M17 Suppose prospective clerical worker fallo one etwo categ

M17 Suppose prospective clerical worker, fall-o one e?two categorn·n e high preductivity HP) and low productivity (L.P) An HP worker\'s valun to the em is 545K per year a LP worker\'s value is $.JKper year The fie\'s workers stay on average for five years. An HP workers cost of scholarships, more study time reduces possibilty Suppose, however, that college has no effect on productivity Can the firm stin benett of working, might need longer) from paying more to job candidates with acollege education? A Yes, if the pay differential is right, then oniy HP workers want to so to collegn and the firm avoids overpaying LP workers ends up paying more to everybody cannot increase their productivity by doirg so. 8) No, LP workers would always want to get s college degree, too, so the firm just C) t makes no difference because nobody would get a college education i Headquarters wants to know the productive the plant manager to operate the plant at capacty. The plan capacity Q is actually 10,000 units, but can report any forecast Qr of his choosing. bonus 8 gets him to forecast and deliver the real capacity (Q-Qr-10,000) M18 capacity of one of its plants and encourage t manager knows that the , Which A plaintiff is suing a defendant for $100,000. The cost of going to court is $15,000 for each side. If the parties agree that there is a 50% chance that the plaintiff wins the case, what is the range of mutually beneficial agreements the parties might negotiate in an out-of-court settlement? 19 A) B) $15,000 to $100,000 $35,000 to $65,000 C) $50,000

Solution

Answers: M17 B); M18 C); M19 B)

M17: Assuming firm cannot differentiate between HP and LP workers, it will offer wage = 45K*0.5 + 30K*0.5 [since, half of the workers are HP and other half, LP] = 37.5K per year to each worker. So paying this for 5 years to say n workers, cost = 37.5K*5*n= 187.5Kn

Now any HP or LP worker thus earns $187.5K in 5 years without obtaining college degree.

HP workers will obtain degree only if payoff is then atleast 187.5K.

x*5 - 60K >= 187.5K

x>=49.5K ... So, firm should pay the differential very high (49.5K - 37.5K = 12K).

If HP workers obtain degree, they can be differentiated as HP workers by the firm, thereby receiving $49.5K per year, and firm can pay LP workers as low as $30K per year ($150K for 5 yrs). But in this case then, LP workers will also prefer to obtain a degree (49.5K*5 - 90K = 157.5K > 150K) and firm ends up paying higher to everyone.

M18: We will solve this by closely verifying each bonus values. First, we shall consider one important fact: Since, headquarters want plant manager (PM) to forecast exact capacity Q (i.e 10,000 units). So bonus should be such that it decreases as the forecast, Qt by PM deviates more (lies far from) the true capacity Q.

Now, in A. B=0.5(Q-Qt), as the difference between Q and Qt increases, B increases (which contradicts our above fact). Thus, this cannot be the answer.

In B. B= 0.4Qt + 0.5(Q-Qt) = 0.5Q - 0.1Qt, which is decreasing in Qt. So, if PM reports low values of Qt, he gets higher bonus. (with B maximum if Qt=0)

In C. B = 0.4Qt +0.3(Q-Qt) if Q>Qt and 0.4Qt +0.5(Q-Qt) if Q<Qt

or 0.3Q + 0.1Qt if Q>Qt and 0.5Q - 0.1Qt if Q<Qt. in this case, if PM reports lower Qt than actual, he gets lower bonus also since then B is increasing in Qt; and if he reports higher Qt than actual, he gets lower bonus, as then B is decreasing in Qt. So, any deviation from Q fetches him a lower bonuns. Thus, the best forecast to be made by PM in order to receive maximum bonus is Qt=Q=10,000.

M19: For this we estimate the expected payoffs of both, plaintiff and defendant, for scenarios: if they go court, or not go court, and we have to find range such that EU(no court) > EU(court) for both, plaintiff and defendant; where EU means payoff.

For plaintiff: EU(court)= 100,000*0.5 + 0*0.5 - 15000 = 35000 < EU(no court) ... (1)

For defendant: EU(court) = (-100,000)*0.5 + 0*0.5 - 15000 = -65000 < (-)EU(no court)

= 65000> EU(no court) ... (2)

[we put minus in front of EU(no court) as defendant has to pay, thus negative payoff]

From (1) and (2), EU(no court) out of court settlement must lie between $35,000 and $65,000.