# UCLA STATS 100C - midterm1_practice_solution (4 pages)

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- School:
- University of California, Los Angeles
- Course:
- Stats 100c - Linear Models

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UCLA Economics 11 Professor Mazzocco PRACTICE MIDTERM ANSWER KEY NAME ID TA Part 1 Multiple Choices 1 Indifference curves a are non intersecting b are contour lines of a utility function c are negatively sloped d all of the above 2 For an individual who consumes only two goods X and Y the opportunity cost of consuming one more unit of X in terms of how much Y must be given up is reflected by a the individual s marginal rate of substitution b the market prices of X and Y c the slope of the individual s indifference curve d none of the above 3 The slope of the budget constraint line is a the ratio of the prices px py b the negative of the ratio of the prices px py c the ratio of income divided by price of y I py d none of the above 4 If an individual s indifference curves are convex his or her MRS will a diminish as X is substituted for Y b increase as X is substituted for Y c be undefined except in special cases d always depend only on the ratio of X to Y 5 If utility is given by U X Y Min X 3Y then the bundle 3 2 provides the same utility as the bundle a 1 3 b 2 3 c 4 1 d 4 2 6 Suppose that an individual has a constant MRS of shoes for sneakers of 3 4 that is he or she is always willing to give up 3 pairs of sneakers to get 4 pairs of shoes Then if sneakers and shoes are equally costly he or she will a buy only sneakers b buy only shoes c spend his or her income equally on sneakers and shoes d wear sneakers only 3 4 of the time 7 Suppose an individual s MRS of steak for beer is 2 1 That is at the current consumption choices he or she is willing to give up 2 beers to get an extra steak Suppose also that the price of a steak is 1 and a beer is 25 cents Then in order to increase utility the individual should a buy more steak and less beer b buy more beer and less steak c continue with current consumption plans 8 Suppose that at current consumption levels an individual s marginal utility of consuming an extra hot dog is 10 whereas the marginal utility of consuming an extra soft drink is 2 Then the MRS of soft drinks for hot dogs that is the number of hot dogs the individual is willing to give up to get one more soft drink is a 5 b 2 c 1 2 d 1 5 9 An increase in an individual s income without changing relative prices will a rotate the budget constraint about the X axis b shift the indifference curves outward c shift the budget constraint outward in a parallel way d rotate the budget constraint about the Y axis 10 If the price of X falls the budget constraint a shifts outward in a parallel fashion b shifts inward in a parallel fashion c rotates outward about the X intercept d rotates outward about the Y intercept Part 2 Exercises 1 David likes only peanut butter P and toast T and he always eats each toast with two ounces of peanut butter a Find David s demand for peanut butter and toast It is a case of perfect complements The utility function U T PB min 2T P represents David s preferences Indifference curves are L shaped with corners located on the line 2T P Since optimal consumption will always take place at the corner of an indifference curve demands can be found as a solution of the system of equation consisting of P 2T and the budget line ppP ptT I The solutions of this system are T I 2pp pt and P 2I 2pp pt b Find the indirect utility function and the expenditure function U min 2I 2pp pt 2I 2pp pt U 2I 2pp pt E U 2pp pt 2 c How much of each good will David consume in a week if he has 4 of income the price of peanut butter is 0 02 and the price of a toast is 0 06 Using the demands T 4 2 0 02 0 06 40 and P 2T 80 Utility is 80 d Suppose that the price of a toast rises to 0 11 How will his consumption change T 4 2 0 02 0 11 26 7 and P 2T 53 3 Utility is 53 3 e How much should David s income be to compensate for the rise in the price of the toast David must enjoy a utility of 80 to be back on his indifference curve This means that he must consume T 40 with the new prices Therefore Y must solve 40 Y 2 0 02 0 11 Therefore Y 6 2 Susan s utility function is U XY X 2Y She has a monthly income of I and the prices of the goods are PX and PY a Find Marginal Rate of Substitution MRS Y 1 X 2 b Find Susan s marshallian demand for X and Y X I 2Px Py 2Px Y I 2Px Py 2Py c How do changes in PY and I affect the demand for X What do these results tell us about the properties of this demand function X I 0 meaning that X is a normal good X Py 0 X and Y are gross substitutes since demand for X increases when the price of Y increases d Find Susan s Indirect Utility Function U I 2Px Py I 2Px Py 4PxPy I 2Px Py 2Px I 2Px Py Py

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