Assume 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). Suppose the firm chooses to hold costs C at $50.
1. What is the optimal amount of labor and capital that should be hired if the wage rate, w, is $5 and the rental rate for capital, r, is $2?
2. How will the optimal amount of labor hired change if the wage rate increases to $10?