=+17.9 Business Application: Diversifying Risk along the Business Cycle: Suppose you own a business that does well during economic expansions but not so well during recessions, which happen with probability

d. Let xE denote your consumption level during expansions and let xR denote your consumption level during recessions. Unless you do something to diversify risk, these consumption levels are E 5 1eE

, eR 2

where eE is your income during expansions and eR your income during recessions (with eE . eR

). Your tastes over consumption are the same during recessions as during expansions and you are risk averse.

For any asset purchases described here, assume that you pay for these assets from whatever income you have depending on whether the economy is in recessions or expansion.

A. * Suppose I own a financial firm that manages asset portfolios. All I care about as I manage my business is expected returns, and any asset I sell is characterized by 1p, bR

, bE 2 where p is how much I charge for 1 unit of the asset, bR is how much the asset will pay you (as, say, dividends) during recessions, and bE is how much the asset will pay you during expansions.

a. Is someone like me—who only cares about expected returns—risk averse, risk loving, or risk neutral?

b. Suppose that all the assets I offer have the feature that those who buy these assets experience no change in their expected consumption levels as a result of buying my assets. Derive an equation that expresses the price p of my assets in terms of

d, bR and bE

.