Question

Texts: Suppose that you are a manufacturer that uses parts that can be made in-house or bought from a foreign supplier upstream. Denote by 𝑞𝐼 the quantity manufactured in-house, by 𝑞𝐹 the quantity purchased from the foreign supplier, and by 𝑞 = 𝑞𝐼 + 𝑞𝐹 the total quantity. The cost of manufacturing in-house is 𝑐𝐼(𝑞𝐼) = 15𝑞𝐼 while the cost of purchasing from the foreign supplier is 𝑐𝐹(𝑞𝐹) = 116(𝑞𝐹)². a. From which option will you initially source from? Why? b. How many units will you acquire before switching suppliers? c. What is the minimum cost 𝑐(𝑞) of acquiring 𝑞 units for any arbitrary quantity 𝑞? 2. (10 points) A specific tariff is a tax placed on each unit of a good purchased from abroad. For example, if a specific tariff of $4 is placed on each kilogram of aluminum imported from Canada, then the cost of importing each aluminum from Canada is the original cost plus the $4 tax per unit imported. Consider the suppliers and costs from Question 1 but suppose that a specific tariff of $4 per unit is imposed on each unit imported from the foreign supplier. a. From which option will you initially source from? Why? b. How many units will you acquire before switching suppliers? c. What is the minimum cost 𝑐(𝑞) of acquiring 𝑞 units for any arbitrary quantity 𝑞? d. How do these costs compare to your answer to Question 1(c)? e. What does your answer to part (d) suggest regarding how tariffs affect domestic businesses with international supply chains?

Texts:

Suppose that you are a manufacturer that uses parts that can be made in-house or bought from a foreign supplier upstream. Denote by 𝑞𝐼 the quantity manufactured in-house, by 𝑞𝐹 the quantity purchased from the foreign supplier, and by 𝑞 = 𝑞𝐼 + 𝑞𝐹 the total quantity. The cost of manufacturing in-house is 𝑐𝐼(𝑞𝐼) = 15𝑞𝐼 while the cost of purchasing from the foreign supplier is 𝑐𝐹(𝑞𝐹) = 116(𝑞𝐹)².

2. (10 points) A specific tariff is a tax placed on each unit of a good purchased from abroad. For example, if a specific tariff of $4 is placed on each kilogram of aluminum imported from Canada, then the cost of importing each aluminum from Canada is the original cost plus the $4 tax per unit imported. Consider the suppliers and costs from Question 1 but suppose that a specific tariff of $4 per unit is imposed on each unit imported from the foreign supplier.

a. From which option will you initially source from? Why?
b. How many units will you acquire before switching suppliers?
c. What is the minimum cost 𝑐(𝑞) of acquiring 𝑞 units for any arbitrary quantity 𝑞?
d. How do these costs compare to your answer to Question 1(c)?
e. What does your answer to part (d) suggest regarding how tariffs affect domestic businesses with international supply chains?

Added by Elena H.

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