Assume That a Country's Production Function Is Y = K1/2L1/2

question 16

Essay

Assume that a country's production function is Y = K1/2L1/2. a. What is the per-worker production function y = f(k)?
b. Assume that the country possesses 40,000 units of capital and 10,000 units of labor. What is Y? What is labor productivity computed from the per-worker production function? Is this value the same as labor productivity computed from the original production function?
c. Assume that 10 percent of capital depreciates each year. What gross saving rate is necessary to make the given capital-labor ratio the steady-state capital-labor ratio? (Hint: In a steady state with no population growth or technological change, the saving rate multiplied by per-worker output must equal the depreciation rate multiplied by the capital-labor ratio.)
d. If the saving rate equals the steady-state level, what is consumption per worker?

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Definitions:

Adverse Supply Shock

An unexpected event that suddenly decreases the supply of a product or commodity, leading to higher prices and potential scarcity.

Federal Reserve

The central banking system of the United States, responsible for implementing the country's monetary policy.

Money Supply

The entire amount of financial assets existing in an economy at a certain time.

Inflation

A widespread inflation of prices leading to a diminished ability to purchase with money.