You are a bidder in an independent private values auction, and you value the object at $4,000. Each bidder perceives that valuations are uniformly distributed between $1,500 and $9,000. Determine your optimal bidding strategy in a first-price, sealed-bid auction when the total number of bidders (including you) is:

a. 2 bidders $2,750

b. 10 bidders $3,750

c. 100 bidders $3,975

Explanation:

Calculation to determine what your optimal bidding strategy in a first-price, sealed-bid auction when the total number of bidders (including you) is:

Using this formula

Optimal bidding = Bidder's own valuation - (Bidder's own valuation - Lowest valuation) ÷ Number of bidders

Let plug in the formula

a) 2 bidders

Optimal bid = $4,000 - [($4,000 - $1,500) ÷ 2]

Optimal bid = $4,000 - ($2,500÷2)

Optimal bid = $4,000 - $1,250

Optimal bid = $2,750

b) 10 bidders

Optimal bid = $4,000 - ($4,000 - $1,500) ÷ 10

Optimal bid = $4,000 - ($2,500÷10)

Optimal bid = $4,000 -$250

Optimal bid =$3,750

c) 100 bidders

Optimal bid = $4,000 - ($4,000 - $1,500) ÷ 100

Optimal bid = $4,000 - ($2,500÷100)

Optimal bid = $4,000-$25

Optimal bid = $3,975

Therefore your optimal bidding strategy in a first-price, sealed-bid auction when the total number of bidders (including you) is:

a. 2 bidders $2,750

b. 10 bidders $3,750

c. 100 bidders $3,975

a manufacturer of printed circuit boards uses exponential smoothing with trend to forecast monthly demand of its product. at the end of december, the company wishes to forecast sales for january. the estimate of trend through november has been 200 additional boards sold per month. average sales have been around 1000 units per month. the demand for december was 1100 units. the company uses α = 0.20 and β = 0.10. make a forecast including trend for the month of january.