ECO 313: Economics Assignment 6 and 7 - Vertical Separation and Merger

This document provides solutions and analyses for two economics assignments. Assignment 7 explores the concepts of consumer surplus and industry profit under conditions of vertical separation and vertical merger, computing equilibrium prices, quantities, and profits for upstream and downstream firms. It also compares consumer surplus under both scenarios. Assignment 6 delves into industry profit under different entry constraints and research and development scenarios, calculating profit, marginal revenue, and total cost for firms under varying conditions, including the impact of R&D investment. The solutions demonstrate the application of economic principles and calculations to real-world scenarios, showing the impact of market structure and strategic decisions on profitability and consumer welfare.

Assignment number 7- Economics
Introduction:
The assignment pertains to computation of consumer surplus, industry profit and difference
in surplus under vertical separation and vertical merger. Vertical Separation means that the
production and distribution are done by different entities. Accordingly, there is an upstream
firm mainly a manufacturer and a downstream firm namely a distributor. Further, in case of
vertical merger all the functions are done by the manufacturer itself.
Question 1
Based on above notion sheet 1 of the assignment 7 tab vertical separation is solved as under:
Given
a=1
b=100
implying demand equation is : Qd= 100 – P
Downstream fixed cost = $50
Upstream fixed cost = $50
Upstream Firm Marginal Cost = $ 4 (Considered variable cost)
Based on the above given data the computation has been done in the following manner:
Upstream Firm Price under equilibrium is computed by using the formula i.e. (a+e)/2 which
gives the result as 52
Based on the result derived, the computation of equilibrium quantity is done by reducing the
equilibrium price for upstream firm from a and dividing the same by 2 i..e (a-P*)/2=24
Further, the said value of quantity is placed in the demand equation to derive the sale price of
downstream firm and the value of sales has been determined at 76$. The formula used is
stated as under: P=100-Qd
Upstream total revenue is derived by multiplying the Quantity Demanded with Price=
Qd*P*= 24*52= $1248
Upstream firm total cost is determined by using the formula: Marginal Cost * Qd*+Fixed
Cost=4*24+50=$146
Upstream total Profit is worked out at $1102 which is difference between total revenue and
total cost
Marginal Revenue is Selling Price as the situation is equilibrium and price shall remain
constant;
Marginal Cost shall be upstream firm marginal cost as the same shall remain same in the
absence of any new data.
For Downstream firm

Downstream total revenue is derived by multiplying the Quantity Demanded with Price=
Qd*P*= 24*76= $1824
Downstream firm total cost is determined by using the formula: Marginal Cost * Qd*+Fixed
Cost=76*24+50=$1298
Downstream total Profit is worked out at $526 which is difference between total revenue and
total cost
Marginal Revenue is Selling Price as the situation is equilibrium and price shall remain
constant;
Marginal Cost shall be upstream firm total cost as the same shall remain same in the absence
of any new data.
Industry Profit shall be summation of profit of downstream firm profit and upstream firm
profit which works out to be $1628.
Consumer Surplus is computed by using the formula : (a-e)^2/8 which results in 1152
consumer surplus.
Question 2
Based on above notion sheet 2 of the assignment 7 tab vertical merger is solved as
under:
Given
a=1
b=100
implying demand equation is : Qd= 100 – P
Integrated fixed cost = $100
Firm Marginal Cost = $ 4 (Considered variable cost)
Based on the above given data the computation has been done in the following manner:
Firm Price under equilibrium is computed by using the formula i.e. (a+marginal cost)/2
which gives the result as 52
Based on the result derived, the computation of equilibrium quantity is done by reducing the
equilibrium price for firm from a i..e (a-P*)= 48
total revenue is derived by multiplying the Quantity Demanded with Price= Qd*P*= 48*52=
$2496
firm total cost is determined by using the formula: Marginal Cost * Qd*+Fixed
Cost=4*48+100=$292
Upstream total Profit is worked out at $2204 which is difference between total revenue and
total cost

Marginal Revenue is Selling Price as the situation is equilibrium and price shall remain
constant;
Marginal Cost shall be firm marginal cost as the same shall remain same in the absence of
any new data.
Consumer surplus under vertical merger shall be higher than that of vertical separation.
Accordingly, margin has been derived by using the formula:
(a-marginal cost)^2/4 which works out to be $2304 and the difference between the consumer
surplus under vertical merger and vertical separation is derived at $1152.
Question 3
On comparison of the output and margin under the conditions, it may be seen that margin is
max under vertical merger and further there is higher quantity of goods sold at lower price
resulting in higher consumer surplus as middlemen is eliminated and the margin of trader is
removed.
Thus, as a snapshot consumers are more benefitted under vertical merger than on vertical
separation.
Question 4
Consumer surplus under vertical merger shall be higher than that of vertical separation.
Accordingly, margin has been derived by using the formula:
(a-marginal cost)^2/4 which works out to be $2304 and the difference between the consumer
surplus under vertical merger and vertical separation is derived at $1152. Thus, there is
differential of $1152.
Assignment 6: Economics
Introduction:
The assignment pertains to computation of industry profit under different constraint of entry
and research and development. The analysis is presented as under:
Question 1
Under Period 1
Given
a=12
b=1
implying demand equation as Qd=12-P
c=0
d=0

