Question

9. Consider an economy described by the following production function: Y=K^0.2L^0.8

Suppose the depreciation rate is 10%.

1. Explain what the golden rule level of capital is.
2. For this economy, calculate the golden rule level of capital per worker, output per worker, depreciation per worker and consumption per worker.
3. Plot the results obtained in (b) above.
4. Calculate the saving rate that would give the golden rule level.
5. Explain what happens to the consumption level if the saving rate departs from the one that gives the golden rule level.
6. If the economy was to have a lower saving rate than the one that gives the golden rule level, what kind of public policy would raise the saving rate to the golden rule level?

Answer 1

DELTA PO NO v=kO.220.8 8=011, a Golden rule mul of capital i at is tue steady state capital stock per worker which maximises me consumption per worker in steady state when , não, go MPK=g golden where rule capital stocks is when c(k) is maximesed. au per capita terms, v = 210.8 y=ffk) = ko. 2 where r= capital per worker. weknow : at strady state, k Btk) =S Stein - sftk)= fk. - CR= f(k) - sf(K) ='flk) – Sk (using oo) dek) = MPK-f=o dk = IMPK - 87 this is maxima andition as t² = f(R) Lo (due to diminishing e marginal returns heuce e is maximised. OR?

oft ner capital perworker (k) wolder, brak even I had te) ct gold - stk) capital per worker (2) Qu the about fig, goldm rule head of capital perworker occurs at point urresponding to MPK = f ie when slope of production function = slope of sk=(8). This occurs at nout A & capital correspondip to A is kiald.

Dale DELTA PO NO Also mis is the strady state as at the gold, sk=stk) the corresponding alt is yo gold. Golden mile consumuption per worker in area between flk) & stk) ie y-i-c. Also the area is maximised at point A. Marked as ct Gold. saungs rate : c (s) = f(k) -s f(x) = (1-5) f(x) =(1-5) koz at steady state k =s ko2 f. 7 ko.8 = 5/8 or k = (3/8)08. now ((5) = (1-1)/5.199 de = (1946.). 7x4 + )" (J) 30 out (1-3) (3,394 = 6o.)" is is 0.4 01 a 1-s=45 58=1 Isays=0.2 c) is 0.2 golden rule revel of samnings (which maximise eto Is gold = 0.21 . 2 d

f) We know, when s< sgold, increasing the savings rate will increase consumption per worker till the golden rule savings rate is reached. Therefore, we must encourage savings in the economy.

Ways to increase savings rate:

1. Reduce tax rates because tax rates on savings reduces the savings rate

2. The government can also save more by reducing the budget deficit. One way of doing this is to reduce government purchases.

note: Saving too much is not always optimal as more savings today will eman less consumption in short run