You are running a small factory that uses labour (L) and capital (K) to produce output Q. Your production function is Q = 10L 1 2 K 1 2 . For every unit of labour you use you have to pay a wage (w) of $20 and for every unit of capital you use you have to pay a rental rate (r) of $5. You’ve signed a contract that you will produce Q = 700 units of output.

(a) What are the Returns to Scale of your production function?

(b) What is your total cost equation?

(c) What is your output constraint?

(d) Find the cost-minimizing bundle of L and K.

(e) What is the total cost of using the optimal bundle?

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