Consider a Competitive Economy in Which Factor Prices Adjust to Keep

Essay

Consider a competitive economy in which factor prices adjust to keep the factors of production fully employed, and the interest rate adjusts to keep the supply and demand for goods and services in equilibrium. The economy can be described by the following set of equations: $$\begin{array} { l } L = \bar { L } , K = \bar { K } , G = \bar { G } , T = \bar { T } \\Y = A K ^ { \pi } L ^ { ( 1 - \omega ) } \\Y = C + I + G \\C = C ( Y - T ) \\I = I ( r )\end{array}$$ How does an increase in government spending, holding other factors constant, affect the level of: a. public saving?
b. private saving?
c. national saving?
d. the equilibrium interest rate?
e. the equilibrium quantity of investment?