An economist estimated that the cost function of a single-product firm is: C(Q)

Question

An economist estimated that the cost function of a single-product firm is: C(Q) = 50 + 25Q + 30Q^2 + 5Q^3 Based on this information, determine the following: The fixed cost of producing 10 units of output. The variable cost of producing 10 units of output. The total cost of producing 10 units of output. The average fixed cost of producing 10 units of output. The average variable cost of producing 10 units of output. The average total cost of producing 10 units of output. The marginal cost when Q = 10.

Explanation / Answer

a. $50.

Fixed cost is that cost which do not vary with the level of output. So, the part of the cost function which is independent of the output level is $50. This cost is born with 10 units of output and with 0 units of output.

b. Total cost is the summation of fixed cost and variable costs.

Since $50 is the fixed cost, then the remaining values are the variable cost.

VC = 25Q + 30Q2 + 5Q3.

At Q = 10,

VC = 25*10 + 30*10*10 + 5*10*10*10

VC = 250 + 3000 + 5000.

VC = $8250.

c. TC = FC + VC

AT Q = 10,

TC = 50 + 8250

TC = $8300.

d. Average fixed cost = fixed cost/output, at Q=10,

AFC = 50/10

AFC = $5.

e. Average variable cost = variable cost/output, at Q=10,

AVC = 8250/10

AVC = $825.

f. ATC = total cost/output, at Q=10,

ATC = 8300/10

ATC = $830.

g. MC = change in total cost/change in output.

To calculate Mc at Q=10, we need to find the change in TC with Q=9.

At Q=9, TC = 50 + 25*9 + 30*9*9 + 5*9*9*9.

TC = 50 + 225 + 2430 + 3645

TC = $6350.

Change in total cost (Q=10 - Q=9) = 8300 - 6350

= $1950.

Change in output = 10 - 9 = 1.

MC = 1950/1 = $1950.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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