tt econ 302.

You're having a party, and need to buy beer ($5 a unit) and pizza ($10 a unit). You have $100. Suppose pizza and beer are perfect complements, what would you buy? Suppose pizza and beer are perfect substitutes, what would you buy? Martha receives utility from consuming two commodities: x = food & y = milk. Her preferences over x and y are given by the following utility function: U(x, y) = 4 ln(x) + 6 ln(y). Martha's income is $10. The price of milk is $3 and the price of food is $2. Note: ln(x) = loge(x) Compute the marginal rate of substitution of food (x) for milk (y). What is Martha's budget constraint? Find the optimal consumption of food that Martha would choose. Suppose that the price of the food increases to $4. What is the optimal bundle of goods for Martha?

\fQUESTION 1 There are two customer service workers; worker 11' (f E {l_.2}) chooses an effort level (a)2 15 for worker I and a}. E [H.oo) to exert in helping a customer. The cost of eort is 31(31) = 2 (32] 1C! workers exert. up to a maximum satisfaction level of 10. that is= it is equal to rn_in{.el + 2,113} . 02(82} = for worker 2. The customer's satisfaction level equals the total effort that the Each worker's payoH is the difference between the customer's satisfaction level and his-"her own effort cost. Consider rst the game G in which the two workers choose their eHorts simultaneously. (a) Write down each worker's payoff function in G. (h) Describe each worker's best response (or reaction) function in G. (e) Draw the two best response functions in the same diagram and find all the pure-strategy Nash equilibria of G. Now consider sequential versions of the interaction. In game I}. rst Player 1 (= worker I) selects an effort level. then Player 2 (= worker 2) after observing Player 1's choice chooses her own effort level. (d) Completely describe all the pure-strategy subgame perfect equilibria of I}. In game I}. the sequence of events starts with those in F2 . but after Player 2 moves. Player 1 observes Player 2's choice and decides whether to exert some additional effort 51 E [,co) . so that his own total eort is e1+ ('51. (e) (e.1} What is a pure strategy for Player 1 in 13'? {13.2} What is a pure strategy for Player 2