things i must learn (calculation examples) Flashcards
Indefinite Repetition in grim strategies (prisoners dilemma)
The law as a third party intervention (math example) prisoners dilemma
Mock exam 14.1
Key Ideas from the Question:
The repairperson can put in high effort (costs them $2,000) or low effort (no cost to them).
High effort increases the firm’s revenue in all random scenarios (good, medium, bad).
However, the firm cannot monitor how much effort the repairperson puts in, so effort and its effect on revenue cannot be verified.
The repairperson prefers low effort, as high effort costs them $2,000.
Why Fixed-Wage Causes Moral Hazard:
Fixed wage = same pay regardless of effort: The repairperson earns the same fixed wage whether they put in high effort or low effort.
Since low effort costs them nothing (while high effort costs $2,000), the repairperson maximizes their own payoff by choosing low effort and claiming that the outcome was due to “bad random factors” rather than lack of effort.
The firm’s profit suffers because the repairperson chooses low effort, reducing expected revenue.
Expected Revenue with Low Effort:
From the table, with low effort, the expected revenue
1/3(15,000) + 1/3(9000) + 1/3(3000) = 9,000
Impact on the Firm:
With low effort, the firm’s expected profit is
revenue−fixedwage=9,000−W.
Since the repairperson chooses low effort regardless, the firm’s profit is suboptimal.
Mock exam 14(ii) How could a wage contract linked to revenue solve moral hazard?
To address the moral hazard problem, the firm must design a wage contract that provides the repairperson with a strong incentive to exert high effort. This can be achieved by linking the repairperson’s pay to the firm’s revenue or profits, ensuring their earnings are positively correlated with their performance. For example, the firm could offer a positive wage ( W ) (greater than the cost of high effort) only when revenue reaches $15,000 or more, and zero otherwise. Under high effort, the repairperson’s expected wage would be ( \frac{2}{3}W ), as high effort results in revenue ≥ $15,000 in two-thirds of cases, minus the $2,000 effort cost. With low effort, the expected wage would only be ( \frac{1}{3}W ), as revenue ≥ $15,000 occurs less frequently. This setup motivates the repairperson to choose high effort to maximize their earnings.
Another approach would involve a “boiling-in-oil” contract, where the repairperson is paid ( W ) unless revenue drops to $3,000, at which point they are terminated. This severe penalty for low performance strongly discourages the repairperson from exerting low effort. A specific numerical example highlights how this could work: if the repairperson is offered $12,000 when revenue equals $18,000 and nothing otherwise, high effort would result in expected earnings of ( \frac{1}{3}(12,000) - 2,000 = 2,000 ), which is greater than zero. This positive net earning incentivizes high effort. In this case, the firm’s expected revenue is $14,000, and profits are $14,000 - ( \frac{1}{3}(12,000) = 10,000 ), which exceeds profits under low effort or fixed-wage arrangements.
Alternatively, the firm could adopt a revenue-sharing model, such as paying the repairperson the difference between revenue and $9,000 when revenue exceeds $15,000, and zero otherwise. If the repairperson exerts high effort, expected earnings would be ( \frac{1}{3}(9,000) - 2,000 = 1,000 ), which is positive and thus motivates hard work. In this scenario, the firm’s expected revenue remains $14,000, and profits are $14,000 - $3,000 = $11,000, exceeding the $9,000 generated under low effort.
It is important to consider additional factors when implementing these contracts. First, the firm must ensure that expected profits exceed $9,000 (the revenue generated under low effort) minus the wage ( W ), to justify the new incentive structure. Additionally, performance-based contracts transfer much of the risk associated with uncertain production outcomes to the repairperson, which may deter risk-averse workers. To mitigate this, the firm could include a fixed component in the wage, independent of revenue, to reduce the repairperson’s exposure to risk. Finally, the repairperson may have alternative employment options offering a fixed wage ( X ). To make the contract attractive, the firm must ensure that expected earnings are at least ( X + ) the cost of effort in some scenarios and exceed ( X ) in others to justify the repairperson taking on additional effort and risk.
By carefully structuring the wage contract using thresholds, revenue sharing, or mixed schemes with fixed and variable components, the firm can effectively resolve the moral hazard problem, improve profits, and motivate the repairperson to exert high effort.
Explain how and why moral hazard problems are likely to arise in this scenario if the salesperson is paid a fixed salary of £Y (regardless of the number of sales made). How will this impact on the employer’s profits? - what diagram to add
In this scenario, what sort of contract could be offered to the salesperson so that he would accept the job and be incentivised to work really hard?
