Suppose that there is no fixed production input (i.e. long run.) With the production function above, the slope of the isoquant is given by MRTS = -(K/2L). Assume the firm chooses to hold costs C at $50.
a. If the wage rate, w, is $5 and the rental rate for capital, r, is $2, what is the optimal amount of labor and capital that should be hired?
b. If the wage rate increases to $10, how will the optimal amount of labor hired change?