Either you say yes Or you say no and explain the differences between the

# Either you say yes or you say no and explain the

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Either you say “yes”, Or you say “no” and explain the difference(s) between the contexts. p D ( p ) Pictures that have boxes representing revenue/profit underneath the demand curve are common in market segmentation and volume discounting. Each box indicates some more revenue.
Page 18 utdallas.edu /~metin Calculating Differentiated Prices by Eliminating Arbitrage Arbitrage happens when a lower priced product i is transport ed to be sold as a higher priced product j transportation cost a ij upgrade d to be sold as a higher priced product j upgrade cost a ij stock ed to be sold as a higher priced product j inventory holding cost a ij Arbitrage can be eliminated with constraints 𝑝 ? ≤ 𝑝 ? + 𝑎 ?? and 𝑝 ? ≤ 𝑝 ? + 𝑎 ?? on the price decision variables. Constraints are called arbitrage elimination constraint ”. The constraint makes the cost of using arbitrage p i + a ij higher than the price p i . i j 𝑎 ?? 𝑎 ??
Page 19 utdallas.edu /~metin Motivating Example of Chips Intel chips are sold both in US (country 1) and in Brazil (country 2). The demand functions are given by p p b a p d p p b a p d 10000 48600 ) ( and 100000 508000 ) ( 2 2 2 1 1 1 Since the constraint is not satisfied, an arbitrageur can buy chips in Brazil and transport them to US to sell them in US. We need to jointly optimize prices in US and Brazil to eliminate arbitrage rather than separately as we have done above. The transportation cost per chip is \$0.08 between these countries. With the constant slope demand curves (lines), the revenue maximizing prices are given as 21 0 2 0 1 2 2 0 2 1 1 0 1 51 . 2 54 . 2 but 43 . 2 2 and 54 . 2 2 a p p b a p b a p
Page 20 utdallas.edu /~metin Quadratic Program Formulation to Eliminate Arbitrage When we have linear demands d i ( p i ), the profit (p i -c i ) d i ( p ) is a quadratic function (it is a polynomial of degree 2). Summing these profits over N regions, we still have a quadratic objective for the joint optimization problem: N i p N j i a p p p d c p i ij i j N i i i i i p p N 1 for 0 1 for subject to ) ( ) ( max 1 ... 1 This is a quadratic programming problem and it can be solved efficiently with algorithms similar to those used to solve linear programming problems.
Page 21 utdallas.edu /~metin Solving Quadratic Program for N =2 When there are two regions (US and Brazil), N=2 and we can solve the quadratic program without a software. 0 , and subject to ) ( ) ( max 2 1 12 1 2 21 2 1 2 2 2 2 1 1 1 1 , 2 1 p p a p p a p p p b a p p b a p p p If the separately found prices satisfy the arbitrage eliminating constraints, they are optimal and we stop. Else let the region with higher price be 1 and the other be 2, we have 12 0 1 0 2 21 0 2 0 1 and a p p a p p In the optimal solution, the violated constraint must be satisfied as an equality, so we can let next find shall that we some for and 2 21 1 p p p a p p