4. Your production function is Q = LK. The wage for L is w and the rental rate for K is r. You need to produce Q units of output.

(a) What is your total cost equation?

(b) What is your output constraint?

(c) Find the Marginal Rate of Technical Substitution (MRTS) for your production function.

(d) In general (for any values of w and r), what relationship must hold between L and K at the cost minimizing bundle?

(e) What is your Input Demand Function for L? (HINT: your answer will be a function of w, r and Q)