Question

CPT Inc. is a local manufacturer of conveyor systems. Last year, CPT sold over $2 million worth of conveyor systems that netted the company $100,000 in profits. Raw materials and labor are CPT’s biggest expenses. Spending on structural steel alone amounted to over $500,000, or 25 percent of total sales. In an effort to reduce costs, CPT now uses an online procurement procedure that is best described as a first-price, sealed-bid auction. The bidders in these auctions utilize the steel for a wide variety of purposes, ranging from art to skyscrapers. This suggests that bidders value the steel independently, although it is perceived that bidder valuations are evenly distributed between $8,000 and $22,000.

You are the purchasing manager at CPT and are bidding on three tons of six-inch hot-rolled channel steel against 5 other bidders. Your company values the three tons of channel steel at $11,000. What is your optimal bid?

Answer 1

Answer:-

The first-price, sealed-bid auction with independent private valuation has the optimal bidding strategy to bid less than her evaluation of the steel. With n number of bidders, assuming the evaluations to be uniformly distributed, the optimal bid by a player is given by:

where

V = Bidder's own valuation

n = number of bidders

L = Lowest valuation

The lowest valuation is $8,000 and the number of bidders is 5. Company's own valuation for a six-inch hot-rolled channel steel is $11,000. Given this information, the optimal bid is:

= 11000 – 11000 – 8000 / 6

    = 11000 – 500

   = 10500

Hence the optimal bid by CPT in the first-price, sealed-bid auction with 6 bidders is $10,500