Question

nuuupuen. Table 1 AY a. Suppose the marginal propensity to spend out of GDP, z, is 0.5. If autonomous spending increases by $2.000, fillin Table 1 to the right (Round Round ΔΑΕ your responses to the nearest dollar) b. The sum of the values in the third column should be AY-$2,000+ (0.5) xS2.000+ (0.5)2 $2.000 The total change in GDP is thus equal to Second Third Fourth Table 2 Round ADeposits AReserves ALoans c. Now consider the process of deposit creation from this chapter. Consider a new deposit of $30,000 and a target reserve ratio, v, of 0.2 (with no cash drain) Fill in the new table, Table 2 Round your responses to the nearest dollar) Second Third Fourth d. The sum of the values in the first column should be: AY $30,000+(1-0.2)x$30,000+ +(1-0.2)2 x$30,000+ The total change in deposits is thus equal to e. A reserve ratio for the deposit mukiplier is similar to A. changes in government purchases for the simple multiplier O B. taxes and imports for the simple multiplier ° C. the cash drain for the simple multiplier 0 D. the marginal propensity to consume for the simple multiplier

Answer 1

a).

consider the given problem here the “MPC” is given by “z=0.5”. Now, if the autonomous spending increases by “$2000”, => in the 1^st round the “Y” will increase by the same amount. Now, in the 2^nd round “Y” will increase the “C=consumption by “MPC*dY” amount that will further increase the “AE”, => “Y” will increase by “MPC*dY” amount.

Now, in the 3^rd round increase in “Y” will further increase “C” by “MPC*dY = MPC^2*d(AE)”, => “Y” will further increases by “MPC^2*d(AE)” and so on. Consider the following table.

Roundd(AE) 1st PrIdd 3rd 4th Calculation dY $2,000 $2,000 $1,000 "-0.5*2000"$1,000 $500 -0.5A2*2000" $500 $250-0.5A3*2000" $250

b).

So,

dY = ($2000 + 0.5*$2000 + 0.5^2*$2000+…….) = ($2000/1- 0.5) = $4000, => dY=$4,000.

c).

Now, consider the process of deposit creation, there is a deposit of “$30,000” and the reserve ratio is given by, “v=0.2”, => the bank will “reserve of amount “$30,000*0.2=$6,000” and will make a loan of amount “$30,000*(1-0.2)=$24,000”. Now, because there is no cash holding, => the deposit in the 2^nd round is “$24,000” and the “R=0.2*$24,000 = $4,800”, => the loans is given by, “$24,000*0.8=$19,200”. So, in this way we can derive all the “deposits”, “reserve” and “loans”. Consider the following table.

Round d(Deposit) d(Reserve) Calculation d(Loans) Calculation 1st 2nd$24,000.0 3rd 4th $30,000 $6,000 "-0.2*30,000" $24,000.0 "-0.8"30,000" $4,800 .2*24,000" $19,200.0 0.8*24,000 19,200.0 15,360.0 $3,840 "-0.2*19,200" $15,360.0-0.8 19,200" $3,072"=0.2*15,360" $12,288.0"-0.8*15,360"

d).

So, here the sum of the 1^st column is given by.

=> dY = [$30,000 + (1-0.2)* $30,000 + (1-0.2)^2* $30,000+ (1-0.2)^3* $30,000+…….].

=> dY = [$30,000 + 0.8* $30,000 + 0.8^2* $30,000+ 0.8^3* $30,000+…….].

=> dY = [$30,000 + 0.8* $30,000 + 0.8^2* $30,000+ 0.8^3* $30,000+…….]

=> dY = $30,000/(1-0.8) = $150,000, => dY = $150,000.

Thus the total change in deposit is given by,”$150,000”.

e).

a reserve ratio for the deposit multiplier is similar to “the MPC” for the simple multiplier. So, here the correct answer is “D”.