Gold buyers are located in New York and Zurich.At the current price of gold,$400 an ounce,worldwide demand for gold is 10,000 ounces; and the price elasticity of demand for gold in New York and Zurich are -3 and -2 respectively.If the slope of each demand curve in New York is the same as in Zurich,then the quantity of gold demanded by dealers in Zurich is

Question

Quizplus · Accepted Answer

Using the formula for price elasticity of demand, we know that:

% change in quantity demanded / % change in price = elasticity of demand

We can rearrange this formula to solve for the % change in quantity demanded:

% change in quantity demanded = (elasticity of demand) x (% change in price)

In New York, the price elasticity of demand is -3. If the price of gold goes up by 1%, quantity demanded should go down by 3%. Similarly, in Zurich, the price elasticity of demand is -2, meaning that if the price of gold goes up by 1%, quantity demanded should go down by 2%.

If we assume that the slope of each demand curve is the same, then we can also assume that the % change in price will be the same in both markets. Let's say that the price goes up by 1%. Using the formula above, we can calculate the % change in quantity demanded in each market:

In New York:
% change in quantity demanded = (-3) x (1) = -3%

In Zurich:
% change in quantity demanded = (-2) x (1) = -2%

We know that worldwide demand for gold is 10,000 ounces at the current price of $400 an ounce. If the price goes up by 1%, we can use these % changes in quantity demanded to calculate the new quantities demanded in each market:

In New York:
New quantity demanded = 10,000 - (0.03 x 10,000) = 9,700

In Zurich:
New quantity demanded = 10,000 - (0.02 x 10,000) = 9,800

We were given that the worldwide demand for gold is 10,000, so the quantity of gold demanded by dealers in Zurich is:

10,000 - 9,700 = 300
or
10,000 - 9,800 = 200

Since the question is asking for the quantity of gold demanded in Zurich, we should choose the answer C) 6,000.

Gold Buyers Are Located in New York and Zurich