e=6 Marginal cost
f=1
Cost equation is 1+6Qd
Q* has been computed in the following manner:
Profit =P*Q-C
(12-Qd)*Qd-1-6Qd
6Qd-Qd^2-1
By doing first order differentiation of Qd
We get
Qd=3
Based on above Quantity has been determined at 3.
Further, putting the value of equilibrium quantity determined price has been derived at $9 by
putting the same under the demand equation P=12-Qd
Total revenue has been worked out using the formula= P*Qd
Total cost has been worked out using the formula= e*Qd+f
Profit has been worked by taking difference of total revenue-total cost
Marginal Revenue is Selling Price as the situation is equilibrium and price shall remain
constant;
Marginal Cost shall be firm marginal cost as the same shall remain same in the absence of
any new data.
Under Period 2
Given
a=12
b=1
implying demand equation as Qd=12-P
c=0
d=0
e=6 Marginal cost
f=1
Cost equation is 1+6Qd
Q* has been computed in the following manner:

Profit =P*Q-C
(12-Qd)*Qd-1-6Qd
6Qd-Qd^2-1
By doing first order differentiation of Qd
We get
Qd=3
Based on above Quantity has been determined at 3.
Further, putting the value of equilibrium quantity determined price has been derived at $9 by
putting the same under the demand equation P=12-Qd
Total revenue has been worked out using the formula= P*Qd
Total cost has been worked out using the formula= e*Qd+f
Profit has been worked by taking difference of total revenue-total cost
Marginal Revenue is Selling Price as the situation is equilibrium and price shall remain
constant;
Marginal Cost shall be firm marginal cost as the same shall remain same in the absence of
any new data.
Sum of incumbent profit is determined by adding the both.
Question 2
Under Period 1
Given
a=12
b=1
implying demand equation as Qd=12-P
c=0
d=0
e=6 Marginal cost
f=1
Cost equation is 1+6Qd
Q* has been computed in the following manner:
Profit =P*Q-C
(12-Qd)*Qd-1-6Qd

6Qd-Qd^2-1
By doing first order differentiation of Qd
We get
Qd=3
Based on above Quantity has been determined at 3.
Further, putting the value of equilibrium quantity determined price has been derived at $9 by
putting the same under the demand equation P=12-Qd
Total revenue has been worked out using the formula= P*Qd
Total cost has been worked out using the formula= e*Qd+f
Profit has been worked by taking difference of total revenue-total cost
Marginal Revenue is Selling Price as the situation is equilibrium and price shall remain
constant;
Marginal Cost shall be firm marginal cost as the same shall remain same in the absence of
any new data.
Under Period 2
Given
a=12
b=1
implying demand equation as Qd=12-P
For firm 1
d=0
e=6 Marginal cost
f=1
For firm 2
d=0
e=6 Marginal cost
f=1
Cost equation is 1+6Qd
Q* has been computed in the following manner:
Profit For 1 =P*Q-C
(12-Qd1-Qd2)*Qd1-1-6Qd1

6Qd1-Qd1^2-Qd1*Qd2-1
By doing first order differentiation of Qd
6-2Qd1-Qd2
Profit For 2 =P*Q-C
(12-Qd1-Qd2)*Qd2-1-6Qd2
6Qd2-Qd2^2-Qd1*Qd2-1
By doing first order differentiation of Qd
6-2Qd2-Qd1
Taking Qd1=Qd2
We get Qd1=2=Qd2
Based on above Quantity has been determined at 4.
Further, putting the value of equilibrium quantity determined price has been derived at $8 by
putting the same under the demand equation P=12-Qd
Total revenue has been worked out using the formula= P*Qd
Total cost has been worked out using the formula= e*Qd+f
Profit has been worked by taking difference of total revenue-total cost
Marginal Revenue is Selling Price as the situation is equilibrium and price shall remain
constant;
Marginal Cost shall be firm marginal cost as the same shall remain same in the absence of
any new data.
Sum of incumbent profit is determined by adding the both.
Question 3
Under Period 1
Given
a=12
b=1
implying demand equation as Qd=12-P
c=0
d=0
e=6 Marginal cost

f=1
Cost equation is 1+6Qd
Q* has been computed in the following manner:
Profit =P*Q-C
(12-Qd)*Qd-1-6Qd
6Qd-Qd^2-1
By doing first order differentiation of Qd
We get
Qd=3
Based on above Quantity has been determined at 3.
Further, putting the value of equilibrium quantity determined price has been derived at $9 by
putting the same under the demand equation P=12-Qd
Total revenue has been worked out using the formula= P*Qd
Total cost has been worked out using the formula= e*Qd+f
Profit has been worked by taking difference of total revenue-total cost
Marginal Revenue is Selling Price as the situation is equilibrium and price shall remain
constant;
Marginal Cost shall be firm marginal cost as the same shall remain same in the absence of
any new data.
Under Period 2
Given
a=12
b=1
implying demand equation as Qd=12-P
c=0
d=0
e=4 Marginal cost
f=1
Cost equation is 1+4Qd
Q* has been computed in the following manner:
Profit =P*Q-C

