# ECON 402 ECON402 Midterm 2 with Answers (Penn State University)

ECON 402 ECON402 Midterm 2 Answer (Penn State University)

1. Two people, J and D, go hiking at the same time every day. Neither carries a cellphone. Both prefer solitude (i.e. hiking by him/herself), but they have not made an agreement on which hike each will take: ridge (R), mountain side (S), or valley (V). They must choose simultaneously and independently which hike to take. Based on their choices, they each receive the sum of two payoffs, one for hiking alone and one for how much they enjoy the particular hike. Each receives a payoff of 2 if s/he hikes alone. The ridge hike gives an additional payoff of 2, the mountain side hike a payoff of 1, and the valley hike a payoff of 0. For instance, if J goes on the ridge hike and D on the valley hike then the payoff vector is (4,2).Â

2. Suppose that P1, P2 are firms producing an indistinguishable good at a marginal cost of $3. Suppose that each firm chooses a price simultaneously with and independently of the other firm and that they can each produce up to 7 units. Suppose further that there are 10 consumers, each willing to pay up to $10 for a single unit, purchasing from the firm posting the lowest price, sharing the market equally in the case of ties.Â

Two countries, U and I, are involved in negotiations. Suppose that the normal form is asÂ follows.Â

4. SupposethatbusinessBfirstdecideswhethertoobey(O)orbreak(B)alawsetbygovernment G. If B obeys the law then the game ends and both players receive 0. If B breaks the law then G can decide whether to punish (P) or not to punish (N) B for breaking the law. If B breaks the law and G punishes B then the payoff vector is (-5,-10) and if B breaks the law and G does not punish B then the payoff vector is (5,-4).Â

5. Please find all (pure strategy) subgame perfect Nash equilibria in the following game. [5]Â

6. SupposethataretailerRhassixTVâ€™sinstockandsixpotentialcustomers:H1,H2,L1,L2,L3,L4 who can choose to buy a total of at most one TV each in period 1 or in period 2. Customers maximize the difference between benefit (expressed in $) and price. The order in which decisions are made is as follows.Â