5. Henry Shortchap is the only blacksmith in the small village of Chestnut Tree.

Question

5. Henry Shortchap is the only blacksmith in the small village of Chestnut Tree. The village is composed of twenty-one households evenly distributed one-tenth of a mile apart along the main street of the town. Each such household uses at most one unit of smithing services per month. In addition, each household incurs a there-and-back-again transport cost of $0.50 for every tenth of a mile it lives from Shortchap’s smithery. The reservation price of each household for such services is $10. Henry’s cost of providing smithing services is $2 per unit. However, he can operate only one shop at most.

A). Where should Henry locate his shop and what price should he charge? B). Suppose instead that Henry could operate a mobile smithy that allowed him to offer his services at his customers’ homes. However, it would cost him$0.75 there-and-back-again transport costs for every tenth of a mile he has to move his smithy. Should he switch to this mobile service?

Explanation / Answer

Given,

Village has 21 Houses

Transportation cost of $0.50

Total reservation price = $210

Smithing cost = $2

Condition – He can only operate 1 shop at most.

He should charge a price of $ 212.50

As for very move the transportation cost increase by $0.75 hence it is advisable not to switch his mobile service.

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