(2) We have studied auctions being run by sellers, but there are also auctions run by...

(2) We have studied auctions being run by sellers, but there are also auctions run by buyers. These are called reverse auctions or procurement auctions. Suppose that a company wants to buy one unit of a good. This company announces that they will run a second price procurement auction. The company will collect offers to sell one unit of the good from each of a group of firms and will buy the good from the firm that offers to sell it at the lowest price. This firm will be paid the second lowest offer. So for example if three firms, 1, 2 and 3, make offers of $1,000, $2,500 and $2,000, respectively, then the company will buy the good from firm 1 and will pay firm 1 a price of $2,000 for it. There are in fact three firms that are willing to sell the good. The cost of the good for firm i is ci . These costs are private information to the firm and they are independent. If firm i sells the good at price p then firm i makes a profit of p − ci . If firm i does not sell the good its profit is 0. The objective for each firm is to maximize its own profit. Each firm knows its own cost but not the costs of the other firms. You make decisions for firm 1. Your cost is $5,000. What offer should you submit and why?

Solutions

Expert Solution

In this case, if firm 1 is not selected, the profit is zero.

If firm 1 is selected, at price p, then it means that the next best price is at least p + 1 which will be paid to firm 1.

Now to get a profit, p+1 should be higher than 5000.

So let us have 2 scenarios.

Firm 1 quotes a price of 4999.

Firm 1 quotes a price of 5000.

In case of scenario 1, if firm 1 is selected, then the minimum price it will get is 5000. In that case, the profit will be zero. The firm is thus indifferent between pricing it at Rs. 4999 and not getting the contract. However, if the price quoted is below 4999, then it can get the contract at a price lower than its cost price of 5000 and end up making a loss. So the minimum quote to be done is 4999.

However, if the firm quotes 5000, it can either get or not get the contract. If it gets the contract, it will be paid at least 5001, if not then profit is zero.

So to ensure that there is some profit, the minimum price should be 5000.

But to maximize the profit, it pays for the firm to quote abnormally high numbers which will give them high profit or no profit. Thus it is better to go for 5001 and get an assured profit.

Rahul Sunny answered 5 months ago

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