Question

Suppose you have a society of n identical individuals. Repeat part (b) except this time plotuinstead ofh. Canyou reach any conclusions about the level of consumption thatmaximizes utility?

Answer 1

Answer:

Explanation:

1. (3.6) Suppose you have a society of n identical individuals and the environment.

Each individual likes his or her material possessions as well as access to parks and

wilderness areas. In fact, the utility function of each individual is U(x;H) = x+H1

x

1

H , where x is consumption goods and H is environmental health. H attains its highest

level when it is pristine: H = 100. Consumption of goods degrades the environment

but the environment has some ability to heal itself. In fact, the environment has health

Ht = Ht1 + g(100 Ht1) nx, where Ht is today’s H and Ht1 is yesterday’s H. The

environment’s ability to clean itself, g, is fixed.

(a) Simply focusing on the utility function (ignoring the evolution of H), discuss the

extent to which the utility function is consistent with biocentrism or anthropocentrism.

(b) Suppose we start at H = 100. Assume g = 0:1 and n = 1. Plot how H would evolve

for x = 0:01; 0:1 and 1.

(c) Repeat part (b) except this time plot U instead of H. Feel free to try other values

of x. Can you reach any conclusions about the level of consumption that maximizes

utility?