(a) Consider a firm with the following production function. Q = 2*L*L + K*K. The price of capital (K) is $100 and the price of labor (L) is $50. The marginal product of labor is 4L and marginal product of capital is 2K. If K=10, what is L at the point of cost minimization?
(b) What is the cost associated with this level of K and this level of L? What is total product?
(c) What is the slope of the iso-cost?
(d) Draw a graph illustrating the tangency between the iso-cost and the iso-quant from the above problem (label your axes and the point of tangency, including the amount of labor and capital.)
(f) Finally is the function, increasing, decreasing or constant returns to scale?