1. Given the production function Y= RK, L )-K 1/3L2/3 in Biwei economy, answer q
ID: 1131423 • Letter: 1
Question
1. Given the production function Y= RK, L )-K 1/3L2/3 in Biwei economy, answer questions: Derive the per-worker production function. a. b. Does this production function have constant returns to scale? Explain. >c. Biwei starts off with one unit capital stock per worker. At this point in time, what are th levels of income per worker and consumption per worker? d. Suppose a capital depreciation rate of 20% per year (out of total capital) and a saving rat of 10% each year (out of total output), derive the steady-state level of capital per worker the steady-state levels of income per worker and consumption per worker. e. Show how the capital stock per worker will evolve over time. For each year, calculate income per worker and consumption per worker. How many years will it take to reach steady-state? f. What is the Golden Rule level of capital in Biwei economy? Why and how will Biwei choose the Golden Rule level capital?Explanation / Answer
Answer for C
1 unit of Capital stock per worker is given by K/L=1 then Income per worker is y=Y/L=(K/L)^(1/3)=(1)*(1/3)=1
and consumeptio per worker is giben by c = (1- s)*y=(1-s)
Answer for F
Golden rue level of capital is that level which maximises consumption per labour c**= f(k)-depreciation*k
We heed to find FOC to find this Golden rule level we get
dy.dk =depreciation=f'(k)=1/3(k^-2/3)=depreciation rate
k** =(3*depreciation rate)*(-1.5)
THis is golden rule level of capital
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