Cost Curves (Numerical Problems and Solutions) | Class 12 Economcis

COST CURVES (NUMERICAL QUESTIONS)

This article contains all the important numerical problems with their solutions of cost curves of economics of class 12. 

Problem 1

If a firm produces 4 pieces of mobile phones at a cost of Rs. 20,000 per piece, then find the total cost.

SOLUTION

Given

Quantity produced (Q) = 4 piece

Cost per piece (AC) = Rs. 20,000

We know that Total cost (TC) = AC x Q

= 20,000 x 4

= Rs. 80,000

Problem 2

If the total cost of producing 20 pieces of plastic chairs of an industry is Rs. 1,000, then find the average cost.

SOLUTION

Given

Quantity produced (Q) = 20 piece

Total Cost (TC) = Rs. 1,000

We know that Average cost (AC)

= TC / Q

= 1,000 / 20

= Rs. 50

Problem 3

A firm produces 10 units of output, where its total fixed cost is Rs. 100 and total variable cost is Rs. 150. Find TVC and AVC.

SOLUTION

Given

Output Q = 10 units

TFC = Rs. 100

TVC = Rs. 150

We know that

TC = TFC + TVC

= 100 + 150

= Rs. 250

TVC = TC - TFC

= 250 - 100

= Rs. 150

AVC = TVC / Q

= 150 / 10

= Rs. 15

Problem 4

If the total cost of producing 3 units and 6 units of a commodity are Rs. 250 and Rs. 300 respectively, then find marginal cost.

SOLUTION

Given

Total cost (TC₁) = Rs. 250

New total cost (TC₂) = Rs. 300

MC = TC₂ - TC₁

 = 300 - 250

= Rs. 50

Problem 5

Let cost function, TC = 80 + 50Q + 0.30Q³. What is the value of fixed cost?

SOLUTION

Given

Cost function, C = 80 + 50Q + 0.30Q³ C

 = TFC [When Q = 0]

 = 80 + 50 x 0 + 0.30 x 0³

= 80

Hence, total fixed cost (TFC) = Rs. 80

Problem 6

Let the cost function of a firm is given by TC = 30Q² - Q + 2. Find average cost and marginal cost functions.

SOLUTION

We have Cost function, TC = 30Q² - Q + 2

Average cost (AC) = TC / Q = 30Q² - Q + 2 / Q = 30Q - 1 + 2/Q

Marginal cost (MC) = d(TC) / dQ = d/dQ (30Q² - Q + 2) = 60Q - 1

Problem 7

If total cost of producing 8 pieces and 16 pieces of bread by a bakery are Rs. 40 and Rs. 50 respectively, then find marginal cost.

SOLUTION

Given

Total cost of producing (TC₁) = Rs. 40

New total cost (TC₂) = Rs. 80

Change in total cost (ΔTC) = TC₂ – TC₁ = 80 – 40 = Rs. 40
Initial quantity produced (Q₁) = 8
New quantity produced (Q₂) = 16
Change in quantity produced (ΔQ) = Q₂ – Q₁ = 16 – 8 = 8
Marginal cost (MC) = ΔTC / ΔQ = 40 / 8 = Rs. 5

Problem 8

 Complete the following table.

Quantity	TFC	TVC	TC
0	100
1	100
2	100
3	100
4	100
5	100
6	100

SOLUTION
We know that TFC remains constant and TC is the sum of TVC and TFC.

Quantity	TFC	TVC	TC
0	100	0	100
1	100	60	160
2	100	80	180
3	100	105	205
4	100	140	240
5	100	180	280
6	100	210	310

PROBLEM 9

Complete the following table.

Quantity	TFC	TVC	TC
0			60
1		30	90
2		40	100
3		45	105
4		55	115
5		75	135
6		120	180

[Note: TFC equals to TC when TVC is zero]

SOLUTION

Quantity	TFC	TVC	TC
0	60	0	60
1	60	30	90
2	60	40	100
3	60	45	105
4	60	55	115
5	60	75	135
6	60	120	180

PROBLEM 10

Complete the following table and draw TC, TVC, and TFC curves in the same figure.

