A Country Has the Per-Worker Production Function Y_t = 5k_t⁰

question 58

Essay

A country has the per-worker production function y_t = 5k_t^0.5, where y_t is output per worker and k_t is the capital-labour ratio. The depreciation rate is 0.2 and the population growth rate is 0.05. The saving function is S_t = 0.2 y_t, where S_t is total national saving and Y_t is total output.
a. What is the steady-state value of the capital-labour ratio?
b. What is the steady-state value of output per worker?
c. What is the steady-state value of consumption per worker?

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