The employer needs to offer a wage contract that gives the sales person an offer to put in more effort i.e. to work really hard. He can do this by making the wage conditional on sales (payment by result). But this would mean that the salesperson would take on all the risk embodied in the uncertain selling environment. The salesperson may not be willing to do this since he has a choice of staying in his current job where he is paid £X. So the employer needs to pay the salesperson at least £X whatever the state of the world if he wants the salesperson to accept the contract. He could for instance pay a guaranteed income of £X and then a bonus conditional on sales. This would be an acceptable contract that would also be incentive compatible: it is rational for the salesperson to accept it (the contract pays at least as much as his current job and in good states of the world it will pay more) and it gives him the incentive to put in the extra effort required by the employer.
- Answer all parts of the question
In a regional labour market there are only two types of labour: high productivity types (H, with marginal productivity 20 units per hour) and low productivity types (L, with marginal productivity 8 units per hour). Half the workers are H types but employers cannot differentiate between H and L types in the hiring process. Workers know their type.
a) Explain why a wage a wage equal to the average marginal product of H and L workers will lead to adverse selection in this labour market. (Assume price = 1)
The average marginal product is ½ 20 + ½ 8 = 14. If the employer offers a wage equal to 14 then only L types will accept since workers know their type and H types will want to be rewarded at least their Marginal Revenue Product (MRP) which is 20. As only low quality workers will take the job, this is adverse selection - only the low quality workers are hired.
In a regional labour market there are only two types of labour: high productivity types (H, with marginal productivity 20 units per hour) and low productivity types (L, with marginal productivity 8 units per hour). Half the workers are H types but employers cannot differentiate between H and L types in the hiring process. Workers know their type.
In this scenario, what wage will employers offer? Why? With what results?
The profit maximising condition is that the wage = MRP. If W > MRP the firm makes losses. Therefore if the employer offers a wage equal to 14 he will make losses since only the L types will be employed and 14 > MRP of the L types (their MRP = 8). The only wage contract the employer can sensibly offer is one where the wage = 8. In this case only low productivity types will accept but they are being paid their MRP so the employer breaks even. This doesn’t solve the adverse selection problem though, it is still an inefficient outcome, but at least the employer is not making losses.
In a second hand car market, 50% of cars are good quality (peaches of value £20,000) and 50% are of low quality (lemons of value £10,000). There is imperfect information so that buyers do not know whether a car is a peach or a lemon, but sellers do have this information. Buyers and sellers value cars equally.
If the valuation gap is large enough then the adverse selection problem could be resolved. The gap needs to be sufficiently large so that if both peaches and lemons are sold buyers’ expected value is > 20,000. In this case the offered price would be high enough to induce the owners of peaches sell.
Formally if the valuation gap is z, then z needs to satisfy the following condition:
½(1+z)20,000 + ½(1+z)10,000 > 20,000
To solve for the minimum value of z, let the inequality be an equality and divide through by ½ leading to: (1+z)20,000+ (1+z)10,000= 40,000 or (1+z)(30,000) = 40,000
or 1+z = 40,000/30,000 = 4/3 implying z = 4/3 - 1 = 1/3 or 0.333
This means that to resolve the adverse selection problem, buyers need to value cars a third as much again as sellers.
Assume there is some uncertainty for the entrant about whether or not the monopolist has incurred the sunk cost and in fact it has not. Briefly describe the circumstances under which entry could still be deterred.
If there is enough asymmetric information, entry could be deterred if the entrant perceives the risk that the monopolist will fight entry is too high. This would be the case if the perceived probability of the monopolist being strong (has incurred the sunk cost and will therefore fight entry) is high enough.
In the example above if P is the entrant’s belief regarding the probability that the monopolist has invested in the sunk cost and will fight entry then the entrant’s expected payoff from entering is: -1.P + 1(1-P). The expected payoff from staying out is 0.
So the entrant will only enter if -1.P + 1(1-P) > 0 that is: 1 > 2P or P < ½. P= ½ is the critical value of the probability the monopolist is ‘strong’ and will fight that deters entry – even if the monopolist is actually ‘weak’ and would concede if there were entry.
What is happening here is that there is enough uncertainty about the market to effectively allow the monopolist to acquire a false ‘reputation’ for being tough and so deter entry. The reputation effect is embodied in the construction of beliefs about P. Reputation is in this sense a rent-generating asset.
Reputation is based on a firm’s or a market or an individual’s history of behaviour and in this case involves the entrant inferring future behavior based on knowledge of past behaviour. To acquire a reputation requires a time horizon - the game needs to have history of some kind to generate P. It could be repeated or a player could make an initial move of some kind e.g. the monopolist sending a costly signal of strength. Signaling could require the entrant to revise P upwards (e.g. using Bayes rule).
If instead of a potential net return of £100,100, the potential return on the investment was only £99,000 (with 1% probability as before) and Mrs Flutter made the investment, what would you have concluded about her attitude to risk? Explain (referring to at least one diagram). - What diagram to add to this
risk preferring individual graph
what diagram for someone who is risk neutral
risk aversion graph
Adverse selection in second hand markets graphs
