Finding the Value of Elasticity
- Consider an economy that operates under competitive markets and meets the assumptions of theSolow model. The production function is given as follows:
Y ( t) = K ( t) 0.3(A( t)L( t)) 0·7
Assume a saving rate of 15%, labor force growth rate of 2% and depreciation rate of 5% and effectiveness of labor growth rate of 8% .
- Show that the production function exhibit constant return to scale?
- Derive the production function for output per capita.
- Derive the production function for output per effective unit of labor.
- Find equilibrium real wage as a function of capital per unit of effective labor and effectiveness of labor.
- Find equilibrium real rental price of capital as a function of capital per unit of effective labor and effectiveness of labor.
- Solve for steady state level of capital per unit of effective labor.
- Find steady state level of output per unit of effective labor.
- Find growth rate of output and output per worker on the balanced growth path.
- Which one would increase consumption per unit of effective labor:an increase in saving rate or a decrease in saving rate. Explain.
- Find the golden-rule level of capital per uni t of effective labor and optima l saving rate.
- Describe how a decrease in saving rate affects the break-even line and actual investment line and use graphs to show the impact on k ,k, growth rate of f,Ln (f) and c over time.
- Describe how an increase in growth rate of effectiveness of labor affects the break-evenline and actual investment line and use graphs to show the impact onk. , k, growth rate of Y/L and Ln (y/L)and c over time
- Describe how a decrease in growth rate of labor affects the break-even line and actual investment line and use graphs to show the impact onk ,k, growth rate of Y/L ,Ln (Y/L) and c over time.
Solve the Problem
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September 12, 2023
QUESTION:
Find the elasticity of output per unit of effective labor on the balanced growth path y* with respect of rate of population growth, n if production function is given as:
Y(t) = K(t)^0.3(A(t)L(t))^0.7
Assume that the growth rate of effectiveness of labor, g, is equal to 8% and depreciation rate of 4%. By about how much does a fall in n from 2% to 1% raise y*
ANSWER:
In order to answer the problem, it is essential to consider the formula and the function first. The production function provided is a Cobb-Douglas type with capital K(t) and effective labor A(t)L(t) as inputs.
According
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