answer the following question a to f

4. (28 points} A village of 100 households is pooling money to purchase land for a community garden. Each household either donates $100 or does not donate. Two plots of land are available for purchase for the community garden. Land A oosts $3070 and gives utility of $150 to each household that uses the garden. Land B costs $6000 and gives a total utility of 3'." which is equally divided among the households that use it. (For example, if 100 households use Land B, each household gets a utility of V,' 100) The village can buy one plot of land at most, as follows: 0 If the total sum of contributions is less than $3070, they cannot a'ord either land; a 1f the total sum of contributions is greater than or equal to $3070 and less than $6000, the village council buys land A; o if the total sum of contributions is greater than or equal to $6000, the viilage council buys land B. Unused contributions are not returned to households. (a) Suppose that V = $12000 and that a household can use the village garden whether or not they contributed to purchase it. Formulate this situation as a strategic form game. (Consider the payoff function very carefully.) (b) Evaluate whether having exactly 32 households contribute is a Nash Equilibrium. (Hint: what is the payoff for a household that con- tributes? What would happen if they choose not to contribute?) (c) Find all Nash equilibria. Show your work clearly. (:1) Now suppose (for the remainder of the question} that only the house- holds that contribute can use the garden. The payoii' that households that contribute receive from having a community garden in Land A is $150 regardless of the number of contributors. but the pay-00' V that households receive from having the cormnunity garden in Land B is split evenly among its contributors. What is the payoff function in this case? (B) For what values of V will action proles with exactly 71 households contributing be Nash equilibria? (f) Suppose V = $9000. Find all Nash equilibria of this game