Onsider a survival game in which a large population of animals meet and either fight over or share a food source. There are two phenotypes in the population: one always fights, and the other always shares. For the purposes of this question, assume that no other mutant types can arise in the population. Suppose that the value of the food source is 200 calories and that caloric intake determines each player's reproductive fitness. If two sharing types meet one another, they each get half the food, but if a sharer mets a fighter, the sharer conceeds immediately, and the fighter gets all the food.

Suppose that the cost of a fight is 50 calories (for each fighter) and that when two fighters meet, each is equally likely to win the fight and the food or to lose and get no food. Draw the payoff table for the game played between two random players from this population. Find all of the ESSs in the population. What type of game is being played in this case?

3. saving two consumers, larry and jeff, have utility functions defined over the two periods of their lives: middle age (period zero) and retirement (period 1). they have the same income in period 0 of m dollars and they will not earn income in period 1. the interest rate they face is r. larry’s and jeff’s utility functions are as follow. = 0.5 + 0.5 and = 0.5 + 0.5 for each person is between zero and one and represents each consumer’s temporal discount econ 340: intermediate microeconomics. ben van kammen: purdue university. rate. a. write the budget constraint that applies to both jeff and larry in terms of consumption in each period and ), interest rate, and m. b. what is larry’s and what is jeff’s marginal rate of intertemporal substitution? c. what is the slope of the budget constraint? d. write each consumer’s condition for lifetime utility maximization. e. re-arrange the conditions from part (d) to solve for the ratio, . f. if > which consumer will save more of his middle age income? g. if > 1 1+ , in which period will larry consume more: = 0 or = 1?