Question

4. (a) Consider an economy with - production function Y-F(KL)-VK.L -depreciation of capital-16% -saving rate-24% population growth=2% G) if K-196 and L-100 in the eurent period, find T T andT in the eurent and the next periods. (ii) Find the steady state levels of ^. ^. and (b) Find the answers in (a) ifthe saving rate is changed to 30%. (c) Find the answers in (a) if the production function is changed to Y=F(KL)-1.08.,K·L.

Answer 1

Q 4(a)(i) if K = 196 l = 100 then Y = squareroot KL = squareroot 196 times 100 = 140 rightdoublearrow K/L = 196/100 1.96 rightdoublearrow = 140/100 = 1.40 rightdoublearrow C/L = 0.76 times 140/100 = 106.4/100 = 1.064 (ii) to find the steady state we convert everything in percapita term L = population lets define y = Y/L K = K/L C = C /L now we know that K(t) = I(t) - partial differential K(t) -(1) K(t) = change in capital stock i(t) = investment at any time delta = depreciation rate but we know that I(t) = & Y where s = saving rate hence equation (1) become k(t) = sY - delta k(t) we divided both sides of above equation by rightdoublearrow k(t)/L = sY/L - delta K(t)/L rightdoublearrow k(t)/l = sy - delta K -(2) we know that K = K/L we take the derivation of K with respect ton time get K = d(K/L)/dt = K/L - nk -(3)