Question

a) Because of my heavy teaching load this term, I did not have time to finish the table below, which relates output and cost. Please do it for me. The marginal cost figures refer to the marginal cost of moving from the previous unit to the unit of the row specified. Quantity Total Fixed Variable AverageAverageAverage Marginal (Q) Cost Cost Cost Cost Fixed Cost Variable Cost (TC) (FC)(VC)(AC) (AFC) Cost (AVC)(MC) 0 25 20 24 30 38 48 2 4 30

Please explain in details with step by step solution, Thank you very much

Answer 1

a)

Total cost = Fixed cost + Variable cost

TC = FC + VC

Average cost is given by total cost divided by total output.

$AC = \frac{TC}{q}$$= \frac{FC+VC}{q} = \frac{FC}{q} + \frac{VC}{q} = AFC + AVC$

i.e. Average cost is given by the summation of average fixed cost and average variable cost.

Marginal cost is the cost of producing one additional unit of output. It is given by

$MC = \frac{\mathrm{d} TC}{\mathrm{d} q} = \frac{ \Delta TC}{\Delta q}$

Now let us start filling the table -

Given AFC = 30 at q = 6

=> TFC = q*AFC = 30*6 = 180 which is constant for all q

Thus AFC at -

q = 0 is undefined

q = 1; AFC = 180/1 = 180

q = 2; AFC = 180/2 = 90

q = 3; AFC = 180/3 = 60

q = 4; AFC = 180/4 = 45

q = 5; AFC = 180/5 = 36

Also AVC = VC = 0 at q = 0

And thus AC at q = 0 is AVC+ AFC which is undefined.

At q=0, MC is not defined by the very definition of it.

At q = 1,

MC = TC₁ - TC₀ / (1-0) = 25

=> TC₁ - 180 = 25 => TC₁ = 205

Thus VC = TC - FC = 205 - 180 = 25 = AVC (= VC/q where q = 1)

AC = AFC + AVC = 180 + 25 = 205

At q = 2,

MC = TC₂ - TC₁ / (2-1) = 20

=> TC₂ - 205 = 20 => TC₂ = 225

Thus VC = TC - FC = 225 - 180 = 45

AVC = VC/q = 45/2 = 22.5

AC = TC/q = 225/2 = 112.5

At q = 3,

MC = TC₃ - TC₂ / (3-2) = 24

=> TC₃ - 225 = 24 => TC₃ = 249

Thus VC = TC - FC = 249 - 180 = 69

AVC = VC/q = 69/3 = 23

AC = TC/q = 249/3 = 83

At q = 4,

MC = TC₄ - TC₃ / (4-3) = 30

=> TC₄ = 249 + 30 = 279

Thus VC = TC - FC = 279 - 180 = 99

AVC = VC/q = 99/4 = 24.75

AC = TC/q = 279/4 = 69.75

...

Proceeding this way to complete the table, we get the following table -

Q	TC	FC	VC	AC	AFC	AVC	MC
0	180	180	0	undefined	undefined	0	undefined
1	205	180	25	205	180	25	25
2	225	180	45	112.5	90	22.5	20
3	249	180	69	83	60	23	24
4	279	180	99	69.75	45	24.75	30
5	317	180	137	63.4	36	27.4	38
6	365	180	185	60.83	30	30.83	48