Question

Question 5. (4 points each) Consider the Solow model in Chapter 6. Production function is given by Yt = A+KENZ The notations of variables are the same as the slides for Ch.6.The depreciation rate d is 0.1, the population growth rate n is 0.1, and the saving rate s is 0.2. The level of productivity is constant, so At = 2 all the time.

PS addtional info

Answer 1

First we will derive the savings rate at golden level and then see the effect on consumption:

The policy for increasing the savings rate is not always good for the household as it reduces their consumption of goods and services. This reduction in consumption per worker is explained in the images below:

Y+= Azki z 2 (6) Y= 9KA NA Get a real estate inte Y+= 2 2 1 2] where, k = k/N at steady state, Akt zo → $f (Rt) - (d tn) kt = 0 3 ox ak'? – (.1 +0.1)kt =0 * 28 = 0.2kt 8 = 0.1 Relike nga kain 0.1 » (10p)*= K 0

At Golden Rule, MPK = dan Now, MPK = f (k)= 8x So, it = 0.1+0.1 >> The = 5 > Kjold = 25 Put kgold = 25 in equation ④ (10%)2 = 25 [ Bgold = 1/2 = 0.5 ] Ano

(7) Page 3 We know, Ye= (a + It where (z= (1-8) Yt + H = (1-6)ýt (per-worker terms) Old 8 = 0.2 New I gold = 0.5 & It= Byt → it = pyt ^ in savings will increase it & shift it= sy a curve upwards. - y = f(x) SR - iq=sigt - T 4-soft k* ki Consumption before a insa Distance AB Consumption after p in a Distance CD Distance AB > Distance CD So, consumption per worker Falls Offer in B Transition Path Log Consumption -peo worker . to Time an 1 in se reducen s sharply at to and then consumption gradually but does not reach to steady state path, increases