A seller is bargaining to sell a good to a buyer. The good is worth $0 to the seller and $1 to the buyer. The bargaining is in two periods. In period 1, one party is chosen with probability 1/2 to propose a sale price. The other party then accepts or rejects. Acceptance results in sale with the proposed price. Rejection moves the game to the second period. In the second period, one party is again chosen with probability 1/2 to propose a sale price, and the other party accepts or rejects. Acceptance results in sale at the proposed price. Rejection results in no sale, in which case each player receives zero payoff. Both players discount period 2 payoffs with a discount factor de (0,1): if a sale occurs at price pı in period 1, then the seller and the buyer collect p1 and 1-P1, respectively; but if a sale occurs at price p2 in period 2, the parties collect ∂p2 and ∂(1 – P2), respectively. Required:
a. For any pe [0, 1], show that there is a Nash equilibrium in which a sale occurs at price p in period 1.
b. Find all subgame perfect Nash equilibria (SPNE). (You must describe the associated strategy profile, and prove that it is a SPNE.)

Which statement best explains the relationship between points a and b? a. consumption reaches its highest point, and then supply begins to fall. b. inflation reaches its highest point, and then the economy begins to expand. c. production reaches its highest point, and then the economy begins to contract. d. unemployment reaches its highest point, and then inflation begins to decrease.

Thomas kratzer is the purchasing manager for the headquarters of a large insurance company chain with a central inventory operation. thomas's fastest-moving inventory item has a demand of 6,000 units per year. the cost of each unit is $100, and the inventory carrying cost is $10 per unit per year. the average ordering cost is $30 per order. it takes about 5 days for an order to arrive, and the demand for 1 week is 120 units. (this is a corporate operation, and the are 250 working days per year.)a) what is the eoq? b) what is the average inventory if the eoq is used? c) what is the optimal number of orders per year? d) what is the optimal number of days in between any two orders? e) what is the annual cost of ordering and holding inventory? f) what is the total annual inventory cost, including cost of the 6,000 units?

1. revising for conciseness - eliminating flabby expressions, limiting long lead-ins, and dropping unnecessary fillerstime is money in any business environment. people want information communicated quickly and clearly. to make your writing more concise and understandable, avoid flabby expressions, long lead-ins, and unnecessary fillers. your audience will appreciate your brevity.1. if your writing contains a flabby expression like in view of the fact that, replace it with the word because / although / probably .for each of the following two sentences, choose the best revision.2. i am sending you this letter to inform you that we have experienced an unexpected surprise within our expense sheet, but we are positively certain we will solve it.1) we need to inform you that we have experienced an unexpected surprise with our expense sheet, but we are midway to an end result.2) we have identified a problem with our expense sheet, but we will solve it.3) i am sending you this letter to inform you that we have a problem with our expense sheet, but we are positively certain we have a solution.3. it is the user who should contact the center.1) everyone knows that it is the user who should contact the center.2) the user should contact the center.3) if there is a problem, the user should contact the center. read the following passage, and then answer the question.[1] you scheduled seven conference calls for this morning between 10 and 11 a. m. [2] generally, the company limits the number of conference calls to three per hour. [3] i’m letting you know that in the future, we should be more careful about scheduling.4. which revision limits the long lead-in in sentence 3? 1) in the future, we should be more careful about scheduling.2) i’m letting you know so that in the future we are more careful about scheduling calls.3) so that you know in the future, we should be more careful about scheduling.