Problem%20Set%200%20-%20Math%20Prep - Economics 3010 Fall...

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Unformatted text preview: Economics 3010 Fall 2009 Professor Daniel Benjamin Cornell University Problem Set 0 This problem set is not to be handed in. If you are comfortable answering the questions in this problem set, then you have the level of math preparation required for the course. px x + py y = m, x ≥ 0, y ≥ 0 1. Solve maxx,y c ln(x) + d ln(y) subject to where c, d, px, py, and m are all strictly positive constants. (Hint: There are two ways to solve this constrained maximization problem. If you have taken multivariable calculus, you can use the Lagrangian method. If not, you can use the constraint to substitute out x in terms of y, and then solve a single‐variable unconstrained optimization problem.) 2. Solve maxx,y x1/2 + y subject to p x + y = m, x ≥ 0, y ≥ 0 where c, d, p, and m are all strictly positive constants. (The same hint as in Problem 1 applies here, as well. But make sure you check for corner solutions!) 3. Suppose you gamble on the outcome of a fair coin flip. If the coin comes up heads, you get $2, and if it comes up tails, you lose $1. What is the expected value of your winnings from this gamble? What if you flip the coin twice? (If you know how to calculate variance, calculate the variance of both of these gambles. If not, don’t worry…you will learn how to do so during the course.) ...
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