(Solution) - David is leaving on a three day business trip He has -(2025 Original AI-Free Solution)

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David is leaving on a three-day business trip. He has a meal allowance of $60. Let's use X to stand for the amount he spends on food the first day, Y for the amount he spends the second day, and Z for the amount he spends on the third day. David's budget constraint is X + Y + Z = 60. Before he leaves, he would like to choose his spending to maximize the utility function ln (X) + ln (Y) + ln (Z), where ln stands for the natural logarithm. But on the first day of his trip, he would like to choose his spending to maximize the utility function 2ln(X) + ln (Y) + ln (Z), and on the second day he would like to choose his remaining spending to maximize the utility function 2ln(Y) + ln (Z). If he could commit to a plan before leaving, how would he spend his money? If he could commit to a plan on the first day of his trip, how would he spend his money? Assuming he cannot commit to a plan, and that he correctly anticipates his decisions on subsequent days, how will he actually spend his money? Is he dynamically consistent? Why or why not?