Assume that someone has inherited 2,000 bottles of wine from a rich uncle. He or she intends to drink these bottles over the next 40 years. Suppose that this person's utility function for wine is given by u(c(t)) = (c(t))0.5, where c(t) is each instant t consumption of bottles. Assume also this person discounts future consumption at the rate 8 = 0.05. Hence this person's goal is to maximize of40 e-0.05tu(c(t))dt = 0/40 e-0.05t(c(t))0.5dt. Let x(t) represent the number of bottle of wine remaining at time t, constrained by x(0) = 2,000, x(40) = 0 and dx(t)/dt = c(t): the stock of remaining bottles at each instant t is decreased by the consumption of bottles at instant t. The current value Hamiltonian expression yields: H=e-0.05t(c(t))0.5 + XA(- c(t)) + x(t) (dλ/dt). This person's wine consumption decreases at a continuous rate of 15.60 percent per year. The number of bottles being consumed in the 30th year is
Assume that someone has inherited 2,000 bottles of wine from a rich uncle. He or she intends to drink these bottles over the next 40 years. Suppose that this person's utility function for wine is given by u(c(t)) = (c(t))0.5, where c(t) is each instant t consumption of bottles. Assume also this person discounts future consumption at the rate 8 = 0.05. Hence this person's goal is to maximize of40 e-0.05tu(c(t))dt = 0/40 e-0.05t(c(t))0.5dt. Let x(t) represent the number of bottle of wine remaining at time t, constrained by x(0) = 2,000, x(40) = 0 and dx(t)/dt = c(t): the stock of remaining bottles at each instant t is decreased by the consumption of bottles at instant t. The current value Hamiltonian expression yields: H=e-0.05t(c(t))0.5 + XA(- c(t)) + x(t) (dλ/dt). This person's wine consumption decreases at a continuous rate of 15.60 percent per year. The number of bottles being consumed in the 30th year is
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.14P
Related questions
Question
See attachment. This is not a writing assignment. I need to understand the mathematical steps to calculate the continuous rate of wine consumption, and also the number of wine bottles being consumed in the 30th year.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Recommended textbooks for you