Formulas Flashcards
Show that the marginal curve is twice as steep as the market demand curve when market demand is given by:
Q(p)=a - bp
Where Q is quantity, p is price and a, b >0
First lets solve for TR
TR(Q) = P X Q
= P X (a-bp)
= pa - bp2
Now we use partial derivative for P
MR = a - 2bp
The marginal revenue is twice as steep, we can already expect this because the formula is minus
Does Mcdonalds or burgerking have a dominant strategy
Identify all nash
- Low price 18,18 / 20,16 / 18,14
- status quo 16,20 / 25,25 / 15,19
- heavy ad 14,18 / 17,14 / 19,17
X is the payoff for Mcdonalds and Y is the payoff for burger king
No and No
This is because the values needs to be greater than all other options avialable
Low price and status quo is a nash
Now suppose that burger king moves first, Identify all the SPNE, Explain
- Low price 18,18 / 20,16 / 18,14
- status quo 16,20 / 25,25 / 15,19
- heavy ad 14,18 / 17,14 / 19,17
25,25
Suppose that a firms total cost function is given by:
C(q) = 800 + 8q + 8Q2
where is q is quantity produced
- derive the firms average and marginal cost functions
- what is the range of production
- How is question 1 and 2 related
Average cost function
AC(q) = (800 +8q + 8q2)/q
AC(q) = 8q + 8 + (800/q)
Marginal cost function
MC(q) = (800 + 8q + 8q2)d
C(q)d = 8 +16q
Regarding range of production
MC = AC
8+16q = (800 + 8q + 8q2)/q
8q + 16q2 = 800 + 8q + 8q2
8q2 = 800
q2 = 100
q = 10
The crossing point is 10, everything before that is economies of scale and everything after that is diseconomies of scale
Therefor the range is 0;10
you need both functions to calculate this range
Suppose that firm 1 pays firm 2 an advance of 5 million to perform an activity. To perform this activity an contract is set up and with certrain requirements. firm 2 spends 100,000 to perform the activity. After reviewing the performed activity firm 1 claims that is fails to live up to the contractual requirements and wants to renegotiate. Given the ambiguity of the contract, firm 2 has to agree.
What is firm 2 its rent?
What is firm 2 its quasi rent?
Is the risk of hold up, positively or negatively associated with the amount of quasi rent?
Firm 2 its rent is the profit it would expect minus the amount they must spend to make it worthwile
therefor 5.000.000 - 100.000 = 4.900.000
Firm 2 its quasi rent is the amount firm 2 would receive if the deal went trough minus the revenue the seller must receive not to exit the relationship
therefor 5.000.000 - 0 = 5.000.000
A positive amount of quasi rent is associated with hold up, because it means the asset is already used in the most valuable way and therefor the other firm might recognize your dependance on it.
These firms have the following market shares in the market:
Firm 1: 45%
Firm 2: 30%
Firm 3: 15%
Firm 4: 10 %
Compute the 4-firm index
Compute the herfindal index
45+30+15+10 = 100
0,45^2 + 0,30^2 + 0,15^2 +0,10^2 = 0,3225
How closer to 1 how more concentrated it is
Consider two competitors firm A and firm B, and suppose the demand is given for firm A by:
QA= a-bApA+bBpB
QA is the number of goods
pA is the price of firm A good
pB is the price of firm B good
What is the price elasticity of firm A
Suppose that a = 500, ba = 10, bB = 5 and Pa = Pb = 50
what is the price elasiticity and cross price elasticity
are the products substitutes or compliments
N= - ▲qa/qa/▲pa/pa = -▲qa / qa X pa / ▲pa
= -▲qa /▲pa X pa / qa = -ba x pa / qa
▲qa /▲pa = ba
Remember that price elasticity of demand is the change in price devided by the change in quantity demanded
500-(1050)+(550) = 250
ba x pa/qa = 10 X 50/250 = 2
N = 2 which means it positive therefor they are substitutes
A certain industry is a duopoly, there are two firms in it, Firm A and Firm B, these firms compete through cournot quantity setting competition. The demand curve is P(Q) = 120 - Q. where Q is the total quantity produced by firm A and firm B, both firms have a marginal cost of 60 and no fixed costs.
