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
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