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EC 340: Homework Set #1 ECO340

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Question;EC 340: Homework Set #1;Due Date: Sept. 22, 2014;Problem #1;Consider the following demand function;Q =A?BP.;Find the price elasticity of demand. Illustrate how the;elasticity changes as the price changes.;Problem #2;Give an example of a demand function characterized by a;constant price elasticity equal to 5.;Problem #3;Consider the set, X, of pairs of (a, b), where a and b;are integers not smaller than 0 and not bigger than;9. Define 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 #4;Consider the following utility function;U (x 1, x 2) = x 1;x 2?12.;Which of the following functions represents the same;preferences as the above utility function. Justify your;answer.;a) V (x1, x2) =? (x1x2)?1 b) V (x1, x2) =x1 +x2;+4;c) V (x1, x2) =x1x2;2 d) V (x1, x2) =e;x 1x 2?167;Problem #5;Imagine that preferences of a given individual are;represented with;U (x 1, x 2) =x?;1 x 1??;2 +5.;Assume that the prices of the two goods consumed by this;individual are given by p1 and p2. 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 with;U (x 1, x 2) =x 1 + x 2.;Assume that the prices of the two goods consumed by this;individual are given by p1 and p2. Normalize the;price of the first good to 1, i.e., set p1 =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.

 

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