John is a rational consumer withwhoseindifference curves defined over various bundles of "petrol" and "everything else"have the standard smooth, convex shape.

Currently, petrol costs 1.50/litre, and John consumes 1000 litres/year.

One of two possibilities is about to occur, and you should evaluate the effect of each of these changes on John's welfare relative to the original status quo presented above:

1. John is given an extra 1000/year by the government, but the price of petrol rises to 2.50/litre

1. John is forced to pay an extra 1000/year in tax to the government, but the price of petrol falls to 0.50/litre

Jane is visiting a broker to decide where to invest her retirement fundsfor the next 20 years(which constitute 100% of her savings). She visits her broker and he offers her two investments: she can invest in Project A, which is guaranteed to double her money overthe 20 years, or she can invest in Project B, where thereis a50/50 chance that she will triple her money, and a 50/50 chance that she will make no gains at all and just have her original savings returned to her.

Airi meanwhile, visits her brokerto invest all of her savings for a 25-year period and getsdifferent offers: Airi's broker offers Project C, which is guaranteed totriple the funds over a 25-year period, or Project D, which has a 50/50 chance ofquadruplingher money, and a 50/50 chance that she will make no gains at all and have her original money returned to her.

Consider the different utility functions over wealth (W)that Jane and Airi could have and state which projects they will invest in:

1. With a utility functionw^2Jane will invest in project A
2. With a utility functionw^(1/2)Jane will invest in project A
3. With a utility functionw^2Airi will invest in project C
4. With a utility functionw^(1/2) Airi will invest in project C

GOOD explanations PLEASE