Statement:

The lower our real exchange rate is, the less expensive domestic goods are relative to foreign goods, and the greater the demand is for next exports.

I don't get the above statement, please look below to see if there is fault in my reasoning and explain why it is wrong.

From the real exchange rate equation:

E = eP/P* (where E = real exchange, e = norminal exchange, P = foreign price, P* = domestic price)

If E is low, that means the more expensive the domestic goods are compared to foreign goods. This is my observation because E and P* are inversely related according to the equation above. Since E is low, NX is high. This is because e and NX are inversely related and e and E are positively related.

I don't get why a lower real exchange rate leads to a lower price of domestic goods. Please explain. Thanks.

I think of the exchange rate as the number of a foreign currency units per dollar. e.g., euros/dollars. From this perspective, the statement makes perfect sense.

Let me elaborate with an example. Say something costs 2 euros and the euros to dollars ratio is 1. So, I need 2 dollars to purchase. (I take my 2 dollars to the exchange, and get 2 euros). Now let the euros/dollars exchange ratio drop to 0.5 NOW, I need to spend 4 dollars to get that same item. (I take 4 dollars to the exchange to get 2 euros). Conversely some guy in France now only needs to give up 1 euro to get 2 dollars.)

Hummmm, exchange rate went down, price of foreign good went up (domestic goods became relatively less expensive). To foreigners, the price of american goods just went down, so demand american exports just went up.

Which is exactly what your statement stays.

Consider an economy with a constant nominal money

supply, a constant level of real output Y = 100, and a
constant real interest rate r = 0.10. Suppose that the
income elasticity of money demand is 0.5 and the interest
elasticity of money demand is --0.1.
a. By what percentage does the equilibrium price level
differ from its initial value if output increases to Y =
106 (and r remains at 0.1O)? (Hint: Use Eq. 7.11.)
h. By what percentage does the equilibrium price level
differ from its initial value if the real interest increases
to r = 0.11 (and Y remains at 100)?
c. Suppose that the real interest rate increases to r =
0.11. What would real output have to be for the equilibrium
price level to remain at its initial value?

Your observation has some faults in reasoning. Let's break down the statement and correct the misunderstanding:

Statement: The lower our real exchange rate is, the less expensive domestic goods are relative to foreign goods, and the greater the demand is for next exports.

First, let's clarify the meaning of the terms:

- Real exchange rate (E): It represents the relative value of domestic goods compared to foreign goods, taking into account inflation and exchange rates.
- Nominal exchange rate (e): It measures the relative value of one currency to another.
- Foreign price (P): It refers to the price of goods in the foreign country.
- Domestic price (P*): It represents the price of goods in the domestic country.

Now, let's examine your reasoning:

You mentioned the real exchange rate equation: E = eP/P*. However, you stated that if E is low, it means domestic goods are more expensive relative to foreign goods. This is incorrect. When the real exchange rate (E) is low, it actually means that domestic goods are cheaper relative to foreign goods.

Why is this the case?
A lower real exchange rate implies that domestic goods are relatively cheaper compared to foreign goods. This means that for a given domestic price (P*), you would need fewer units of domestic currency to buy foreign currency, making foreign goods relatively more expensive.

So, when the real exchange rate is low, it becomes more affordable for foreigners to purchase domestic goods, leading to an increase in demand for domestic goods, including exports. This is because foreign buyers can obtain more of the domestic currency in exchange for their own currency, making domestic goods appear cheaper to them.

In summary, a lower real exchange rate actually makes domestic goods cheaper relative to foreign goods, leading to an increase in demand for domestic goods, including exports.