Answer to Question #45682 in Microeconomics for mohammed

Question

The Blair Company’s three assembly plants are located in California, Georgia and New Jersey. Previously, the company purchased a major subassembly, which becomes part of the final product, from an outside firm. Blair has decided to manufacture the subassemblies within the company and must now consider whether to rent one centrally located facility (e.g., in Missouri, where all subassemblies would be manufactured) or to rent three separate facilities, each located near one of the assembly plants, where each facility would manufacture only the subassemblies needed for the nearby assembly plant. A single, centrally located facility, with a production capacity of 18,000 units per year, would have fixed costs of $900,000 per year and a variable cost of $250 per unit. Three separate decentralised facilities, with production capacities of 8,000, 6,000 and 4,000 units per year, would have fixed costs of $475,000, $425,000 and $400,000, respectively, and variable costs per unit of only $225 per unit, owing primarily to the reduction in shipping costs. The current production rates at the three assembly plants are 6,000, 4,500 and 3,000 units, respectively.
a. Assuming that the current production rates are maintained at the three assembly plants, which alternative should management select? Justify your answers.
[8 marks]
b. If demand for the final product were to increase to production capacity, which alternative would be more attractive? Why?

Answer 1

Single: Q = 18,000 units per year, FC = $900,000 per year, AVC = $250 per unit.
Three separate: Q1 = 8,000, Q2 = 6,000 and Q3 = 4,000 units per year, FC1 = $475,000, FC2 = $425,000 and FC3 = $400,000, AVC = $225 per unit.
The current production rates at the three assembly plants are 6,000, 4,500 and 3,000 units, respectively.
a. Assuming that the current production rates are maintained at the three assembly plants:
single plant will have total costs TC = FC + AVC*Q = 900,000 + 250*(6,000+4,500+3,000) = $4,275,000.
three plants will have total costs TC = (475,000+225*6000) + (425,000+225*4500) + (400,000+225*3000) = $4,337,500
So, management should select the first alternative.
b. If demand for the final product were to increase to production capacity,
single plant will have total costs TC = FC + AVC*Q = 900,000 + 250*18,000 = $5,400,000.
three plants will have total costs TC = (475,000+225*8000) + (425,000+225*6000) + (400,000+225*4000) = $5,350,000
So, in this case the second alternative would be more attractive.