Lent - Lecture 12 - Exchange Rates in the Classical Model

Question 1

What is the definition (equation) for the real exchange rate, ε?

Answer 1

• (price of home goods in home currency x nominal exchange rate) / price of foreign goods in foreign currency
• ε = eP / P*
• where the nominal exchange rate, e, is defined as units of foreign currency per unit of home currency

Question 2

What are two ways in which a real appreciation of the exchange rate affect NX? Which of these do we assume to dominate?

Answer 2

• real appreciation ⇒ home goods more expensive ⇒ quantity of exports falls, quantity of imports rises
• real appreciation ⇒ real price of imports lower ⇒ value of imports falls
• general assumption is that the first of these dominates

Question 3

Derive the Marshall Lerner condition

Answer 3

• NX = X - (1/ε)(M)
• d(NX)/dε = dX/dε - (1/ε)(dM/dε) + M/(ε^2)
• we will have d(NX)/dε < 0 whenever:
• 0 > (ε^2/M)(dX/dε) - (ε/M)(dM/dε) + 1
• if we are close to trade balance then X ≈ M/ε, in which case this becomes:
• −(ε/X)(dX/dε) + (ε/M)(dM/dε) > 1
• −(ε/X)(dX/dε) = η(X) > 0: elasticity of exports with respect to ε
• (ε/M)(dM/dε) = η(M) > 0: elasticity of imports with respect to ε
• so for a real appreciation to worsen NX, we need:
• η(X) + η(M) > 1

Question 4

Given that NX(ε) = S - I(r*), what is the role of ε in this classical model

Answer 4

ε adjusts to ensure aggregate demand equals Y̅

Question 5

Do we graph NX as increasing or decreasing in ε?

Answer 5

NX as decreasing in ε

Question 6

In the Classical small open economy, what drives the equilibrating mechanism?

Answer 6

ε

Question 7

In this model, explain what happens as G increases

Answer 7

• an increase in G causes an inward shift of the savings curve
• causing ε to rise and NX to contract
• increase in G by ∆G puts pressure on market for loanable funds (r)
• foreign lenders attracted to invest ⇒ capital inflows, ensuring r = r∗ still holds
• inflows cause e to appreciate ⇒ ε appreciates, until eqm restored
• note that it is NX, not I, that ends up being crowded out here!

Question 8

What is the law of one price? What is the logic behind this law?

Answer 8

• should be no difference between price at home in home currency, and price in foreign country in foreign currency, corrected by nominal exchange rate
• p = p*/e
• logic based on arbitrage, a difference from this would lead to a profitable opportunity

Question 9

What is the purchasing power parity (PPP) hypothesis?

Answer 9

• when the law of one price is applied to an entire basket of goods
• P = P*/e
• or in terms of ε: ε = 1

Question 10

Give 2 reasons why PPP (ε = 1, P=P*/e) is unlikely to occur in the real world

Answer 10

• trade costs, tariffs, taxes ⇒ scope for arbitrage limited
• some goods in consumer ‘basket’ cannot be traded (haircut, restaurant meals, etc)

Question 11

From the data, what is the relationship between ε and how rich the country is

Answer 11

apparent tendency for richer countries to have a more appreciated ε

Question 12

Derive the Balassa-Samuelson effect

Answer 12

• suppose t of goods are tradable and (1 − t) are non-tradable
• P = t(p-t) + (1 − t)(p-nt)
• suppose also that when growth happens, it reduces costs more quickly in tradable sectors (electronics vs haircuts)
• will lead to more developed countries have higher relative price for non-tradables, p-nt /p-t (relative cost of production is higher)
• law of one price holds only in terms of tradables
• ε = eP/P* = e(t(p-t) + (1 − t)(p-nt)) / (t(p٭-t) + (1 − t)(p*-nt))
• = e(t + (1 − t)(p-nt / p-t)) / (t + (1 − t)(p٭-nt / p*-t))
• the real exchange rate will be more appreciated the higher is the relative price of home non-tradables vs tradables, compared to foreign