Finance 475

Solutions to Problem Set #3

 

1)      Recall, elasticity of demand is defined as

(% change in quantity demanded)/(% change in price)

            In this example, price fall from $10 to $8 - (approximately) a 20% drop – while quantity demanded rises from 40 to 60 - (approximately) a 50% increase.  Therefore, the elasticity of demand is

                                    50/20 = 2.5

2)      a) The marshal – lerner condition states that for exchange rate stability, the sum of the (absolute values) of import demand and export supply must exceed one.  If we calculate the elasticities of export supply, we get as follows (approximately):

Price

Elasticity

$2

12

$2.33

5

$2.80

1

For example, at a price of $2.00, if the price rises to $2.33 (a 16.5 % increase), quantity exported rises from 2 to 6 (a 200 % increase).  Therefore, elasticity equals 200/16.5 = 12.  The rest are calculated accordingly.  Notice that the marshal-lerner condition is already satisfied at all prices (presuming that the elasticity of import demand is at least positive). 

            b) Consider the following exchange rates: (in Y/$)  80, 100, 120, 140.

Exchange Rate

$s Demanded

$s Supplied

80

52,500

14,670

100

33,600

14,472

120

13,980

13,995

140

4,000

14,105

 

For example, at an exchange rate of 80Y/$, the domestic price of a TV is

                        (Y18,000)/80 = $225.

At a price of $225, 65.2 TVs are imported, so $225*65.2 = $14,670 must be supplied to the market to purchase them.

At an exchange rate of 80Y/$, the domestic price of wheat is

                        (Y280)/80 = $3.50

At a price of $3.50, 15 million bushels of wheat are exported, so $3.50*15,000 = $52,500 must be demanded in the market to buy the wheat.

c) It appears that supply and demand are approximately equal at an exchange rate of 120 Y/$.  Note that for values of the exchange rate below 120, dollars demanded are greater than dollars supplied, suggesting that the dollar should rise in value (a dollar appreciation).  For exchange rates greater that 120, dollars supplied are greater than dollars demanded, suggesting a fall in the value of the dollar ( a depreciation).  Therefore, it appears as of the equilibrium exchange rate of 120Y/$ is stable (as assured by the marshal lerner condition).

3)      The main result under the elasticities approach is that countries running trade deficits will experience depreciation in their exchange rate.  As the country’s currency drops in value, the domestic prices of all goods will rise.  This rise in domestic prices will have two effects.  First, imports become more expensive.  This should reduce the quantity of imports demanded.  Second, export prices increase, causing the quantity of exports supplied to rise.  Rising exports and falling imports should correct a trade deficit.  However, the current account surplus/deficit doesn’t depend on quantities of imports and exports, it depends on expenditures for imports and exports.  Recall that if demand is sufficiently inelastic (ie, less than one), as the price of a good rises, quantity demanded falls, but expenditures actually increase.  If the marshal – lerner condition is not satisfied, import demand and export supply are sufficiently inelastic so that as a country’s currency depreciates, expenditures on imports actually rise.  In fact they rise faster that expenditures on exports, causing the trade deficit to actually worsen.

4)      When the dollar falls in value by 10%, the domestic prices of both television sets and petroleum rise by 10% in the U.S. As prices rise, quantities fall.  The degree to which quantities fall depend on elasticities of demand.  It is reasonable to think that petroleum has a lower elasticity (petroleum is a necessity), so quantities demanded of petroleum should fall by less than TVs.