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##### EC 340 Homework Set 1 Assignment

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**Question**

Question;Problem #1Consider the following demand functionQ = A? BP.Find the price elasticity of demand. Illustrate how the elasticity changes as the price changes.Problem #2Give an example of a demand function characterized by a constant price elasticity equal to 5.Problem #3Consider the set, X, of pairs of (a, b), where a and b are integers not smaller than 0 and not bigger than9. De?ne the preferences over elements of X as?????a, b??? c, d??? { a > c.a =c b?d????Can you think of a utility function that represents?.Problem #4Consider the following utility functionU (x 1, x 2) = x 1x 2? 12.Which of the following functions represents the same preferences as the above utility function. Justify youranswer.a) V (x 1, x 2) =? (x 1x 2)? 1 b) V (x 1, x 2) = x 1 + x 2 + 4c) V (x 1, x 2) = x 1x 22d) V (x1, x2) = ex 1x 2? 167Problem #5Imagine that preferences of a given individual are represented withU (x 1, x 2) = x? x 1?? + 5.1 2Assume that the prices of the two goods consumed by this individual are given by p 1 and p 2. Furthermore,assume that the individual earns income I.i) Derive the demands of the individual for the two goods.ii) Verify that the demands happen to be homogenous of degree 0.iii) Plot the two demands as a function of income.Problem #6Imagine that preferences of a given individual are represented withU (x 1, x 2) = x 1 + x 2.Assume that the prices of the two goods consumed by this individual are given by p 1 and p 2. Normalize theprice of the?rst good to 1, i.e., set p 1 = 1. Furthermore, assume that the individual earns income I.,i) Derive the demands of the individual for the two goods.ii) Plot the two demands as a function of income.

Paper#56390 | Written in 18-Jul-2015

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