Question

conceptual overview: compare the costs of in - house production versus outsourcing. the fixed costs of in - house production (fc) and the cost per unit produced (vc1) versus the cost per unit if outsourced determines the break - even point for deciding between the two. when the graph first loads, the parameter values represent a decision for which the fixed costs are $250,000 (the intercept of the blue in - house line is fc = 2.5) and the cost per unit produced in - house is $20 (vc1 = 20 is the slope of the blue in - house line). the red line for outsourced production has an intercept of $0 because there are no fixed costs; its slope represents a unit price of $35 (vc2 = 35). the point at which the lines cross is the break - even point of 16,670 units. for quantities above the break - even point, in - house production is less expensive but for quantities below that point, outsourcing has the lower cost. drag vertically on the right - side of the to change the unit cost for either in - house or outsourcing production. the graph enforces that the unit cost of outsourcing is always greater than the unit cost of in - house production. drag on the left side to change the fixed cost for in - house production. observe how the changes in the parameters affect the break - even point.

1. which of the following is least accurate for the case illustrated?

a. an increase in the in - house fixed costs will increase the break - even point.
b. a decrease in the out - sourcing unit cost will increase the break - even point.
c. production quantities smaller than the break - even point will result in a net loss.
d. a decrease in the in - house unit production costs will decrease the break - even point.

• select -

1. suppose your in - house fixed costs are $200,000, in - house unit production cost is $10, and the outsourcing unit cost is $30. what is the break - even point?

a. 5,000
b. 10,000
c. 20,000
d. 30,000

• select -

Explanation:

Question 1

• Option a: Increasing in - house fixed costs (FC) means the in - house cost function \(C_{in}=FC + VC1\times Q\) shifts up. To find the break - even point where \(C_{in}=C_{out}=VC2\times Q\), solving \(FC + VC1\times Q=VC2\times Q\) gives \(Q=\frac{FC}{VC2 - VC1}\). An increase in FC will increase Q (break - even point), so this is accurate.
• Option b: The break - even point formula is \(Q=\frac{FC}{VC2 - VC1}\). If we decrease \(VC2\) (outsourcing unit cost), the denominator \(VC2 - VC1\) decreases. Since \(FC\) is positive, \(Q=\frac{FC}{VC2 - VC1}\) will increase (because dividing by a smaller positive number gives a larger result). So a decrease in outsourcing unit cost will increase the break - even point, not decrease it. This statement is inaccurate.
• Option c: For production quantities \(Q\lt\) break - even point, \(C_{out}=VC2\times Q\) and \(C_{in}=FC + VC1\times Q\). Since \(VC2>VC1\) (from the graph's enforcement and the concept), at \(Q\) below break - even, \(C_{in}>C_{out}\) if we consider profit (Profit = Revenue - Cost, assuming revenue is same for both, but here we compare costs. If we produce in - house, cost is higher, so net loss (if revenue is enough to cover outsourcing cost but not in - house cost) or more loss. So this is accurate.
• Option d: From \(Q=\frac{FC}{VC2 - VC1}\), a decrease in \(VC1\) (in - house unit cost) increases the denominator \(VC2 - VC1\), so \(Q\) (break - even point) decreases. This is accurate.

Step1: Recall the break - even formula

The cost of in - house production \(C_{in}=FC + VC1\times Q\), and the cost of outsourcing \(C_{out}=VC2\times Q\). At break - even, \(C_{in}=C_{out}\), so \(FC+VC1\times Q = VC2\times Q\).

Step2: Rearrange the formula to solve for Q

\(FC=VC2\times Q - VC1\times Q=(VC2 - VC1)\times Q\), then \(Q = \frac{FC}{VC2 - VC1}\).

Step3: Substitute the given values

Given \(FC = 200000\), \(VC1 = 10\), \(VC2 = 30\). Substitute into the formula: \(Q=\frac{200000}{30 - 10}=\frac{200000}{20}=10000\).

Answer:

b. A decrease in the out - sourcing unit cost will increase the break - even point.

Question 2