Quantity	TFC	TVC	TC
0	60	0	60
1	60	30	90
2	60	40	100
3	60	45	105
4	60	55	115
5	60	75	135
6	60	120	180

The graph shows the cost curves for TC, TVC, and TFC plotted against Quantity (Output). The TFC curve is horizontal, indicating constant fixed costs. The TVC curve increases with quantity, and the TC curve is the vertical summation of TFC and TVC.

Here is the extracted text from the image:

PROBLEM 11

Complete the following table.

Output	TFC	TVC	TC	AFC	AVC
0	200	0
1		50
2		90
3		120
4		140
5		170
6		210
7		300
8		400

SOLUTION

Output (Q)	TFC	TVC	TC = TFC + TVC	AFC = TFC/Q	AVC = TVC/Q
0	200	0	200	-	-
1	200	50	250	200	50
2	200	90	290	100	45
3	200	120	320	66.7	40
4	200	140	340	50	35
5	200	170	370	40	34
6	200	210	410	33.3	35
7	200	300	500	28.6	42.9
8	200	400	600	25	50

Problem 12

Given the following schedule.

Output	TC	AC	MC
1	15
2	28
3	39
4	52
5	70
6	96

a. Find AC and MC at various levels of output.
b. Plot AC and MC schedules on the same graph.

SOLUTION

a.

Output (Q)	TC	AC = TC/Q	MC = ΔTC / ΔQ
1	15	15	15
2	28	14	13
3	39	13	11
4	52	13	13
5	70	14	18
6	96	16	26

 

 

The graph shows the AC and MC curves plotted against Quantity (Output). The MC curve intersects the AC curve at its minimum point.

Problem 13

Complete the following table. Draw AC and MC curve and also explain the relationship between them.

Output	TC	AC	MC
1	30
2	50
3	60
4	72
5	85
6	102
7	126
8	160

SOLUTION

Output (Q)	TC	AC = TC/Q	MC = ΔTC / ΔQ
1	30	30	30
2	50	25	20
3	60	20	10
4	72	18	12
5	85	17	13
6	102	17	17
7	126	18	24
8	160	20	34

The graph shows the AC and MC curves with the MC curve intersecting the AC curve at its lowest point, illustrating the typical U-shaped cost curves.

The relationship between AC and MC can be pointed out at output as follows:
- At the beginning, both AC and MC are declining.
- When MC is decreasing, it declines faster than AC.
- MC is minimum at the third unit of output and AC is minimum at the sixth unit of output.
- AC = MC at the sixth unit of output and at this output, AC is minimum.
- Beyond the minimum point of AC, MC > AC.

Problem 14

Consider the following table and answer the questions.

Q	TFC	TVC (Rs.)	TC	AFC	AVC	AC	MC
0	12	0
1	12	6
2	12	8
3	12	10
4	12	14
5	12	18
6	12	21

a. Complete the above table.
b. Derive AVC, AC, and MC curves on the same diagram from the completed table.

 

SOLUTION

Q	TFC	TVC (Rs.)	TC	AFC	AVC	AC	MC
0	12	0
1	12	6
2	12	8
3	12	10
4	12	14
5	12	18
6	12	21

Problem 15

If the total cost function for a commodity is given by

TC = 150 + 15Q + Q^2

and output produced is 10 units, find:
a. Average cost
b. Marginal cost

SOLUTION

Given:

C(Q) = 150 + 15Q + Q^2

a. Average cost (AC)

AC=TC/Q

=150+15Q+Q^2 / Q

When Q=10Q = 10,

= Rs. 40

b. Marginal cost (MC)

MC=d(TC)/Q

=d(150+15Q+Q2)/dQ

=d(150)/dQ + 15(dQ/dQ)+(dQ² /dQ)

= 15+2Q

When Q=10

MC=15+2×10

=15+20

=35MC = 15 + 2 \times 10 = 15 + 20 = 35

= Rs. 35