Problem 04.

1. Supreme Cola is a supplier of fountain equipment to restaurants, bars and cafeterias. The fountain equipment is manufactured at their York PA plant site. A national distribution center (DC) for the fountain equipment is also maintained adjacent to the plant. Supreme has one common platform design to which they add various features and accessories to create 10 different product options. The lead time for manufacturing and delivering a batch of products to the distribution center is 2 weeks. They review inventory and order weekly. For product ACola, Supreme uses a Normal distribution with mean 100 and standard deviation 20 to model weekly demand. Demands across weeks are independent. ACola sells for $15,000 and they enjoy a 50% gross margin. The annual holding cost for inventory in the DC is 25% of the product's cost. In the event that a customer order cannot be filled from the warehouse due to an out-of-stock situation, Supreme expedites the manufacture and delivery of the item. It estimates that such expediting increases their cost by $770 per unit.

a. What order upto level should Supreme choose to minimize their inventory for ACola while achieving at least a 99.25% in-stock probability?

b. Supreme uses an order up-to policy with a base stock level equal to 250 for ACola. What is the probability that Supreme will have more than 150 units on order of that product at the start of any given week?

2. An industrial company requires argon gas cylinders for its work. Weekly demand is normally distributed with a mean of 35 and a standard deviation of 15. Demands are independent across weeks. Orders are placed weekly and the lead time to receive an order is 1 week. They want to hold enough cylinders to ensure a 97% in-stock probability. If they use an order up-to model, what base stock level should they implement? (Do not round to an integer value, i.e., leave your response in decimal form.)

3. Radio Shack sells a 32GB flash drive. Weekly demand for the 32GB flash drive in one of their stores is normally distributed with a mean of 3 and a standard deviation of 0.5. The store places orders weekly and there is a one week lead time to receive orders.

a. On average, how many units will the store have on order?

b. Suppose they operate with a base stock level of 7. What in-stock probability would they achieve?

4. A large toy company Mttel currently allows toy retailers to place orders with delivery in 4 weeks. The Gigantic Pocket Monster (Gipokmon) is a new toy that Mttel has introduced. Demand per week for the toy at one of their stores is estimated to be normally distributed with a mean of 25 units and standard deviation of 5 units. Assume TOYS-are-MINE uses the order-up-to model to plan orders and deliveries to this store.

a. Suppose TOYS-are-MINE uses an order-up-to level of 20. After receiving their delivery for this week, they have 2 units on-hand. Last week's order was for 5 units. How many units will they order this week?

b. Again, suppose they use an order-up-to level of 20 for this store. On average, how many units will this store have on-order?

c. Suppose an order-up-to level of 140 is established. What is the resulting in-stock probability?

d. Suppose an order-up-to level of 130 is established. What would be the expected end-of-period on-hand inventory of Gipokmons?

Problem 05.

3 An Anticipated Output Shock [30 points] Consider a two-period small open endowment economy populated by a large number of households with preferences described by the lifetime utility function: 11 U = C 10 C 11 (1) Suppose that households receive exogenous endowments of goods given by Q1 = Q2 = 10 in periods 1 and 2, respectively. Every household enters period 1 with some debt, denoted B0?, inherited from the past. Let B0? = ?5. The interest rate on these liabilities, denoted r0, is 20 percent. Finally, suppose that the country enjoys free capital mobility and that the world interest rate on assets held between periods 1 and 2, denoted r?, is 10 percent.

a (14 points) Compute the equilibrium levels of consumption, the trade balance, and the current account in periods 1 and 2. Do not forget to show step by step your algebraic calculations. Explain in detail your reasoning. No credit without an explanation.

b (16 points) Assume now that the endowment in period 2 is expected to increase from 10 to 15. Calculate the effect of this anticipated output increase on consumption, the trade balance, and the current account in both periods. Provide intuition. Do not forget to show step by step your algebraic calculations. Explain.

ii.

1 Impatient Households [18 points] Consider a two-period endowment economy populated by identical households with preferences defined over consumption in period 1, C, and consumption in period 2, C2, and described by the utility function In(C1) + 8*In(C2) (1) where C, denotes consumption in period 1, C, denotes consumption in period 2. Each period, the economy receives an endowment of Q units of a baskets of goods (Q1 = Q2 = Q). Households start period 1 carrying no assets or debts from the past (B;;). In period 1, the individual can borrow or lend at the interest rate r, > 0 via a bond denoted Bi. Assume perfect capital mobility, so "1 = "*. Use chapter 3 to answer this question. 1. Find the optimal levels of consumption in periods 1 and 2 as functions of the individual's lifetime wealth, Y, and the interest rate. Hint: Recall that Y = (1 + ro) B; + Q1 + 1+m. 21, Do not forget to include all your derivation and equations. (7 points] 2. Find the optimal levels of consumption in periods 1 and 2 as functions of the individual's lifetime wealth, Y, and the interest rate but now assuming the following life-time utility: In(Ci) + In(C2). [7 points] 3. Explain why the two answers in parts (a) and (b) are different. Provide your intuition. [4 points