Consider a Cobb-Douglas production function;

It is assume that

• The interest rate R is 5%.
• The depreciation rate of physical capital is 3%.
• The capital gain will be 2%.
• The desired growth rate for the capital stock is 6%.

Compute the optimal investment rate (that is, the share of over investment I _l over output Y _t ) for this firm for the following values of a: 0.1, 0.3, 0.5? Show how you obtained these results. Plot the optimal investment rate as function of ? in a graph.

Y = AKN, for 0 < a < 1