Task 03.

The unemployment rate in April 2020 was 14.7%, while in March 2020 was 4.4%. What is your best estimate for the real output growth rate in this period? Assume the US real output was growing at its long rate of 3% until March 2020. Assuming inflation stayed at the Fed's target rate of 2% during this period, how should the Fed react to this according to the Taylor rule? Assume that the equilibrium real interest rate is 2%. Can the nominal interest rate implied by the Taylor be implemented by the Fed? Explain it carefully.

Task 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?

Part ii.

Show the points of the profit maximization outputs under these three different market structures on the above three figures. Compare these output levels Qc, and Qm.

Show the points of the prices under these three different market structures on the above three figures. Compare these price levels Pc, and Pm.

Compare the consumer surpluses under these three market structures by using notations CSc, and CSm.

Compare the producer surpluses under these three market structures by using notations PSc, and PSm.

Compare the total surpluses under these three market structures by using notations TSc, and TSm. Which market structures can yield economic efficiency?

2. Show the points of the prices under these three different market structures on the above three figures. Compare these price levels Pc, andPm. rinciples of Microeconomics Yiqing Xie 3. Compare the consumer surpluses under these three market structures by using notations CSc, and CSm.Summary for perfect competition and single price monopoly: (c stands for perfect competition, and m stands for single price monopoly.) Perfect competition Single price monopoly Cost/Revenu e Cost/Revenue S MC .1 MR 341? 1. Show the points of the prot maximization outputs under these three different market structures on the above three gures. Compare these output levels Qc, and Qm