Let's use the Euler equation two ways. First, to find out the optimal consumption path, taking the interest rate as a given and then to find out the equilibrium interest rate that will eliminate demand for saving and investment, taking the consumption path as a given. Both times, the utility function will be the same. U = In(c₂) + 0.9 ln(c+₁) t+1 So the future counts 90% as much as the present. In Part 1, income each period is 100, and the interest rate is 20%. In Part 2, consumption in each period is 100 -- in other words, income each period is 100, but income isn't

Let's use the Euler equation two ways. First, to find out the optimal consumption path, taking the interest rate as a given and then to find out the equilibrium interest rate that will eliminate demand for saving and investment, taking the consumption path as a given. Both times, the utility function will be the same. U = In(c₂) + 0.9 ln(c+₁) t+1 So the future counts 90% as much as the present. In Part 1, income each period is 100, and the interest rate is 20%. In Part 2, consumption in each period is 100 -- in other words, income each period is 100, but income isn't

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter17: Capital And Time

Section: Chapter Questions

Problem 17.3P

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In class discussions about uncertainty we assumed that the utility levels in each state of nature depends on c, which we might interpret as some aggregate con- sumption and we expressed utility as U(c). Now, let's extend this to a case where the utility level depends on consumption of two goods (this was the type of utility we used mainly in this course). Ben is a farmer who grows wheat and barley. However, his harvest is uncertain. If weather is good, he gets 200 lbs of wheat and 200 lbs of barley. If weather is bad, he gets only 100 lbs of wheat and 100 lbs of barley. His utility in each state of nature is U(w, b) = w¹/46³/4, where w and b represent his consumption of wheat and barley, respectively. Prices of wheat and barley are $1 in both state of nature. The probability of good weather is π. Question 3 Part a Express Ben's expected utility function. (Hint: find Ben's optimal consumption in each state of nature first) Question 3 Part b Let's assume π = 0.5. Knowing that bad weather…
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