The Brain Bucket Company (BBC) produces helmets for winter sports. It has production facilities in Toronto and Winnipeg. The production function for the Toronto facility is Q(T) = √L(T) , (1) where L(T) is the quantity of labour hired in Toronto. The production function for the Winnipeg facility is Q(W) = √L(W) , (2) where L(W) is the quantity of labour hired in Winnipeg. The wage rate in Winnipeg is one and the wage rate in Toronto is two. Answer the following: (a) If BBC wishes to produce Q helmets at the lowest possible cost, how should it distribute production between the two cities? Use your answer to find a function showing the cost of producing Q helmets. (b) Suppose the production function for the Toronto facility is given by Q(T) = 2L(T) instead, while the production function for the Winnipeg facility remains as above. What is the cost of producing Q helmets? How should output be allocated between the two cities? Are there any situations in this case where only one facility would be used? Explain.
The Brain Bucket Company (BBC) produces helmets for winter sports. It has
production facilities in Toronto and Winnipeg. The production function for the Toronto facility is
Q(T) = √L(T) , (1)
where L(T) is the quantity of labour hired in Toronto.
The production function for the Winnipeg facility is
Q(W) = √L(W) , (2)
where L(W) is the quantity of labour hired in Winnipeg. The wage rate in Winnipeg is one and the wage rate in Toronto is two. Answer the following:
(a) If BBC wishes to produce Q helmets at the lowest possible cost, how should it distribute production between the two cities? Use your answer to find a function showing the cost of producing Q helmets.
(b) Suppose the production function for the Toronto facility is given by Q(T) = 2L(T)
instead, while the production function for the Winnipeg facility remains as
above. What is the cost of producing Q helmets? How should output be
allocated between the two cities? Are there any situations in this case where only one facility would be used? Explain.
Step by step
Solved in 5 steps with 26 images
