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Problem Set 1 - Problem Set#1 Name Econ326 Intermediate...

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Problem Set #1 Name: _____________________ Econ326 Intermediate Micro Student ID: _____________________ Instructor: Ginger Jin Section No. _____________________ Due Date: February 14, 2011 TA Name: _____________________ =============================================================== 1 1. Sally consumes two goods, X and Y. Her utility function is given by the expression The current market price for X is $10, while the market price for Y is $5. Sally's current income is $600. a. Sketch two indifference curves for Sally in her consumption of X and Y so that one curve represents U=240000 and the other curve represents U=480000. Mark two points on each curve, write down the precise numbers of X and Y for each point. (Note: you can choose whatever unit of X and Y that you think are most appropriate in the following graph.) b. Calculate the marginal rate of substitution for each of the four points you have marked on the above graph. MRS = MUx /MUy = Y 2 /2XY= Y/2X
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Problem Set #1 Name: _____________________ Econ326 Intermediate Micro Student ID: _____________________ Instructor: Ginger Jin Section No. _____________________ Due Date: February 14, 2011 TA Name: _____________________ =============================================================== 2 ! # $%& '( )*+,,-.- ,(( -( /0+-,111 '(( ,( ,,+.-'0/ -1 1( ,( '/ c. Write the expression for Sally's budget constraint. Graph the budget constraint and determine its slope. Sally’s Budget constraint is given by 10X + 5Y = 600 and its slope is -2.This can be seen by rewriting the budget constraint as Y= 120-2X ( Form : y= m*x+c, where ‘m’ is slope of the line) d. Determine the X,Y combination which maximizes Sally's utility, given her budget constraint. Show her optimum point and its corresponding indifference curve on the graph. Compute the utility level at this optimum point. Note that this utility function belongs to the category Cobb – Douglas Utility functions. For a utility function of the general form U = A X ! Y " , we can write the optimal demands (X*,Y*) as follows: X* = [ ! M] / [( ! + " )P x ] Y* = [ " M] / [( ! + " )P y ] Where M : Income, Px : Price of good X; Py : Price of good Y For our problem, ! = 1 and " =2; M= 600;Px=10;Py=5. Therefore, X* = 20 ; Y*= 80. The utility corresponding to the optimum point is U = 3*20*1600 = 96000
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Problem Set #1 Name: _____________________ Econ326 Intermediate Micro Student ID: _____________________ Instructor: Ginger Jin Section No. _____________________ Due Date: February 14, 2011 TA Name: _____________________ =============================================================== 3 e. Suppose Sally’s utility function changes to U=2lnX + 4lnY. Recalculate the optimal point that Sally will choose (given the same budget constraint). Is this answer different from the solution in part d? Why? If we recalculate the (X*,Y*) using 1. MRS = Px /Py ie. Y/2X = 2 2. Budget constraint : 10x + 5Y = 600 We obtain (X*,Y*) = (20,80) This is the same as in part d because this utility function is just a MONOTONIC TRANSFORMATION of the previous utility function and therefore will result in the same optimal consumption bundle .
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Problem Set #1 Name: _____________________ Econ326 Intermediate Micro Student ID: _____________________ Instructor: Ginger Jin Section No. _____________________ Due Date: February 14, 2011 TA Name: _____________________ =============================================================== 4 2. Antonio buys five new college textbooks during his first year at school at a cost of $80 each. Used books cost only $50 each. When the bookstore announces that there will be a 10 percent increase in the price of new books and a 5 percent increase in the price of used books, Antonio’s father offers him $40 extra.
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