INSTRUCTIONS This paper contsins SIX questions Candidates sh

INSTRUCTIONS: This paper contsins SIX questions. Candidates should answer FOUR questions. OUEST?ON ONE An agent\'s utility function is uw,e)w-e where w denotes agent\'s payment and e denotes agent\'s effort level. The agent\'s reservation utility is = 2, The agent can exert (er 2) or (e -1). As a result of the agent\'s actions two outcomes Jy and yyare possible. a =½ conditional on high effort and The probability for the better outcome ?? is P 4conditional on low.effort. (a) If Principal is risk neutral, find the optimal contract offered to the agent if Principal desires (i) Low effort [4 marks] (i) High effort [10 marks] How large would the (Vy -Va) gap be for principal to desire agent to exert hish effora

Solution

u(w,e)=w^1/2-e

where w is agent\'s payment

e=agent\'s effort level

Reservation utility is given by u^-=2

e_H=2 and e_L=1

H is high level effort

L is low level effort

Two outcomes are possible

y_H having the probablity equal to p_H=1/2 conditional on high effort

and y_L having the probablity equal to p_L=1/4 conditional on low effort

a) If principal desires low effort

the e_L=1 and the probablity is equal to 1/4

u(w,e)=w^1/2-1

and reservation utility is equal to 2

2=w^1/2-1

2+1=u^1/2

3=u^1/2

u=9

For low effort workers the optimal contract offered is equal to 9.

If principal desires high effort

u(w,e)=e^1/2-2

2=e^1/2-2

2+2=e^1/2

4=e^1/2

e=16

the contract offered to high effort workers is equal to 16.

b) The gap must be equal to 16-9=7

QUESTION FOUR

The production function is given by

q=40E_H+30E_L and sells its output at 10 per unit.

H type workers have high productivity and L type workers have low productivity.

E_H+E_L=10 (given)

pq=10*(40E_H+30E_L)

a)we differentiate with respect to E_H and E_L respectively.

when we differentiate with respect to E_H we get

=400

and when we differentiate with respect to E_L we get

=300

So H- type earn 400 and L- type earn 300.

b) When the firm is not able to distinguish between the two types workers they offer the lower wages due to information asymetry between high productivity and low productivity workers which is equal to 300.

c) Those workers having educational degrees in their hand help the firm to eliminate the situation of asymetry information and those workers will be offered high wages because firms assume that educated workers are more productive than the uneducated workers.