Illustration 65
For a perfectly rivalled industry the following short run function is provided.
TC = 4 + 8V + V^2
If price of the commodity prevailing in the market is $20 at what level of productivity the industry will optimise profits?
Solution
As the Total revenue is price incremented by volume of productivity, total revenue function is
TR = P.V = 20V
TC = 4 + 8V + V^2
We describe below the profit optimisation with both the TR – TC approach and MC – MR approach.
TR – TC Approach
Profits π = TR – TC
= 20V – 4 – 8V – V^2
= 12V – V^2 – 4 …..Equation (1)
Now, profits will be optimum at the productivity level at which first derivative of profit function with respect to the volume of productivity parities zero. Therefore, by considering the first derivative of profit function (1) and fixing it equal to zero, we have:
dπ = 12 – 2V = 0
dV
2V = 12
V* = 12 / 2 = 6
MR - MC Approach
In this approach profits are optimum at the productivity level at which MR parities MC. We thus first derive the marginal revenue and marginal cost from TR and TC functions.
TR = 20V
MR = d
TR = 20
d
V
TC = 4 + 8V + V^2
MC = d
TR = 8
+ 2V
d
V
in order to ascertain profit optimisation productivity we set MR equal to MC. Therefore,
MR = MC
20 = 8 + 2V
2V = 20 – 8
V* = 12 / 2 = 6
Illustration 66
An industry manufactures a perishable consumable commodity in a perfect rivalled market. the industry's variable cost function is provided by:
TVC = 300V – 40V^2 + 2V^3
Where V is level of productivity, determine below what price the industry should shut down manufacturing in the short run?
Solution
In the short run an industry will shutdown operations if the price drops below the level of minimum average variable cost. So we first determine the minimum average variable cost.
AVC = TVC = 300V – 40V^2 +
2V^3
V V V V
= 300 – 40V + 2V^2
To ascertain the level of productivity at which average variable cost is minimum we take the first derivative of the AVC function and set it equal to zero.
dAVC = -
40 V + 4V = 0
dV
40V = 4V
V = 40 / 4 = 10
Now substituting the value of V in the AVC function we know the minimum average variable cost.
AVC = 300 – 40V + 2V^2
= 300 – 40 (10) + 2 (10) ^2
= 300 – 400 + 200
= 100
Therefore, if price drops below $100 per unit the industry will be liquidated.
Illustration 67
Provided is the following short run cost function of a firm
TC = 2000
+ 20V^2
Derive the expression for industry’s short run supply curve.
Solution
An industry's short run supply curve is industry’s short run marginal cost curve. To procure marginal cost function, we have to procure the first derivative of aggregate cost function.
Therefore,
MC = dTC = 40V
dV
to obtain the short run supply curve of an industry we set price equal to marginal cost. Therefore,
P = 40V
V = P / 40 ….Equation (1)
Since the supply curve of an industry is that portion of marginal cost curve that lies above the minimum point of the average variable cost AVC curve.
AVC is minimised at the productivity level where its first derivative parities zero.
AVC = TVC = 20V^2
V V
= 20V
Setting its derivative equal to zero we have
d
(20V) = 0
dV
V = 0
Therefore, AVC is minimised when productivity V is equal to zero. It therefore adopts the whole supply function obtained in Equation (1) such as V = P / 40 denotes the short run supply curve of the industry.
Illustration 68
The following table shows the total cost schedule of a rivalled industry. What is total fixed cost of an industry. Using marginal study ascertain the profit optimisation level of productivity if price of the product for the industry is $16. Compute the profits at this productivity level.
Volume Sold in Units |
Total Cost TC in $ |
0 |
10 |
10 |
18 |
15 |
26 |
20 |
38 |
25 |
45 |
30 |
58 |
35 |
64 |
40 |
79 |
Solution
As the industry incurs a cost of $10 even at zero level of productivity, the industry’s total fixed cost is $10. With respect to ascertain the profit optimisation level of productivity i.e. Symmetry level we have to first compute marginal costs at different levels of productivity. We do so in the below tablet.
Volume Sold in Units |
Total Cost TC in $ |
Marginal Cost in $ |
0 |
10 |
- |
10 |
18 |
8 |
15 |
26 |
8 |
20 |
34 |
8 |
25 |
45 |
9 |
30 |
57 |
11 |
35 |
68 |
11 |
40 |
80 |
12 |
To optimise profits the rivalled industry will equate price with the marginal cost. It will be seen from the tablet that at productivity level of 30 units, the provided price parities marginal cost $11. Therefore, the firm’s optimising profit level of productivity is 30 units. Profits = TR – TC = P.V – TC = 30 * 11 – 57 = $273.
Online Live Tutor TR - TC Approach, MR - MC Approach:
We have the best tutors in Economics in the industry. Our tutors can break down a complex TR - TC Approach, MR - MC Approach problem into its sub parts and explain to you in detail how each step is performed. This approach of breaking down a problem has been appreciated by majority of our students for learning TR - TC Approach, MR - MC Approach concepts. You will get one-to-one personalized attention through our online tutoring which will make learning fun and easy. Our tutors are highly qualified and hold advanced degrees. Please do send us a request for TR - TC Approach, MR - MC Approach tutoring and experience the quality yourself.
Online Perfect Rivalry under Short Run Help:
If you are stuck with an Perfect Rivalry Under Short Run Homework problem and need help, we have excellent tutors who can provide you with Homework Help. Our tutors who provide Perfect Rivalry under Short Run help are highly qualified. Our tutors have many years of industry experience and have had years of experience providing Perfect Rivalry under Short Run Homework Help. Please do send us the Perfect Rivalry under Short Run problems on which you need help and we will forward then to our tutors for review.
- Dead Weight Loss in Welfare under Monopoly
- Establishment of Price and Productivity under Oligopoly Rivalry
- Government Strategies towards Monopoly and Rivalry
- Non-Price Rivalry Advertising Outlay
- Price and Productivity Determination under Perfect Rivalry
- Pricing and Productivity under Monopoly Rivalry
- Perfect Rivalry at Symmetry Level
- Selling Outlay Distinguished from Production Outlay
- Stackelberg's Model
- Surplus Capacity under Monopolistic Competition
- Surplus Capacity under Monopoly Rivalry and Price Productivity Equilibrium
