Question

2. Consider two countries: Mahaliaville and UWIville. Both countries have the same production: Y = K L Neither country experiences population growth nor technological progress and both countries have a depreciation rate of 10%. Ma- haliaville saves 10 percent of ouput each year and UWIville saves 30% of output each year.

Answer 1

Solution-

Each countries have the same production,also depreciation rate is same as 10%. Saving rate of Mahaliaville is 10 percent and Saving rate of UWIville is 30%.

Given :- For country Mahaliaville and uwlville y = k 3/4, 1/4 Y = k 3/4 (14 Y - K314 L3/4 & capital per worker v output per worker ries S= 10% = 0ol in both the countries. Smanaliaville = 10% of Y| Also SM = 0.ly Suwi ville = 30% of Y Su = 0.34 Su = 0-3Y osu = 0.34 in Saving per workere un manaliaville saving per worker in wivelle. 12 &m= Ooly.

At Steady state :- dr= o. Change in capital stock pey won i-SR=0 - C = SR.1 Also, I=s. Tin closed Economy] Now, El Investment per worker = 1 saving per worker / In Mahaliaville :- a At Steady State :- i = 8R SM - SR $ 0.14 -SR. 0." R314 = Od r. f from ② 4 0 ] R314 =R R = 1 R314 - Rucl R=1 so Capital per worker = 1

& Income per worker - y = R314 y=(183/4 = 1 & Consumption per worker : Y = C+I = c + II y= cti - c = you =) c = y-sy. c = y(1-2 saving rate so, c = y(1-0.1) = 0.gy = 0.9x1 = 0.9 In U WI ville At Steady State i = SR su= SR 0.34 = 0.IR 0.3 R 3/4 = 0.IR R 1/4 = 3. het 34 =81) -> capital per worker

Also, y = R314 1 9 27 → Income Deer c= (-s)y saving rate. je= (1 - 0.3) y = (1-0.3 ) 27 = 18-9)

(b) Consumption in Mahaliaville, saving rate. CM = (1-s) y cutput per to • Consumption per Labor Saving Rate in Mahaliaville at the end of each year is 10% of y. 0 CM = (1-0.1 y = Oogy = 0.9 k 314 Consumption in UWI ville Cu = (1-57y saving rate l output per labor consumption per Labor Saving Rate in vwyville is 30% off Co= (1-0.3 y = 0.7y = 0.7 R 3/4 Since the production soutput) Income in both the countries are same, So, at any level of output / Worker or capital per worker consumption in UWg ville is always less than one Mohaliaville as Univelle has a hia a hate than Manaliaville U in Mahaliaville saving rate that

CM Co.gk3/4) cu (0.7 R²14) - C = 0.9 (1334.00 R=1, Cu = 0-7 (1340. I R=2, (n = 0.912 3/4 - 1.681x0.9 R=2, Cu = 0.7 (2314 = = 1.513 I 0.7x 1.681= 1.177 R=3, cm=0.9(3) 3/4=0.9x2.28 R=3, Cu = 0.7 (3,314 = 1.595 - 2.052 At every level of capital per worker, cons umption per worker in Uwlville will be less.