Start at part d**** 10 Consider McDonalds production function for tasty Jr Chickens: JC(K, L) = 10(K1/2 + L1/2) M PK = 5 K1/2 M PL = 5 L1/2 Presume we are initially in the long run a) What returns to scale does this McDonalds exhibit? b) Frame McDonalds profit maximization problem with the production func- tion nested and then solve for the factor demands for K and L. c) When you substitute these into the production function, what expression do you get for JC? What is this function? d) Frame McDonalds cost minimization problem and then solve for the con- ditional factor demands for K and L. e) Derive the long-run cost function. f) Express McDonalds profit maximization problem with the cost func- tion included. If McDonalds marginal cost curve is given by MC = JCrw/50(w+r). Find the supply function. Compare this to your answer in c. g) Suppose K is now fixed at 100 in the short run. Derive McDonalds short- run factor, and conditional factor demands. h) Derive McDonalds short-run cost function. i) Compare McDonalds choice of inputs and costs when r = 1, w = 2, and JC = 150 between the long-run and short-run. What do you notice? j) Compare McDonalds choice of inputs and costs when r = 2, w = 2, and JC = 150 between the long-run and short-run. What do you notice? k) If JC=150 is the optimal output choice in part i and if the price of a Jr Chicken did not change between parts i and j, is JC=150 also the optimal output choice in part j?