Question

Consider two countries, Home and Foreign, with variables in Foreign denoted by asterisks ("*"). Let Y = 2,000, M = 400, P = 1.25; and Y* = 1,500, M* = 300, P* = 2.00. Suppose the demand for liquidity takes the same form in both countries, that is, L(R, Y) = L* (R, Y) = 2Y/100R (notice that the functions have the same form, but in each country the values of Y and R are different). (Advice: once again, don't just compute a number, but try also to sketch a graph.)

5. If Home doubles the money supply to M = 800, and agents do change their expectation about the future exchange rate what happens to the exchange rate in the long run (use four decimal spaces)?

Answer 1

Consider the given problem here the money market equilibrium is given by, “M/P = L(Y, R)”.

Now, in the LR the “P” will adjust to equate these both side.

=> M/P = L(Y, R) = 2*Y/100*R = 400/1.25 = 320, => 100*R = 2*Y / 320 = 2*2000/320 = 12.5.

=> R = 12.5/100 = 12.5% = 0.125, => R = 0.125.

Now, for foreign country, => M*/P* = L(Y*, R*) = 2Y*/100R* = 300/2 = 150,

=> 100R* = 2Y* / 150 = 2*1500/150 = 20, => R* = 20/100 = 20% = 0.2, => R* = 0.2.

Now, under PPP the following relationship will hold.

=> E(H/F) = P/P*, where “P” be the home price and “P*” be the foreign price level.

So, initially for “P=1.25” and “P*=2” the value of the exchange rate is “1.25/2 = 0.625”.

=> E(H/F) = 0.625”.

Now, as the home money supply increases to “800”, => M/P = 2Y/100R = 2*2000/100*0.125.

=> 800/P = 4000/12.5, => P = (800*12.5)/4000 = 2.5, => “P = 2.5”. So, the home money supply increases to “800”, leads to increases in “P=2.5”. Now, the foreign price will not change, => the new value of the exchange rate in LR is “P/P* = 2.5/2 = 1.25”.

=> the new value of the exchange rate is “E(H/F) = 1.25”.

So, in the LR as the home price increases => in the LR the exchange rate will depreciate in terms of home currency.