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					                                                                                 Econ 3070
                                                                               Prof. Barham
                                Problem Set 3 Questions
         (All book questions on this homework are from Edition 2)

Reminder:
Maximization question must be solved using method shown in class not
by using the tangency condition used in the text.


1. Ch5, problem 5.5 (show how you get the marginal utilities that are given in the question)

2. Aunt Joyce purchases two goods, perfume and lipstick. Her preferences are represented
   by the utility function
                                        U (P , L ) = PL ,
   where P denotes the ounces of perfume used and L denotes the quantity of lipsticks
   used. Let PP denote the price of perfume, PL denote the price of lipstick, and I denote
   Aunt Joyce’s income.

   a. Derive her demand for perfume. Your answer should be an equation that gives P as
      a function of PP , PL , and I.

   b. Derive her demand for lipstick. Your answer should be an equation that gives L as a
      function of PP , PL , and I.

   c. Is lipstick a normal good? Draw her demand curve for lipstick when I = 200. Label
      the demand curve D1. Draw her demand curve for lipstick when I = 300 and label
      this demand curve D2.

   d. What can be said about her cross-price elasticity of demand of perfume with respect
      to the price of lipstick?

3. Uncle Bob purchases two goods, tweed sport coats and bow ties. His preferences are
   represented by the utility function
                                     U (B, C ) = B 0.25 C 0.75 ,
   where B denotes the number of bow ties purchased and C denotes the number of sport
   coats purchased. Let $25 be the price of bow ties and $60 be the price of sport coats.
   And finally, let I denote Uncle Bob’s income.

   a. Derive Uncle Bob’s Engel curve for bow ties. Your answer should be an equation
      that gives B as a function of I.

   b. Draw Uncle Bob’s Engel curve for bow ties on a graph with B on the horizontal axis
      and I on the vertical axis.
                                                                                 Econ 3070
                                                                               Prof. Barham
   c. Are bow ties a normal good? What can be said about Uncle Bob’s income elasticity
      of demand for bow ties?

4. Ch 5, problem 5.8
5. Ch 5, problem 5.10
6. Ch 5, problem 5.18

7. Suppose that the production function for lava lamps is given by
                                       Q = KL2 − L3 ,
   where Q is the number of lamps produced per year, K is the machine-hours of capital,
   and L is the man-hours of labor.

   Suppose K = 600.

   a. Draw a graph of the production function over the range L = 0 to L = 500, putting L
      on the horizontal axis and Q on the vertical axis. Over what range of L does the
      production function exhibit increasing marginal returns? Diminishing marginal
      returns? Diminishing total returns?

   b. Derive the equation for average product of labor and graph the average product of
      labor curve. At what level of labor does the average product curve reach its
      maximum?

   c. Derive the equation for marginal product of labor. On the same graph you drew for
      part b, sketch the graph of the marginal product of labor curve. At what level of
      labor does the marginal product curve appear to reach its maximum? At what level
      does the marginal product equal zero?

   d. Relate your answer to part c to your answer to part a.

8. Consider again the production function for lava lamps: Q = KL2 − L3 .

   a. Sketch a graph of the isoquants for this production function.

   b. Does this production function have an uneconomic region? Why or why not?

9. For each of the following production functions, graph a typical isoquant and determine
   whether the marginal rate of technical substitution of labor for capital ( MRTS L ,K ) is
   diminishing, constant, increasing, or none of these.

   a.   Q = LK , for Q=4

   b.   Q = L K , for Q=2

   c.   Q = L2 3 K 1 3 , for Q=8
                                        Econ 3070
                                      Prof. Barham
d.   Q = 3L + K , for Q=3

e.   Q = min{3L , K } , you chose Q

				
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