MMC Part 2 Flashcards
Managerial compensation model
P=a-Q
Ri = (a-qi-q)qi
πi = Ri - cqi
What is manager compensation (Mi)
Mi = μi[(aiπ + (1-ai)Ri]
Where μi is a fraction of a linear combination of profit and revenue.
ai can either be 0 or 1. 0 means max revenue, 1 means max profits
If economic theory is correct then what should ai be?
ai = 1 (manager compensation should be based solely upon profits)
However in reality we see manager compensation/incentives do not strictly align with profits of firm
Managerial compensation can be seen as a 2 stage game:
What are the stages
1st: owner of each firm chooses μi (the fraction of performance based pay) and ai (weighting of profits vs revenue) to maximise profit
2nd: take μi, ai, qj given and manager chooses output qi
Start from 2nd stage, what should happen then
We want to find qi and qj, to add qi+qj to get Q, which we can then also find price as P=a-Q
1. Choose qi (as mentioned) to maximise Mi
Mi = μi(a-qi-qj)qi - aicqi
Which is revenue - costs i.e profit
- FOC respect to qi, solve to find qi. Qj will be the same by symmetry.
… final equation for Q = 2a-c(ai+aj) / 3
Intuition of Q expression if ai/j decreases
B) How can we find P?
C) what happens to price if ai/j decreases
If aij decreases i.e owner places less importance on maximisng profit, industry output and profit increase
B) P=a-Q , so just sub Q in,
C) we see price falls as owners weight profit maximisation less, and more about revenue. So produce more output, and see in our equation, as Q increase, price falls!
(Remember from a level, in general increasing revenue is better by lowering price to increase sales!)
Then we have the first stage: owner chooses μi and ai to maximise profits.
Thus what to they choose?
They can set μ as low s they wish, so assume μ=0 so Mi=0
- So just normal maximise profit,
πo = (p-c)qi - Sub in our values of P and qi from 2nd stage!!!
- then FOC respect to ai, to get response function
ai = 6c-a-caj/ 4c
(So first stage choose output qi (also find P and Q), 2nd stage max profit by subbing them into simple profit max)
so response function:
ai = 6c-a-caj/ 4c
intuition
If owner of firm i places more weight on revenue (decreased a) , owner of firm j will increase aj, weighting profits more.
So if ai falls, aj increases. (i weights revenue more means j weights profit more)
so what happens if aj=1
Means they maximise profits
using ai = 6c-a-caj/ 4c
set aj=1 we get
ai = 5c-a/ 4c
When ai=1 what can we interestingly find for qi?
qi = a-c/ 2
In response to firm j profit maximising (aj=1), it produces standard cournot quantity.
firm i responds by producing monopoly quantity! (working pg 10), sub our ai into qi, and qj into the new qi.
Then we can solve response function (ai= 6c-a-caj/ 4c)
How? And final answer
b) intuition
Solve RF means ai=aj=a*, so solve.
Final answer ai=aj=6/5 - a/5c
b) since expressed in c, so as unit cost increases, ai=aj is larger, so more weighting towards maximising profits!
Is output of firm i (when maximise combination of profits and revenue) higher than standard cournot?
Yes 2(a-c)/5 > qi = a-c/3 (cournot)
2(a-c)/5 by subbing the solved response function into qi BR function qi = a-qj/2 -aic/2
Next model; production in teams
Output of firm depends on effort levels of all workers in team. What is problem
Free rider problem - some may not do work
Assume research lab, product with future value V
Team has N workers
Effort ei
Prod function V = Σ N √ei
Value is a function of the sum of square root effort!
Scientist earn wi
ΣWi = v (sum of wages = future value!)
What do u think utility would be
Ui = wi - e
Wage - effort just like seen previously!
Assumptions for production with teams model (2)
Colleagues can observe each others effort
Collude to maximise their utilities
So what is wage
We said
Σw = V
I.e Nw=V
So w = V/N
Now utility max problem, solve it
- Max u = wi - ei So
Max u = V/N - ei
Then recall production function V = ΣN √ei
So
Max u = N√ei /N - ei
- Then FOC in order to find optimal effort level e*
Final answer e* = 1/4
So if workers collude to maximise their utilities, they each exert effort 1/4
What is optimal future value V*?
V = N√ei
When ei = 1/4
V = N x 1/2 = N/2
But in the real world they often do not collude, scientists maximise own utility taken their collegues effort as given.
What is the optimal e* if they do not collude
B) Intuition?
e* = 1/4N²
Makes sense as when N=1 we get our optimal effort level e*=1/4 , as previous!
B) more N we see effort decreases, proving free-riding!
So previously with collusion V*= N/2
What about V equation now
B) what happens to utility as N increases
V = N√e = N√1/4N²
B) as N increases, utility falls
Ui = V/N - e = 1/2N - 1/1N²
(Wage - effort)
How to solve freeriding?
Mechanism that induces workers to put in optimal effort i.e if team achieves V* (optimal future value) , each scientist receives V*/N, otherwise if not receive 0
Next mode: Regulating a firm under unknown cost
Assume gov decides price of product e.g telecommunications.
Running costs of firm are unknown to gov.
Firm reports it truthfully or not
Gov decides price and subsdiy to cover any fixed cost
What is issue with this
Firm has incentive to lie and claim it has high costs, when it is actually low. So gov will let them set a high price, and increase profits!
What is issue with this incentive
Welfare loss P=MC is maximise welfare, but instead they set a higher price.
So need to find a way for firms to truthfully reveal real cost
Model:
Demand p=a-Q
MC: either cH or cL
Firm declares c^ (declared MC)
What is our
A) True profit expression
B) Declared profit expression
True profits are
π(c) = (p(c) − c)(α − p(c)) + s(c*)
S(c*) is subsidy
Declared profits
π(cˆ) = (p(cˆ) − c∗)(α − p(cˆ)) + s(cˆ)
