Question

In the fall of 2012, the Iranian currency, the rial, was collapsing. World sanctions induced by its nuclear program were crushing the economy and the rial's value against the dollar dropped by 40%. Iranian exporters sell abroad in dollars, but pay their workers and suppliers in rials. Therefore, they must "sell" their dollars to get rials. Iranian importers buy their products with dollars, but get revenue in rials from selling domestically. Therefore, they need to "buy" dollars with their rials. Suppose that the daily supply of dollars (from exporters) is given by S(p) = 1,000 x (p - 20,000) and the daily demand for dollars (from importers) is given by D(p) = 200 x (44,000 - p), where p is the Rial to Dollar exchange rate. The exchange rate (i.e., p) is ____ rials per dollar. Suppose that severe sanctions are placed upon Iran, so that its exports decline by 80% at any price. This means that, at any exchange rate p, the number of dollars supplied in this market drops 80%. The new exchange rate is ____ rials per dollar. Governments often keep reserves of foreign currencies so that they can keep their exchange rates stable. When there is an excess supply of dollars, relative to the local currency, the government buys dollars. When there is excess demand, it sells dollars. Suppose the Iranian government wants to keep the price of the rial at the value you found and start supplying dollars to the market. How many dollars per day would it have to "sell" to keep exchange rates steady at the level you found, given the level of exports? It would have to sell ____ dollars per day. Suppose that the government initially has reserves of $100,000,000. The government will be able to support the rial at the original exchange rate for approximately ____ days before it runs out of dollars.

Answer 1

(A) We know that the exchange rate is given by the intersection of the demand and the supply curve. So to find the exchange rate we will equate the supply and the demand curve:-

1000 ( P - 20,000 ) = 200 ( 44000 - P )

1000P - 20000000 = 8800000 - 200P

1200P = 28,800,000

P = 24000

Hence the exchange rate is 24000 rials per dollar.

(B) Now we know that if the supply of the currency falls than simply results in increase in the exchange rate as the equilibrium point of the market shifts upward.

According to question there is a fall of 80% in the supply of dollars, so we have a new supply function as:-

S = 200 ( P - 20,000 )

To find the new increased exchange rate we will equate the new supply finction with the old demand function:-

200 ( P - 20,000 ) = 200 ( 44,000 - P )

200P - 4000000 = 8800000 - 200P

400P = 12,800,000

2P = 12,800,000 / 200

2P = 64000

P = 32000

Hence the new exchange rate becomes 32000 rials per dollar.

(C) If the iranian goverment wants to keep this new exchange rate steady then the amount of dollars they have to sell at the given level of exports can be found as:-

S = 200 ( P - 20,000 )

Substituting the value of Exchange rate to be 32000 we get:-

S = 200 ( 32,000 - 20,000 )

S = 200 ( 12,000 ) = 24,00,000

Hence the iranian goverment have to sell $24,00,000 dollars per day.

(D) Now if we assume that the goverment have initial reserves of $ 100,000,000 and if it wants to keep the old exchange rate steady than to find the number of days it can do so, we have to first find the amount of dollars to be given away to keep that exchange rate constant.

S = 1000 ( P - 20,000 )

S = 1000 ( 24,000 - 20,000 )

S = 1000 ( 4000 ) = 40,00,000

Hence the iranian goverment has to sell $40,00,000 dollars per day hence for a reserve of $ 100,000,000 the goverment will be able to keep the exchange rate steady for:-

100,000,000 / 40,00,000 = 25

Hence for 25 days the goverment will be able to keep the exchange rate steady

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