6&7 cournot equilibrium

Question 1

illustrate the profit of firm j in a market with j + -j firms, with qj on the x-axis

Answer 1

quadratic diagram, profit of firm j increases with qj up until a point where it begins to decrease

Question 2

illustrate the profit of firm j with supply of all other firms (Q-j) on the x-axis

Answer 2

a downwards sloping curve where the profit of firm j decreases with Q-j

Question 3

what is the equation of inverse demand

Answer 3

P(Q) = a - bQ

Question 4

how can the price of firm j’s output be written

Answer 4

P = 1 - Q

Question 5

what is the problem of firm j

Answer 5

max
qj π(qj, Q−j) = (a−c−bQ−j)qj − bq2

Question 6

what is a cournot equilibrium

Answer 6

is a list of supplies (q∗1, . . . , q∗n) such that every firm maximises profit

Question 7

what are two assumptions we make about a cournot equilibrium

Answer 7

• firms are identical
• supplies are identical

Question 8

who runs firms

Answer 8

directors

Question 9

who appoints directors

Answer 9

the board

Question 10

who appoints the board

Answer 10

the assembly of shareholders

Question 11

who owns firms

Answer 11

shareholders

Question 12

what should the decisions of a firm reflect

Answer 12

the interests of the shareholders

Question 13

when a shareholder has common ownership, what do they want to maximise

Answer 13

the weighted sum of profits of all firms

Question 14

define the cournot equilibrium where there is common ownership

Answer 14

A Cournot equilibrium is (q∗1,q∗2) such that firm i maximises the weighted
sum of profits of firms i and −i with weights wii and wi−i given q∗−i

Question 15

how do you calculate the cournot index

Answer 15

Qwith/Qwithout

Question 16

what does the cournot index show

Answer 16

the impact of common ownership

Question 17

what does a shallow/steep inverse demand curve indicate for change in common ownership

Answer 17

• shallow: prices are less sensitive to changes in CO
• steep: prices are sensitive to changes in CO

Question 18

if the CO index is > 1 what does this indicate

Answer 18

common ownership drives down price as Q is larger

Question 19

what does a CO index of < 1 indicate

Answer 19

CO drives price up as Q decreases

Question 20

if firm i cares less about firm -i, how is this illustrated on a diagram

Answer 20

the inverse demand curve pivots inwards

Question 21

describe the steps to calculate the profit maximising problem for firm i

Answer 21

1. sub in (q1 + q2) to (P = 1 - Q - c)
2. max w respect to qi
3. find FOC
4. illustrate if required by setting qi or q-i to 0 to find x and y axis intercepts

Question 22

describe the steps to calculate the cournot equilibrium s.t. firm i maximises profit

Answer 22

1. take FOC
2. create matrices
3. solve matrix
4. find Q, P, qi* and π* (Pqi)

Question 23

describe the steps to calculate the cournot equilibrium WITH common ownership s.t. firm i maximises profit

Answer 23

1. take FOC
2. set r12 = w12/w22 and r21 = w21/w22
3. create matrices
4. solve matrix
5. find Q, P, qi* and π* (Pqi)
6. if index needed, Qwith/Qwithout

Question 24

For which values of w12/w11 and w21/w22 is the aggregate supply maximized at equilibrium? What steps would you take to calculate this

Answer 24

Once you find the Q* through calculations for cournot equilibrium, differentiate with respect to r12 and r21

Question 25

what is the quotient rule

Answer 25

dy/dx = (v(du/dx) - u(dv/dx))/v^2
where v is the denominator and u is the numerator

Question 26

How could the anti-competitive effects of common ownership be regulated?

Answer 26

Ownership of shares could be regulated: something like if you own x% of the shares
in company i you can not own more f x% of shares in other firms in that markets where
f ∈ (0,1) and is small.