Unit 8 homework key

Ch. 11

13.   Wholesale price of milk represents the marginal cost for retailers, who sell to consumers. In Figure 11.12, suppose prices at the wholesale level fall 30.3% from $2.00 to $1.394 per gallon, or $0.606 per gallon. That is, for retailers, marginal cost shifts from MC to MC¢. If the original retail price were $3.00 per gallon, a 30.3% price decrease would mean the new price of $2.09, a drop of $0.91 per gallon. However, the negative slope of the demand curve results in a price decrease that is less than $0.91. The new retail price, for the given demand curve, is $2.50. In other words, price at the retail level may not fall by the same percentage as the wholesale level due to the slope of the demand curve.

CH11_Q13_F01

Figure 11.12

 

42.   a.    To solve for the expansion path, set the ratio of the marginal products equal to the ratio of the input prices (see Appendix 7C)

              This gives the equation for the expansion path . See Figure 11.18.

b.   Substituting the expansion path into the production function yields L = 2Q, and K = 0.5Q.
Thus C(Q) = wL + rK = w2Q + r 0.5Q = 1(2)Q + 4(0.5)Q = 4Q.

c.    Long-run profit-maximizing output is where LMC = MR.

Q* = 48

p* = 52

d.   To solve, plug the capital labor ratio K = 0.25L and the output level (48) into the production function.

                                                                    L* = 96

                                                                    K* = 0.2596 = 24

See Figure 11.18.

CH11_Q42d_F01

Figure 11.18

 

Ch. 12

2.     To get the profit-maximizing output and price levels, set marginal cost equal to marginal revenue in each market and solve.

                                                       

        Because the reseller can transport goods from Market 1 to Market 2 for $4 per unit, the reseller could underprice the monopolist in Market 2 by $1. This forces the monopolist to reduce the market price to $34 per unit. Output increases to 39 units, and revenue increases to $1326 from $1312.50, but because of the additional output, costs increase by $15, and profits fall by $1.50.

 

8.     By using coupons, firms restrict discounts to those consumers willing to take the time required to
clip the coupons and bring them to the store. Those consumers with more inelastic demand or less information (i.e., they did not know about the coupon) will not clip the coupon and will pay the higher price. This strategy allows the firm to segment the market, and extract more consumer surplus from less-informed and less price-sensitive consumers.

31.   The price charged in Canada is $15 * (1 + 33%) = 20. Using Formula (12.2), we can get the
elasticity of Canadian consumer is -1.05. The price charged in Japan is $25, hence the elasticity
is -25/24 = -1.04.

 

37.   Set marginal revenue in each market equal to marginal cost to determine the quantities. Plug the quantities into the demand functions to determine prices.

MR1 = 100 – 2Q1 = 30 = MC

MR2 = 120 – 4Q2 = 30 = MC

   Q1 = 35; p1 = 65

   Q2 = 22.5; p2 = 75

 

43.   Assume one unit of advertising costs $1. The profit function is

p = (100 – Q + A1/2 )Q – 10Q – A

The resulting first-order conditions are

                                                p/A = (Q/2)A–1/2 – 1 = 0

                                               p/Q = 100 – 2Q + A1/2 – 10 = 0

                                                                  A* = 900

                                                                  Q* = 60

                                                                  p* = 70