Consider an economy with the following aggregate production function: Y = 3K1/3(AL)2/3   Capital grows through investment but also decays due to wear and tear at a constant rate δ per period. Assume that A is growing at the exogenous rate g, that L is growing at the exogenous rate n, and that households save a constant proportion s of their income.   (a ) Find the steady state level of the capital per effective worker (k*), output per effective worker (y*) and consumption per effective worker (c*) - in terms of the parameters of the model.   (B) What is the level of k (k**) that maximizes consumption?    (C) Given a depreciation rate of 7%, population growth rate of 2%, technological progress of 1% and a saving rate of 30%, calculate the steady state levels of k, y and c.   (D) To move to the level of capital that maximizes consumption, how should the saving rate be changed? Explain.    (E) Calculate the saving rate needed to reach the golden rule level of capital per effective worker.

1. Consider an economy that operates under competitive markets and meets the assumptions of the Solow 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%. a. Show that the production function exhibit constant return to scale? b. Derive the production function for output per capita. c. Derive the production function for output per effective unit of labor. d. Find equilibrium real wage as a function of capital per unit of effective labor and effectiveness of labor. e. Find equilibrium real rental price of capital as a function of capital per unit of effective labor and effectiveness of labor. f. Solve for steady state level of capital per unit of effective labor. g. Find steady state level of output per unit of effective labor. h. Find growth rate of output and output per worker on the balanced growth path. i. Which one would…

Please don't copy

The productivity of a country is given by ​f(x,y)=15.21x0.438y0.562​, where x is the amount of labor and y is the amount of capital.   ​(A) Find fx(x,y) and fy(x,y). ​(B) Find fx(67,55) and fy(67,55)​, and interpret the results.