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\(, or 25 percent of total sales. In an effort to reduce costs, CPT now uses an online procurement procedure that is best described as a first-price, sealed-bid auction. The bidders in theseauctions utilize the steel for a wide variety of purposes, ranging from art to skyscrapers. This suggests that bidders value the steel independently, although it is perceived that bidder valuations are evenly distributed between \)8,000 and \(25,000. You are the purchasing manager at CPTand are bidding on three tons of six-inch hot-rolled channel steel against four other bidders. Your company values the three tons of channel steel at \)16,000. What is your optimal bid?

Short answer

The optimal bid is $14,400.

Step-by-step solution

Introduction

In order to reduce costs, CPT Inc. has implemented a first-price, sealed-bid auction online system in which all bidders can observe each other's bids and the auction price of the products.

However, the fact that a wide variety of bidders have different uses for steel indicates that it is possible to have independent private values in which, depending on the use that each bidder will give the product, the price that each one is willing to pay. Despite this, if the bidders do not have this information, each one only knows their valuation; the risk of obtaining a lower price in the auction can be mitigated.

Finding the optical bidding strategy:

The optimal bidding strategy for the first-price, sealed-bid auction with an independent appraisal can be determined with the following equation:

$\mathrm{b}=\mathrm{v}-\frac{\mathrm{v}-\mathrm{L}}{\mathrm{n}}$

Where,

: is the optimal bid.

v: own actual valuation of the item.

L : is the lowest possible valuation of other bidders.

: is the total number of bidders.

Finding the optimal bid for three tons of channel steel

Knowing that apart from our offer there will be 4 more bidders. So, it can be said that$n=5,$ while our maximum valuation for the product will be determined as$v=$ 16,000$ and the minimum valuation of the other bidders will be determined by L= 8,000$. With this information we can substitute in the previous equation to determine b.

$\begin{array}{c}\text{b}=\$16,000-\frac{\$16,000-\$8,000}{5}\\ \text{b}=\$16,000-\$1,600\\ \text{b}=\$14,400\end{array}$

Thus, the optimal bid for the three tons of channel steel is $14,400.