, with utility function U(L, K) = L 2K. This time assume that the individual has a utility constraint of U = 9.

(a) Write down the cost-minimization problem. Clearly specify the objective function and the choice variables. Use pL and pK as the prices of L and K.

(b) Explain how to go about solving this problem if you were given values of pL, and pK.

(c) Assume the prices of L and K are pL = 2 and pK = 3. Find the minimum budget required to reach a utility level of 9. What are the cost-minimizing choices of L and K?

(d) Calculate the individuals Hicksian demand curve for lattes6 if the price of K is pK = 3. Use pL for the price of lattes. Calculate the slope of this demand curve when pL = 2.

(e) Calculate the individuals Hicksian demand curve for cake if the price of L is pL = 2. Use pK for the price of cake. Calculate the slope of this demand curve when pK = 3.