(12-Qd)*Qd-1-4Qd
8Qd-Qd^2-1
By doing first order differentiation of Qd
We get
Qd=4
Based on above Quantity has been determined at 4.
Further, putting the value of equilibrium quantity determined price has been derived at $8 by
putting the same under the demand equation P=12-Qd
Total revenue has been worked out using the formula= P*Qd
Total cost has been worked out using the formula= e*Qd+f
Profit has been worked by taking difference of total revenue-total cost- R&D Cost
Marginal Revenue is Selling Price as the situation is equilibrium and price shall remain
constant;
Marginal Cost shall be firm marginal cost as the same shall remain same in the absence of
any new data.
Sum of incumbent profit is determined by adding the both.
Further, the maximum cost that can be incurred for R&D so as to keep profit above the
question 1 is $6.99 and for ease it is taken at $6.
Question 4
Under Period 1
Given
a=12
b=1
implying demand equation as Qd=12-P
c=0
d=0
e=6 Marginal cost
f=1
Cost equation is 1+6Qd
Q* has been computed in the following manner:
Profit =P*Q-C
(12-Qd)*Qd-1-6Qd

6Qd-Qd^2-1
By doing first order differentiation of Qd
We get
Qd=3
Based on above Quantity has been determined at 3.
Further, putting the value of equilibrium quantity determined price has been derived at $9 by
putting the same under the demand equation P=12-Qd
Total revenue has been worked out using the formula= P*Qd
Total cost has been worked out using the formula= e*Qd+f
Profit has been worked by taking difference of total revenue-total cost-R&D Cost
Marginal Revenue is Selling Price as the situation is equilibrium and price shall remain
constant;
Marginal Cost shall be firm marginal cost as the same shall remain same in the absence of
any new data.
Under Period 2
Given
a=12
b=1
implying demand equation as Qd=12-P
For firm 1
d=0
e=4 Marginal cost
f=1
For firm 2
d=0
e=4 Marginal cost
f=1
Cost equation is 1+6Qd
Q* has been computed in the following manner:
Profit For 1 =P*Q-C
(12-Qd1-Qd2)*Qd1-1-4Qd1

8Qd1-Qd1^2-Qd1*Qd2-1
By doing first order differentiation of Qd
8-2Qd1-Qd2
Profit For 2 =P*Q-C
(12-Qd1-Qd2)*Qd2-1-4Qd2
8Qd2-Qd2^2-Qd1*Qd2-1
By doing first order differentiation of Qd
8-2Qd2-Qd1
Taking Qd1=Qd2
We get Qd1=8/3=Qd2
Based on above Quantity has been determined at 8/3.
Further, putting the value of equilibrium quantity determined price has been derived at $6.67
by putting the same under the demand equation P=12-Qd
Total revenue has been worked out using the formula= P*Qd
Total cost has been worked out using the formula= e*Qd+f
Profit has been worked by taking difference of total revenue-total cost
Marginal Revenue is Selling Price as the situation is equilibrium and price shall remain
constant;
Marginal Cost shall be firm marginal cost as the same shall remain same in the absence of
any new data.
Sum of incumbent profit is determined by adding the both.
Further, the maximum cost that can be incurred for R&D so as to keep profit above the
question 1 is $6.21 and for ease it is taken at $5.22.
Question 5
Under Period 1
Given
a=12
b=1
implying demand equation as Qd=12-P
c=0
d=0

e=6 Marginal cost
f=1
Cost equation is 1+6Qd
Q* has been computed in the following manner:
Profit =P*Q-C
(12-Qd)*Qd-1-6Qd
6Qd-Qd^2-1
By doing first order differentiation of Qd
We get
Qd=3
Based on above Quantity has been determined at 3.
Further, putting the value of equilibrium quantity determined price has been derived at $9 by
putting the same under the demand equation P=12-Qd
Total revenue has been worked out using the formula= P*Qd
Total cost has been worked out using the formula= e*Qd+f
Profit has been worked by taking difference of total revenue-total cost-R&D Cost
Marginal Revenue is Selling Price as the situation is equilibrium and price shall remain
constant;
Marginal Cost shall be firm marginal cost as the same shall remain same in the absence of
any new data.
Under Period 2
Given
a=12
b=1
implying demand equation as Qd=12-P
For firm 1
d=0
e=4 Marginal cost
f=1
For firm 2
d=0