Question

34. For the cost function C = 100 + 10Q + Q2,

a. What is the fixed cost of production when (i) Q = 9, (ii) Q = 10 and (iii) Q = 11?

b. What is the variable cost of production when (i) Q = 9, (ii) Q = 10, and (iii) Q = 11?

c. What is the total cost of production when (i) Q = 9, (ii) Q = 10 and (iii) Q = 11?

d. What is the average fixed cost of production when (i) Q = 9, (ii) Q = 10 and (iii) Q = 11?

e. What is the average variable cost of production when (i) Q = 9, (ii) Q = 10 and (iii) Q = 11?

f. What is the average total cost of production when (i) Q = 9, (ii) Q = 10 and (iii) Q = 11?

g. What is the marginal cost of production when (i) Q = 9, (ii) Q = 10 and (iii) Q = 11?

Answer 1

34) The cost function is C = 100 + 10Q + Q^2

a) The fixed cost is the cost that does not depend on output level. It is fixed. here, the fixed cost is 100 for all the output levels of 9, 10 and 11.

b) The variable cost part varies depending on the output level. In the given function, Variable Cost (VC) = 10Q + Q^2

i) Q = 9, VC = 10*9 + 9^2 = 171

ii) Q = 10, VC = 200

ii) Q = 11, VC = 231

c) Total Cost of production = Fixed cost + variable cost

i) Q = 9, TC = 100 + 10*9 + 9^2 = 271

ii) Q = 10, TC = 300

ii) Q = 11, TC = 331

d) Average Fixed Cost (AFC) is given by, AFC = FC/Q

i) Q = 9, AFC = 100/9 = 11.1111

ii) Q = 10, AFC = 100/10 = 10

ii) Q = 11, AFC = 100/11 = 9.0909

e) Average Variable Cost (AVC) = VC/Q

i) Q = 9, AVC = 171/9 = 19

ii) Q = 10, AVC = 200/10 = 20

ii) Q = 11, AVC = 231/11 = 21

f) Average total cost (ATC) = TC/Q

i) Q = 9, ATC = 271/9 = 30.111

ii) Q = 10, ATC = 300/10 = 30

ii) Q = 11, ATC = 331/11 = 30.0909

g) Marginal Cost (MC) is the change in cost due to change in output by 1 unit. MC = dC/dQ = 10 + 2Q

i) Q = 9, MC = 10 + 2*9 = 28

i) Q = 10, MC = 10 + 2*10 = 30

ii) Q = 11, MC = 10 + 2*11 = 32