Question

A firm plans to begin production of a new small appliance. The manager must decide whether to purchase the motors for the appliance from a vendor at $8 each or to produce them in-house. Either of two processes could be used for in-house production; Process A would have an annual fixed cost of $165,000 and a variable cost of $5 per unit, and Process B would have an annual fixed cost of $190,000 and a variable cost of $4 per unit. Determine the range of annual volume for which each of the alternatives would be best. (Round your first answer to the nearest whole number. Include the indifference value itself in this answer.)

Answer 1

Fixed Cost:

Process A = $165,000

Process B = $190,000

VC per unit:

Process A = $5

Process B = $4

TC = FC + VC*Q

Total cost function for Process A

TC(A) = 165,000 + 5Q

Total cost function for Process B

TC(B) = 190,000 + 4Q

We equate the two function

165,000 + 5Q = 190,000 + 4Q

5Q - 4Q = 190,000 - 165,000

Q = 25,000

25,000 units is the indifference level of production.

As process A has lower fixed cost, it is better process if the production volume is lower than 25,000 units. For more than 25,000 units, process B is better.

Purchase from vendor option is better if the production volume is less than 47,500 units [$190,000/$8-$4].