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Quiz 7 Consider a decentralized supply chain consisting of one manufacturer (mfr

ID: 328727 • Letter: Q

Question

Quiz 7 Consider a decentralized supply chain consisting of one manufacturer (mfr) and one retailer. Mfr decides the wholesale price, w, and retailer decides the retail price, p. The demand is given by D-120-2*p. The mfr's production cost is $20 for each unit of product. From optimization analysis, we know for any given wholesale price w, the retailer's best response of retail price is given by p"-$30+0.5 *w. If the Mfr needs to choose from two potential wholesale prices: $20 and $30, which wholesale price is better for the Mfr?

Explanation / Answer

Relationship between demand and retailer price is given by

D = 120 - 2p

where D is demand and p is retailer price

Relationship between wholesaler price and retailer price is given by

p = 30 + 0.5 * w

where w is the wholesaler price

Production cost per unit for the manufacturer = $ 20

CASE 1

If the wholesaler chooses a price of $20

Retailer price, p = 30 + 0.5 w

p = 30 + 0.5*20

p = $40

When p = $40, demand, D = 120 - 2p

D = 120 - 2* 40

D = 40 units

Total profit = Total sales - Total revenue

= (Difference between selling price and production price) * Total number of units sold

= ( $20 - $ 20 ) * 40

= $0

CASE 2

If the wholesaler chooses a price of $30

Retailer price, p = 30 + 0.5 w

p = 30 + 0.5*30

p = $45

When p = $45, demand, D = 120 - 2p

D = 120 - 2* 45

D = 30 units

Total profit = Total sales - Total revenue

= (Difference between selling price and production price) * Total number of units sold

= ( $30 - $ 20 ) * 30

= $300

Hence from the net profits, we can see that the wholesale price of $30 would be better for the manufacturer