percent would receive the more favorable 4.5 percent interest rate (as
would all the other winning bidders). In this respect, the uniform-price
auction is analogous to a second-price auction.
(i) How does the uniform price rule affect bidding behavior? If a bidder
requires a 4.2 percent interest rate, what interest rate will she bid?
(ii) Why might there be greater bidder participation under the uniform
price rule? How might the uniform price rule affect the average
interest rate the government pays (relative to the pre-1990s price rule)?Spreadsheet Problem
S1. The histogram of best (i.e., lowest) competing bids in Table B of
Problem 11 mirrors closely a normal distribution with a mean of 60 and
a standard deviation of 30. Create a spreadsheet modeled on the sample
given to find the firm’s optimal bid markup. In the sample spreadsheet,
note that a bid at a 60 percent markup has a .5 chance of winning and
implies an expected profit of (.5)(60) 30.
a. First, experiment with other markups in your search for maximum
expected profit.
b. Use your spreadsheet’s optimizer to find the optimal markup.
c. Find the firm’s optimal markups if the BCB distribution has a (less
favorable) mean of 40 or if it has a (more favorable) mean of 80.ABCDE F GH
1
2 OPTIMAL STRATEGY WHEN BCB
3 IS NORMALLY DISTRIBUTED
4
5 Mean 60 Markup Pr(win) E(Profit)
6 St Dev 30
7 20 0.9088 18.176
8 40 0.7475 29.900
9 60 0.5000 30.000
10 80 0.2525 20.199
11
12(Hint:Cells F7 to F10 should be computed utilizing the normal distri-
bution function included with your spreadsheet. This function typi-
cally takes the form:
Normal(value, mean, standard deviation).
Thus, you can simply change the value of the mean in cell C5 to 40 or
80 and reoptimize the problem.)704 Chapter 16 Auctions and Competitive Biddingc16AuctionsandCompetitiveBidding.qxd 9/26/11 1:09 PM Page 704