationship between foreign and domestic real interest rates. Show your work, and explain.
Consider the intertemporal model, where c is consumption, y is the marginal rate of time preference, P is the price level, y is real income, B denotes domestic bonds, and denotes foreign bonds (the other variables are the domestic nominal interest rate i, the foreign nominal interest rate i and the exchange rate s). The Lagrangian Z is as follows: 1 ww Z= u(c) + u(c) +[Py -PC -B-SJ]+[P ^ +1 [² + 1} +1 + (1 + i )B² +(1+i)P] (a) Write 1+ y +1' +1' +1 down the first-order conditions for c,c.B, and J. (b) Using the first-order conditions, derive the 'interest rate parity relationship' that links domestic and foreign interest rates. Comment concisely. (c) Consider the 'law of one price conditions' that link the domestic price to the exchange rate and the foreign price level (denoted P" ): P = s P and P =SPUsing the interest rate parity relationship in part (b), and these law of one price conditions, derive the +1 +1 +1 relationship between foreign and domestic real interest rates. Show your work, and explain. 2. Consider the intertemporal model, where c is consumption, y is the marginal rate of time preference, P is the price level, y is real income, B denotes domestic bonds, and J denotes foreign bonds (the other variables are the domestic nominal interest rate i, the foreign nominal interest rate i*, and the exchange rate s). The Lagrangian Z is as follows: Z = u(c+)+ + 1 1+Y u(C++1) + [Pt yt Ptt - Bt - St Jt] +++ [Pt+1 +1 + (1 + i) B + (1 + i) St+1]t - Pt+1 C++1] (a) Write down the first-order conditions for C, C+1, B₁, and J₁. (b) Using the first-order conditions, derive the 'interest rate parity relationship' that links domestic and foreign interest rates. Comment concisely. (c) Consider the 'law of one price conditions' that link the domestic price to the exchange rate and the foreign price level (denoted P*): Pt=st P and Pt+1 = St+1 P+1 Using the interest rate parity relationship in part (b), and these law of one price conditions, derive the relationship between foreign and domestic real interest rates. Show your work, and explain.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
![Consider the intertemporal model, where c is consumption, y is the marginal rate of time preference, P is the price level,
y is real income, B denotes domestic bonds, and denotes foreign bonds (the other variables are the domestic nominal
interest rate i, the foreign nominal interest rate i and the exchange rate s). The Lagrangian Z is as follows:
1
ww
Z= u(c) + u(c) +[Py -PC -B-SJ]+[P
^ +1 [² + 1} +1 + (1 + i )B² +(1+i)P] (a) Write
1+ y +1'
+1'
+1
down the first-order conditions for c,c.B, and J. (b) Using the first-order conditions, derive the 'interest rate
parity relationship' that links domestic and foreign interest rates. Comment concisely. (c) Consider the 'law of one price
conditions' that link the domestic price to the exchange rate and the foreign price level (denoted P" ): P = s P and
P =SPUsing the interest rate parity relationship in part (b), and these law of one price conditions, derive the
+1
+1 +1
relationship between foreign and domestic real interest rates. Show your work, and explain.
2. Consider the intertemporal model, where c is consumption, y is the marginal rate of time preference, P
is the price level, y is real income, B denotes domestic bonds, and J denotes foreign bonds (the other
variables are the domestic nominal interest rate i, the foreign nominal interest rate i*, and the exchange
rate s). The Lagrangian Z is as follows:
Z = u(c+)+ +
1
1+Y
u(C++1)
+ [Pt yt Ptt - Bt - St Jt]
+++ [Pt+1 +1 + (1 + i) B + (1 + i) St+1]t - Pt+1 C++1]
(a) Write down the first-order conditions for C, C+1, B₁, and J₁.
(b) Using the first-order conditions, derive the 'interest rate parity relationship' that links domestic and
foreign interest rates. Comment concisely.
(c) Consider the 'law of one price conditions' that link the domestic price to the exchange rate and the
foreign price level (denoted P*):
Pt=st P and Pt+1 = St+1 P+1
Using the interest rate parity relationship in part (b), and these law of one price conditions, derive the
relationship between foreign and domestic real interest rates. Show your work, and explain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc850257-eb64-4761-b7ae-f5327435026b%2F8991d863-b699-4c42-9e12-092da100f5b3%2Fzfa3d1e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the intertemporal model, where c is consumption, y is the marginal rate of time preference, P is the price level,
y is real income, B denotes domestic bonds, and denotes foreign bonds (the other variables are the domestic nominal
interest rate i, the foreign nominal interest rate i and the exchange rate s). The Lagrangian Z is as follows:
1
ww
Z= u(c) + u(c) +[Py -PC -B-SJ]+[P
^ +1 [² + 1} +1 + (1 + i )B² +(1+i)P] (a) Write
1+ y +1'
+1'
+1
down the first-order conditions for c,c.B, and J. (b) Using the first-order conditions, derive the 'interest rate
parity relationship' that links domestic and foreign interest rates. Comment concisely. (c) Consider the 'law of one price
conditions' that link the domestic price to the exchange rate and the foreign price level (denoted P" ): P = s P and
P =SPUsing the interest rate parity relationship in part (b), and these law of one price conditions, derive the
+1
+1 +1
relationship between foreign and domestic real interest rates. Show your work, and explain.
2. Consider the intertemporal model, where c is consumption, y is the marginal rate of time preference, P
is the price level, y is real income, B denotes domestic bonds, and J denotes foreign bonds (the other
variables are the domestic nominal interest rate i, the foreign nominal interest rate i*, and the exchange
rate s). The Lagrangian Z is as follows:
Z = u(c+)+ +
1
1+Y
u(C++1)
+ [Pt yt Ptt - Bt - St Jt]
+++ [Pt+1 +1 + (1 + i) B + (1 + i) St+1]t - Pt+1 C++1]
(a) Write down the first-order conditions for C, C+1, B₁, and J₁.
(b) Using the first-order conditions, derive the 'interest rate parity relationship' that links domestic and
foreign interest rates. Comment concisely.
(c) Consider the 'law of one price conditions' that link the domestic price to the exchange rate and the
foreign price level (denoted P*):
Pt=st P and Pt+1 = St+1 P+1
Using the interest rate parity relationship in part (b), and these law of one price conditions, derive the
relationship between foreign and domestic real interest rates. Show your work, and explain.
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