EBK INTERMEDIATE MICROECONOMICS AND ITS
EBK INTERMEDIATE MICROECONOMICS AND ITS
12th Edition
ISBN: 9781305176386
Author: Snyder
Publisher: YUZU
Question
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Chapter 4, Problem 4.3P

a

To determine

To know:Expected utility of trip.

b)

To determine

To ascertain:Increase in utility if insurance is purchased.

c)

To determine

To calculate:Maximum amount to be paid for insurance.

d)

To determine

To ascertain:Fair insurance premium and whether F will buy insurance or not.

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Traders often buy foreign currency in the hope of making money when the currency’s value changes. For example, on April 15, 2015, one U.S. dollar could purchase 0.9428 euro, and one euro could purchase 126.457 yen. Let f(x) represent the number of euros you can buy with x dollars, andlet g(x) represent the number of yen you can buy with x euros.(a) Find a function that relates dollars to euros.(b) Find a function that relates euros to yen.(c) Use the results of parts (a) and (b) to find a function that relates dollars to yen. That is, find (g ∘ f) (x) = g(f(x) ).(d) What is g(f(1000) )?
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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 δ = 0.05. Hence this person’s goal is to maximize 0ʃ40 e–0.05tu(c(t))dt = 0ʃ40 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 + λ(– c(t)) + x(t)(dλ/dt). This person’s wine consumption decreases at a continuous rate of ??? percent per year. The number of bottles being consumed in the 30th year is approximately ???
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