Jim is a salesperson at the DM paper company. The utility function of Jim is given by u(w, b, e)= w + b c(e) where w R is Jims weekly wage,

b is a bonus payment that is conditional on sales revenue, and c(e)is Jims cost of effort where

c(e)= 1 if e < 10 and c(e)= (1(e 10)2) if e 10. 2

Michael is Jim's boss, who is maximising DM's profits which are given by:

(w, b, e)= R(e) w b,

where R(e)is the firms sales revenues and R(e)= 100e

Michael cannot observeJim's effort(e)directly but observesR(e)and can set the bonus level dependent on sales revenues.

1. If Michael setsw=100andb=0, what would be Jim's effort level (e) and DM's profits?(1 mark)
2. If Michael setsw=0andb=1000conditional on reaching a sales target of()= 5000, what would beJim's effort level (e) and DM's profits?(1 mark)
3. If Michael sets w=100 and a bonus payment of 20% of sales revenues (i.e. = 0.2 ())what would be Jim's effort level (e) and DM's profits?(1 mark)
4. What is the optimal wage (w) and bonus payment (b) as a percentage of sales revenuesthat maximises DM's profits?(1 mark)

i. Briefly discuss the potential challenges with implementing such an employment contract in a real-world setting.(1 mark)