(A) Assume the last unit of peanuts consumed increased Sasha's total utility from 40 utils to 48 utils and that the last unit of bananas consumed increase her total utility from 52 to 56 utils.
(i) If the price of a unit of peanuts is $1 and Sasha is maximizing utility, calculate the price of a unit of bananas.
Anytime, you see a utility question use the formula:
(ii) If the price of a unit of peanuts increases and the price of a unit of bananas remains unchanged from the price you determined in (a)(i), how will Sasha's purchase of peanuts change?
Understand that if the price of peanuts increases, then the value of MU (marginal utility) to price will decrease. If the price of peanuts increase then for every dollar spent on peanuts I will be able to buy fewer and fewer peanuts.
(B) Assume that the cross price elasticity (XED) of demand between peanuts and bananas is positive. A widespread disease has destroyed the banana crop. What will happen to the equilibrium price and quantity of peanuts in the short-run? Explain.
Understand what a positive XED means, from the elasticity cheat sheet here.
Since peanuts and bananas are substitutes, when the crop of bananas are destroyed (banana's supply curve shifts leftward) the price of bananas will rise and consumers will demand more peanuts as they are a substitute for bananas they (peanuts) are relatively cheaper. You must understand that if the price of bananas rises and the price of peanuts stays the same, then, per dollar spent, peanuts have now become cheaper.
(C) Assume the price of bananas increase.
(i) Will the substitution effect increase, decrease, or have no effect on the quantity of bananas demanded?
The substitution effect will decrease the quantity of bananas demanded. Price goes up the quantity demanded goes down. The substitution effect is one of the very reasons that the demand curve slopes down....
(ii) What happens to Sasha's real income?
If prices rise/Inflation increases then real incomes/wages fall.
From an earlier post on nominal and real wages here.