Search for notes by fellow students, in your own course and all over the country.
Browse our notes for titles which look like what you need, you can preview any of the notes via a sample of the contents. After you're happy these are the notes you're after simply pop them into your shopping cart.
Title: Integration in economics
Description: A summary on how to use integration to find: consumer surplus, producer surplus, Total revenue from marginal revenue, Total cost from marginal cost.
Description: A summary on how to use integration to find: consumer surplus, producer surplus, Total revenue from marginal revenue, Total cost from marginal cost.
Document Preview
Extracts from the notes are below, to see the PDF you'll receive please use the links above
EECM 3714
Lecture 11: Unit 11
Integration
Renshaw, Ch
...
β’ Example: suppose that ππΆ = 3π + 5
...
5π2 + 5π + π
FINDING FIXED COSTS
β’ Note that ππΆ = πππΆ + ππΉπΆ
β’ In the preceding example, πππΆ = 1
...
β’ Now suppose that ππΆ = 50 when π = 4: Substitute this information in the TC function found and
solve for c
...
e
...
5 4
2
+ 5 4 + c = 50 β π = 6
β’ This means that ππΉπΆ = 6 and
β΄ ππΆ = 1
...
DERIVE TR FROM MR
πππ
β’ Recall that ππ =
...
β’ Example: suppose that ππ = 100 β 2π
...
ππ = 100 β« ππ Χ¬β¬β 2 β« = ππ πΧ¬β¬100π β π2
...
Recall that
π = π β πΆ, π = β«ππ π π Χ¬β¬, πΆ = β«ππ πΆπ Χ¬β¬
...
β’ We can then use definite integration to find the profit (cost and income) associated with a specific
output level (see E
...
15 & E
...
16)
β’ Note that the profit maximising level of output (and the maximum profit) can be found by using
ππ = ππΆ
EXAMPLE 1,
β’ Suppose a firmβs marginal revenue function is ππ = πππ β ππ, while its marginal cost function
is ππ = ππ + ππ + πππ
...
β’ a
...
β’ b
...
β’ c
...
Total revenue (π ), Total cost (πΆ) and Profit functions
π = β« Χ¬ = ππ ππ Χ¬β¬400 β 2π ππ
= 400 ΰΆ±ππ β 2 ΰΆ±π ππ = 400π β
π2
πΆ = ΰΆ±ππ ππ = ΰΆ±40 + 2π + 4π 2 ππ
= 40 ΰΆ±ππ + 2 ΰΆ±π ππ +
4 ΰΆ±π 2
ππ
4
= 40π + π 2 + π 3 + π
3
β’ But, we know that C =200 if π = 3
...
Max profit: Using ππ = ππ or
ππ
ππ
= 0 condition
β’ Using ππ = ππ β 400 β 2π = 40 + 2π + 4π 2
β π 2 + π β 90 = 0
β’
β’ β΄π=
β1Β± 12 β4 1 β90
2 1
4
β΄ π = β3 9
3
β2 9
β’ R= 400 9 β 9
2
2
= 9, β10 β΄ π β₯ 0, π = 9
+ 360 9 β 35 = 2071
= 3519
4
β’ C= 3 (9)3 +(9)2 +40 9 + 35 = 1148
π
β’ c
...
18
...
π(π) is the inverse demand function, while π0 π0 represents total
expenditure on the good
...
e
...
EXAMPLE: CONSUMER SURPLUS
β’ Find the consumer surplus if π = 100 β 0
...
5
β’ πΆπ =
π2
2
100π β 0
...
5π ππ β 20(160)
β 3200 = 100π β 0
...
25π 2
0
...
25 160
2
β αΎ100 0 β
PRODUCER SURPLUS
β’ Producer surplus measures the net benefit the producers
derive from supplying quantity π0 , at price π0
β’ To find PS, we need to find the area above the supply curve
- again use definite integration
...
18
...
β’ where π0 π0 is total income received by producers and π(π)
is the inverse supply function
β’ If you are given the supply function (i
...
π = β(π)), first find
the inverse supply function (π = π(π)) before finding the
definite integral
...
Find PS
β’ Solution:
β’ If π = 65, then π = 20 and ππ = π0 π0 = 1300
π
20
β’ ππ = π0 π0 β β«Χ¬β¬0 0 π π ππ = 65(20) β β«Χ¬β¬0
β’ ππ = 1300 β 3
π2
2
20
+ 5π
β’ ππ = 1300 β 1
...
5π 2 + 5π
π=20
β 1
...
5(20)2 +5(20) β 1
...
2)
Given MPS, find savings functions πππ =
ππ
ππ
This means that the savings function is β« ππ πππ Χ¬β¬+ π
β’ We can also use definite integration to find the value of C or S for given income level
...
β’ the arbitrary constant falls away here, just as with TR
πππ
:
ππΏ
Title: Integration in economics
Description: A summary on how to use integration to find: consumer surplus, producer surplus, Total revenue from marginal revenue, Total cost from marginal cost.
Description: A summary on how to use integration to find: consumer surplus, producer surplus, Total revenue from marginal revenue, Total cost from marginal cost.