Consider a consumer with each of the following utility functions:

i) u(x)=e^-x

ii) u(x)=ln(x)

iii) u(x)= x^1/2

2a. For each of the utility functions above, compute the coefficient of absolute risk aversion and the coefficient of relative risk aversion.

The consumer faces one of two possible risks:

La: with probability 1/2, no loss occurs, and with probability 1/2, a loss of $10 occurs.

Lb: with probability 1/2, no loss occurs, and with probability 1/2, a loss of 10% of wealth occurs.

2b. Compute the maximum a consumer with utility function (i) above will pay for full insurance against risk La when initial wealth is w = 100 and when initial wealth is w = 200.

2c. Compute the maximum a consumer with utility function (ii) above will pay for full insurance against risk Lb when initial wealth is w = 100 and when initial wealth is w = 200.

2d. Compute the maximum a consumer with utility function (iii) above will pay for full insurance against risk La when initial wealth is w = 100 and when initial wealth is w = 200.

2e. Part b of this question illustrates constant absolute risk aversion. Part c illustrates constant relative risk aversion. Part d illustrates decreasing absolute risk aversion. Very briefly explain how.