Optimization of a utility function Assume that a representative household has a budget of 180e to buy fruits. At the supermarket, one can only buy bananas (B), apples (A), and Kiwifruits (K). For one kilogram of the three fruits, the consumer pays a price of pB = 1, pA = 2 and pK = 4. The utility function for the consumption of the three goods is given by the following equation: U(B,A,K) = B1/3 A1/3 K1/3 Tasks 3.1 Assuming that the household is consuming only these three consumption goods, construct the budget constraint.

3.2 Scenario A: The household asked your opinion on what quantities of the three consumption goods would maximize its utility. Use the "Excel Solver" to determine the utility-maximizing quantities of the three goods. Before starting with the "Excel Solver" for the rst time, use 1 as the starting value for each of the quantities of the three goods, that is, B = 1,A = 1,K = 1. Also, determine the expenditure for each good and the utility level achieved. Use the table on page 11 of this document to insert the values you determined from the Excel calculations (round the quantities to one decimal place if necessary).

3.3 Scenario B: After one year, the price of bananas has increased to pB = 2. The federal statistical ocer goes shopping and buys the same quantities as in scenario A. Use the table on page 11 of this document to insert the values you determined from the Excel calculations (round the quantities to one decimal place if necessary). What ination rate does the federal statistical ocer determine? By what amount would the budget have to change from Scenario A for the quantities to still be aordable? What would the budget then be?

3.4 Scenario C: Unlike the federal statistical ocer in scenario B, the optimizing household is directly able to change its purchasing behavior and adjust quantities. Minimize the household's expenditures using "Excel Solver" under the constraint that the utility level from Scenario A is achieved again. Use as initial values for the quantities of the three goods the values determined in Scenario A. Use the table on page 11 of this document to insert the values you determined from the Excel calculations (round the quantities to one decimal place if necessary). What ination rate exists for the private household? By what amount would the budget have to change compared to scenario A in order for the newly calculated quantities to be aordable? What would the budget then be?