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 /2 (e 10)^2) if e 10.

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 observe Jim's effort (e) directly but observes R(e) and can set the bonus level dependent on sales revenues.

1. If Michael sets w=100 and b=0, what would be Jim's effort level (e) and DM's profits? (1 mark)
2. If Michael sets w=0 and b=1000 conditional on reaching a sales target of () = 5000, what would be Jim'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 revenues that maximises DM's profits? (1 mark)

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