(a) (5 pts) Assume that the production function is of the form: r; = AKgNg-s Now assume there is one big competitive rm that operates the production in the economy and hires workers and capital for wage wt and rental rate qt. (Recall from 201 you will solve a prot maximization problem you can assume the FOC's you get with regards to the wage and the rental rate of capital will be the exact wage and rental rate of capital) Solve the rm's prot maximizing problem. Show that the labor share of income (wt%) and the capital share of income (qt%) are constant. Assume all these values are in real terms and you do not need to put a price out in front of the output. In addition, assume the wage rate and capital rental are consistent with the rm's FOC's