An accountant for a car rental company was recently asked to report the firm\'s

Question

An accountant for a car rental company was recently asked to report the firm's costs of producing various levels of output. The accountant knows that the most recent estimate available of the firm's cost function is, C(Q)=100+10Q+Q^2 where costs are measured in thousands of dollars and output is measured in thousands of hours rented.

a. What is the average fixed cost of producing 2 units of output?



b. What is the average variable cost of producing 2 units of output?




c. What is the average total cost of producing 2 units of output?




d. What is the marginal cost of producing 2 units of output?




e. What is the relation between the answers to (a), (b), and (c) above? Is this a general property of average cost curves?

Explanation / Answer

C(Q)=100+10Q+Q^2 Where Q=2 a. What is the average fixed cost of producing 2 units of output? Fixed Cost is the cost that we will pay if Q=0, so Fixed Cost=100+10(0)+0^2=100 AFC=FC/Q=100/2=50 Average Fixed Cost where Q=2 is 50 ($50,000) b. What is the average variable cost of producing 2 units of output? Variable Cost is the part of cost that changes as Q changes (cost that is not fixed). VC=10Q+Q^2 VC where Q=2 is VC=10(2)+2^2=24 AVC=VC/Q=24/2=12 Average Variable Cost where Q=2 is 12 ($12,000) c. What is the average total cost of producing 2 units of output? C(Q)=100+10Q+Q^2 Total Cost of producing where Q=2: TC=100+10(2)+2^2=100+20+4=124 ATC=TC/Q Average Total Cost=124/2=62 d. What is the marginal cost of producing 2 units of output? I assume this means the marginal cost of producing the 2nd unit of output. Marginal Cost means, "what does it cost to produce one more unit?" So, let's find the total cost of producing one unit, then compare it to the total cost of producing 2 units. TC(Q=1)=100+10(1)+1^2=100+10+1=111 TC(Q=2)=100+10(2)+2^2=100+20+4=124 So, it costs 13 ($13,000) to produce the second unit of output. e. What is the relation between the answers to (a), (b), and (c) above? Is this a general property of average cost curves? Answer (a) +(b)=(c) Yes, since TC=VC+FC then, ATC=AVC+AFC so this is always true. Additionally, AFC must always be declining as Q increases, since FC is always the same. This means that the AVC curve will be increasing as ATC increases and decreasing as ATC decreases, but that the space between AVC and ATC (AFC) will decrease. AVC will never be greater than ATC.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.