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Homework answers / question archive / Managerial Economics (ARE) 100A University of California, Davis Spring Quarter, 2008 Homework 2: Due Friday April 11, 2008 1)Draw the indifference curves for the following individuals’ preferences for two goods: hamburgers and beer

Managerial Economics (ARE) 100A University of California, Davis Spring Quarter, 2008 Homework 2: Due Friday April 11, 2008 1)Draw the indifference curves for the following individuals’ preferences for two goods: hamburgers and beer

Economics

Managerial Economics (ARE) 100A

University of California, Davis

Spring Quarter, 2008

Homework 2: Due Friday April 11, 2008

1)Draw the indifference curves for the following individuals’ preferences for two goods: hamburgers and beer.

(a)        Al likes beer but hates hamburgers.  He always prefers more beer no matter how many hamburgers he has.

 

(b)        Betty is indifferent between bundles of either three beers or two hamburgers.  Her preferences do not change as she consumes any more of either food.

 

(c)        Chris eats one hamburger and washes it down with one beer.  He will not consume an additional unit of one item without an additional unit of the other.

 

 

 

 

am

H

burgers

Beer

U

1

U

2

U

3

1

2

3

4

5

6

7

8

9

6

9

3

 

burgers

am

H

Beer

U

1

U

2

U

3

1

2

3

2

1

3

 

 

 

 

Hamburgers

Beer

U

3

U

2

U

1

 

Problem 2:

  1. On two graphs (top and bottom), graph (i) the total utility function and (ii) the marginal utility function for the following.

 

    1. TUX = 10,000X – 0.2X2
    2. TUX = 4X1/2
    3. TUX = 8X

 

  1. Do these utility functions exhibit diminishing MUX?  If not, briefly explain what the given utility function implies about consumer tastes and preferences for X.
  2. For each utility function, find the satiation values of X and TU, that is, the point where TU is maximized.

 

 

 

 

Problem 3:

3. For each of the parts below a utility function, U(X,Y) is given.  For each of the utility functions you are to answer questions (i) – (iv).  You must show your work.

 

    1. Is the assumption more is better satisfied for each of the goods?
    2. Is there diminishing MUX?  Is there diminishing MUY?
    3. Is there diminishing MRSXY?
    4. Graph the indifference curves (place X on the X-axis, etc., and do not worry about scale.)

 

 

(b)        U(X,Y) = X1/6 + Y5/6.

 

(c)        U(X,Y) = 6X1/2 + 3Y.

 

 

(d)        U(X,Y) = X—1/6Y5/6.

 

 

Problem 4

4. Suppose the price of frozen yogurt is $2 per cup, the price of ice cream is $1.50 per cone, and your dessert budget is $12 per week.

(a)        What is the relative price of ice cream to yogurt?

 

  1. Draw the budget line for these two goods, placing ice cream on the X-axis and yogurt on the Yaxis.  Label this budget line BLA.

 

  1. Suppose the price of ice cream increases to $3 per cup.  What is the new relative price of ice cream to yogurt?

 

  1. Draw the new budget line for these two goods, placing ice cream on the X-axis and yogurt on the Y-axis.  Label this budget line BLB.

 

  1. Now, assuming the prices in part (a), suppose your income increases to $18. Draw the new budget line for these two goods, placing ice cream on the X-axis and yogurt on the Y-axis.  Label this budget line BLC.

Problem 5

5. Assume that an individual consumes only two commodities, pears (X) and chestnuts (Y).  This individual chose a bundle with 6 pears and 2 chestnuts over a bundle with 4 pears and 7 chestnuts.  Then she chose a bundle with 2 pears and 8 chestnuts over a bundle with 6 pears and 2 chestnuts.

 

Are these choices consistent with our assumptions about consumer preferences?  (To answer this, you

Problem 7

A consumer purchases two goods, food (F) and clothing (C).  Her utility function is given by:

 

            U(F, C) = F2/5C3/5.

 

The price of F is given as 50, the price of C is given as 20, and income is given as $40,000.  When graphing, place Food on the X-axis and Clothing in the Y-axis.

 

  1. Are there diminishing MUC and diminishing MUF.  You must show this using the MUC equation and clearly explain (that is, do not simply plug values of C and F into the utility function to
  2. Does MRSFC diminish?

 

 

 

(d) Calculate the numeric values of MUF and MUC at optimal solution.

 

 

 

 

Multiple Choice:

  1. An upward sloping indifference curve defined over two goods violates which of the following assumptions from the theory of consumer behavior? a. transitivity.
    1. preferences are complete.
    2. more is preferred to less.
    3. all of the above.
    4. none of the abov

 

  1. If X and Y are perfect substitutes, which of the following assumptions about indifference curves is not satisfied? 
    1. completeness.
    2. transitivity.
    3. more is preferred to less.
    4. diminishing MRS.
    5. none of the above (All of the above assumptions are satisfied).

 

  1. Which of the following statements concerning utility as a measure for well being are false?
    1. It is possible to determine which of two individuals is made happier by consuming a particular market basket.
    2. There is generally a positive relationship between income and utility.
    3. Utility is an abstract representation of an individual’s degree of happiness.
    4. Cross country studies suggest that citizens in wealthier countries are happier than citizens in poorer countries.

 

  1. Pencils sell for 10 cents and pens sell for 50 cents. Suppose Jack, whose preferences satisfy all of the usual assumptions, buys 5 pens and one pencil each semester.  With this consumption bundle, his MRS of pencils for pens is 3.  Which of the following is true?
    1. Jack could increase his utility by buying more pens and fewer pencils.
    2. Jack could increase his utility by buying more pencils and more pens.
    3. Jack could increase his utility by buying fewer pencils and fewer pens.
    4. Jack is at a corner solution and is maximizing his utility.
    5. Jack could increase his utility by buying more pencils and fewer pens.

 

  1. Denise is shopping for lobsters and eclairs.  When she faces budget line b1, she chooses market basket A over market basket B.  When she faces budget line b2, she chooses basket B over basket C.  Which assumption of consumer theory helps us determine Denise’s preference ordering over basket A and basket C? a. completeness
    1. more is better than less
    2. transitivity
    3. convexity

 

  1. If a consumer must spend her entire income on some combination of two commodities and chooses to spend it all on just one of the commodities then: a. the other commodity is an economic bad.
    1. the other commodity must have zero marginal utility.
    2. the other commodity generates less utility per dollar spent on the good.
    3. the two commodities must be perfect substitutes.

 

  1. Marginal utility is
    1. the slope of the total utility function.
    2. the slope of a ray from the origin to the total utility function.
    3. always less than average utility.
    4. always greater than average utility.

 

  1. The principle of diminishing marginal utility implies
    1. indifference curves are concave.
    2. indifference curves are convex.
    3. indifference curves are straight lines.
    4. as your consumption level increases, the marginal utility received from consumption of an additional unit increases.

 

  1. Identify the truthfulness of the following statements.

 

      1. Diminishing marginal utility and increasing total utility are incompatible with each other.
      2. When marginal utility is negative, total utility is decreasing.

 

    1. Both I and II are true.
    2. Both I and II are false.
    3. I is true; II is false.
    4. I is false; II is true.

 

  1. Which of the following statements is true?

 

    1. Because total utility is constant along an indifference curve, the marginal rate of substitution is also constant.
    2. If an indifference curve is convex, the marginal rate of substitution varies along the curve.
    3. The slope of an indifference curve measures the consumer’s marginal rate of substitution.
    4. Both (b) and (c) are true. 

 

 

 

 

 

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