A jewelry firm buys semiprecious stones to make bracelets and rings. The supplier quotes a price of $8.90 per stone for quantities of 600 stones or more, $9.30 per stone for orders of 400 to 599 stones, and $9.80 per stone for lesser quantities. The jewelry firm operates 108 days per year. Usage rate is 26 stones per day, and ordering costs are $46.

a. If carrying costs are $2 per year for each stone, find the order quantity that will minimize total annual cost.

b. If annual carrying costs are 20 percent of unit cost, what is the optimal order size?

c. If lead time is 5 working days, at what point should the company reorder?

What does the phrase limited liability mean in a corporate context?

Suppose a firm faces a fixed price of output, 푝푝= 1200. the firm hires workers from a union at a daily wage, 푤푤, to produce output according to the production function 푞푞= 2퐸퐸12. there are 225 workers in the union. any union worker who does not work for this firm is guaranteed to find nonunion employment at a wage of $96 per day. a. what is the firm’s labor demand function? b. if the firm is allowed to choose 푤푤, but then the union decides how many workers to provide (up to 225) at that wage, what wage will the firm set? how many workers will the union provide? what is the firm’s output and profit? what is the total income of the 225 union workers? c. now suppose that the union sets the wage, but the firm decides how many workers to hire at that wage (up to 225). what wage will the union set to maximize the total income of all 225 workers? how many workers will the firm hire? what is the firm’s output and profit? what is the total income of the 225 union workers? [hint: to maximize total income of union, take the first order condition with respect to w and set equal to 0.]

Evaluate a real situation between two economic actors; it could be any scenario: two competing businesses, two countries in negotiations, two kids trading baseball cards, you and another person involved in an exchange or anything else. use game theory to analyze the situation and the outcome (or potential outcome). be sure to explain the incentives, benefits and risks each face.