Assume U(x, y) = √4 xy.
a) Derive the indirect utility function v(p, Y ).
b) Now assume a consumer is considering a gamble that has a 50% chance of returning 121% of the initial investment (a gain of 21%) and a 50% chance of returning 81% (a loss of 19%). If a consumer’s initial budget is 100, what is the expected outcome of this gamble?
c) Now using the indirect utility function from a), the gamble from b) and assuming prices are equal to 1, find an optimal allocation of consumer’s initial wealth between risky asset from gamble in b) and a risk-free asset. Assume the return on risk-free assets is 1 (no gain/loss).
You have been asked to evaluate whether a project to preserve an area of forest should
go ahead or whether the land should be converted to agriculture. The net benefits of
ecosystem goods and services have been valued over the next four years at R6000, R10
000, R14 000 and R22 000 respectively. The immediate cost of preserving the forest is
R23 500. Assume that MWTP = 90 - 3Q and MC = 10 + 2Q. The discount rate is 7%.