Some Evolutionary Economics of Family Partnerships
Alice and Bob live in the forest. To sustain themselves, they collect fruits and berries and snare an occasional animal. The nights get cold, but Alice is a skillful fire-builder. Bob has never mastered this art. His fires fizzle and he never seems to collect the right kind of wood. Alice divides her time between collecting food and gathering wood. She does this in such a way that her marginal benefit from time spent collecting food is the same as that from gathering wood. Bob does not attempt to build fires. He spends all of his time gathering food, and every night slinks up and huddles beside Alice’s fire. Bob appreciates the fire’s warmth, but wishes it were larger. Bob has learned to leave morsels of food by the fire for Alice. Warmth and food are both “normal goods ” for Alice. The extra food that Bob leaves induces her to increase her total food consumption, but not by the total amount that Bob leaves for her. She uses some of the time saved by Bob’s gifts to gather more firewood. 1.1 Equilibrium with Unilateral Gifts–An Example Alice’s utility function is U(cA, y) = cAy where cA is the amount of food that she eats and y is the amount of wood on the fire. She has T hours to allocate between collecting food and wood. In an hour, she can collect either one unit of wood or πA units of food. If Bob leaves g units of food by the fire, she maximizes her utility by choosing y = 1