Chapter 7, Problem 5P

The following data show the total output for a firm when specified amounts of labour are combined with a fixed amount of capital. Assume that the wage per unit of labour is $20 and the cost of the capital is $100. Labour per unit of time 0 1 Total Output 0 25 T 2 3 4 5 75 137 212 267 The marginal product of labour is at its maximum when the firm changes the amount of labour hired from ○ A. 0 to 1 unit. ○ B. 3 to 4 units. OC. 2 to 3 units. OD. 1 to 2 units. ○ E. 4 to 5 units.

The table below provides the annual revenues and costs for a family-owned firm producing catered meals. Total Revenues ($) 600,000 Total Costs ($) - wages and salaries 250,000 -risk-free return of 7% on owners' capital of $300,000 21,000 - rent 101,000 - depreciation of capital equipment 22,000 -risk premium of 9% on owners' capital of $300,000 27,000 - intermediate inputs 146,000 -forgone wages of owners in alternative employment -interest on bank loan 70,000 11,000 The implicit costs for this family-owned firm are ○ A. $70,000. OB. $97,000. OC. $589,000. OD. $118,000. ○ E. $48,000.

Suppose a production function for a firm takes the following algebraic form: Q= 2KL - (0.3)L², where Q is the output of sweaters per day. Now suppose the firm is operating with 10 units of capital (K = 10) and 6 units of labour (L = 6). What is the output of sweaters? A. 64 sweaters per day OB. 49 sweaters per day OC. 109 sweaters per day OD. 72 sweaters per day OE. 118 sweaters per day

3. Consider a course allocation problem with strict and non-responsive preferences. Isthere a mechanism that is efficient and strategy-proof? If so, state the mechanismand show that it satisfies efficiency and strategyproofness. {hint serial dictatorship and show using example}4. Consider a course allocation problem with responsive preferences and at least 3students. Is there a mechanism that is efficient and strategy-proof that is not theSerial Dictatorship? If so, state the mechanism and show that it satisfies efficiencyand strategyproofness.5. Suggest a mechanism for allocating students to courses in a situation where preferences are non-responsive, and study its properties (efficiency and strategyproofness). Please be creative

3. Consider a course allocation problem with strict and non-responsive preferences. Isthere a mechanism that is efficient and strategy-proof? If so, state the mechanismand show that it satisfies efficiency and strategyproofness. {hint serial dictatorship}4. Consider a course allocation problem with responsive preferences and at least 3students. Is there a mechanism that is efficient and strategy-proof that is not theSerial Dictatorship? If so, state the mechanism and show that it satisfies efficiencyand strategyproofness.5. Suggest a mechanism for allocating students to courses in a situation where preferences are non-responsive, and study its properties (efficiency and strategyproofness). Please be creative

2. a) Consider a market where one firm (firm 1) currently produces, but a second firm (firm 2) is intending to enter and sell an identical product. The market has inverse demand given by p = 40 – Q, where Q is the total output sold in the market. Firm 1 has a marginal cost of 16 and firm 2 has a marginal cost of c < 16, with no fixed cost for either firm. Firm 2 has a choice of competing on price or quantity, with firms making their choices simultaneously (i.e. the market will be either a Bertrand or Cournot duopoly). If you were advising firm 2 on entering this market, how would you advise it to compete? To what extent would the size of firm 2’s cost advantage affect your advice?  b) Now assume that firm 2 is aware that other firms are considering entering the market, so the market may over time change from a duopoly to an oligopoly with more than two firms. This would not change the nature of competition (i.e. any additional firms would set price or quantity in line with the first…

1. Consider two firms (i=1,2) interacting in the market. Assume that firms compete in quantities and therefore they choose either to cooperate or not in each round. If a firm deviates it earns monopoly profit for a round and a punishment phase will follow from next round onwards (for ever) where both firms choose the Cournot quantity. Assume a discounting factor & and that firms meet in the market in every period. The demand facing the industry is p = 1 92. Let Q = q1 + 92 denote the aggregate industry output - 91 - level. Assume further that production is costless.

Q4 (30 points) Subsidy in Auctions Consider a sealed-bid second-price auction with two bidders. Valuation of bidder 1 is drawn from the uniform distribution on [0, 100], and valuation of bidder 2 is independently drawn from the uniform distribution on [0, 300].

$ A C ° Output Refer to the diagram, which pertains to a purely competitive firm. Which of the following statements is most accurate?