Aviella has a utility function over her food consumption F and her housing consumption H. Her utility is given by =. Her marginal utility for food is and her marginal utility of housing is . Assume that the price of both goods is 1.

a. What is Aviella's total utility if her budget is 18?

b. Suppose Aviella is given a choice to play a lottery where, with a 50% probability she could lose $8 (leaving her with $10) and with a 50% probability she could gain $12 (leaving her with $30). Would Aviella take this gamble? Demonstrate your answer.

c. Suppose now that Aviella has already committed to her housing consumption in part (a). In other words, you must set H equal to the value it had when her budget was $18, regardless of the gamble's outcome. Would Aviella take the gamble now? Demonstrate your answer.

d. Explain the relationship between risk aversion and consumption commitments.