Question

Assume an economy is populated by L workers with total capital stock K. Production of this KL. Suppose household's saving rate s economy is organized by Y 0.6, and firm's depreciation rate of capital d = 0.1. The rule for accumulation of captial in per worker terms is of the time-to-build type: A k = i - ôk Standard Transformation of the Production Function a. Show that the production function is constant return to scale (CRS) b. Rewrite the production function in per worker terms c. Define the steady state in your own words Computing the Steady State Variables d. What is capital per worker in the steady state? e. What is the corresponding output per worker, consumption per worker, and break-even investment per worker in the steady state? Comparative Statics across Steady States f. Assume households becomes more inclined to save in this economy, i.e., s = 0.7, what would be the corresponding capital per worker and consumption per worker in the new steady state? Provide intuitions for your results g. Assume capital depreciates in a faster pace, i.e., 8 =0.2, what would be the corresponding capital per worker in the new steady state? Provide intuitions for your results Golden Rule h. What is the steady state capital per worker, output per worker, and consumption per worker under Golden Rule? (Hint: under Golden Rule, a hypothetical social planner will maximize consumption per worker by choosing the optimal steady state capital per worker.) Transitional Dynamics i. Assuming initial saving rate s = 0.6, and depreciation rate equals to 6 = 0.1. Use graphs to show the transitional process of consumption per worker, investment per worker, and output per worker over time

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Answer 1

(") 12.02 1 112 1/2 12 = KL yfltk, tl) = (tk) (t2) y tf (K; L) = {1th ( 1 ) to exponent of it is one Heuse, Constant returns to scale. م عه 12-112 K.L 1612 سے R Steady state occurs where Ak=0, AC=0, Ay=0 economy is at rest of new Investment is sufficient to cover up lte depreciation only. AKF i – ok Ako i-sy) s.y = ok 12 0.6 K² = a.lk 6 - KR k = 367 7 INTIITT y = 36 a= = o obx 6 3-6 ] 2 - 2 y = 6] (= (1-5).Y - v.4x6 = 2.4 T

S. (y) = ok 0.7 K = o.lk O ' TK = 49 1Y = 71 C = 0.387 E 2.1 Increasing in saning insteady state values, raises lime cgo 10.7 K = 0.2k 12 = 3.5 y = 3.5 (K = 12.25 per worker. Depreciation reduly Itu capital