What is the equillibrium price, quantity and profit.
What if Firm A makes a one time sunk cost investment of 200 and and the marginal cost of firm A will be reduced to 40 and of firm B will remain at 60
P = 120 - q1 - q2
TR1 = 120q1 -q1^2 - q1q2
Firm 1 =120 - 2q1 - q2 = 60
Firm 2 =120 - q1 - 2q2 = 60
60-120 = 60
60- q2 = 2q1
30- 0.5q2 = q1
30- 0.5*(30- 0.5q1) = q1
30- 15 + 1/4q1 = q1
15 = 3/4q1
20 = q1
Q = 40
P = 120-40 = 80
πq1 = (80-60) * 20 = 400
πq2 = (80-60) * 20 = 400
Firm 1 =120 - 2q1 - q2 = 40
Firm 2 =120 - q1 - 2q2 = 60
40-120 = 80
80 - q2 - 2q1
40 - 0.5q2 = q1
40 - 0.5*(30 - 0.5q1) = q1
40 - 15 + 1/4 q1 = q1
25 = 3/4 q1
33.333 = q1
60-120 = 60
60 - q1 = 2q2
30 - 0.5q1 = q2
30 - 0.5*(40- 0.5q2) = q2
30 - 20 + 1/4 q2 = q2
10 = 3/4 q2
13.333 = q2
Q = 46.666
P = 120 - 46.666 =73.333
πq1 = (73.333-40) * 33.333 - 200 = 911
πq2 = (73.333-60) * 13.333 = 400 = 177.8
Suppose that the industry demand curve is given by:
P = 200 - Q
And a monopolist faces the following total cost function:
TCI = 50qI
And a potential entrants face the following cost function:
TCE = 60qE
What is the limit price?
What if the monopolist charged its profit-maximizing price, what would its profit equal?
The limit price is 60
The monopolist maximises profit by setting marginal revenue equal to marginal cost
MRI = MCI
R = P*qI = (200 - qI) * qI
= 200qI - qI^2
200qI - qI^2 = 50qI
Then take the derivative
200 - 2qI = 50
150 = 2qI
75 = qI
PI = 200 - 75 = 125
πI = (125 - 50) * 75
= 75^2
= 5625
Suppose a duopoly faces an industry demand curve of
P = 100 - Q
if the firm charge the same price, then each firm faces the following inverse demand function:
Pi = 100 - 2qi, For i = firm 1, firm 2
The firms, however, face the following different marginal costs:
MC1 = 10 + 2q1 and MC2 = 22 + 2Q2
What is the preferred price for firm 1
What is the preferred price for firm 2
First you need to derive to MR
so
P =(100 - 2q1)*q1
100q1 - 2qi^2
100 - 4q1
MR = MC
100 - 4q1 = 10 + 2q1
90 = 6q1
15 = q1
p1 = 100 - 2*15 = 70
100 - 4q2 = 22 + 2q2
78 = 6q2
13 = q2
p2 = 100 -2*13 = 74
Two firms Alpha and Beta are competing in a market in which customer preferences are identical. Alpha offers a product whose benefit B is equal to 100 per unit. Beta offers a product whose benefit B is equal to 75 per unit. Alpha’s average cost c is equal to 60 per unit, while Beta’s average cost is equal to 50 per unit.
Which firms product provides the greatest value created?
Which P-C is greater and how much does it exceed the other
Value created is B-C
Alpha is 100 - 60 = 40
Beta is 75 - 50 = 25
Alpha creates 15 more value
If the consumer surplus parity is 25 then alpha will always have a bigger profit margin of 15 because
100 - 25 - 60 = 15
This profit margin is also exactly the same regarding the difference in value created. This means by exploiting the value fully by achiving consumer suplus parity the value will transform into profit. Because the P determines how much of the value created is captured as profit.
