1) 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 is Jim s 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 firm s 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.

a. If Michael sets w=100 and b=0, what would be Jim's effort level (e) and DM's profits? (1 mark)

b. 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)

c. 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) d. What are the optimal wage (w) and bonus payment (b) as a percentage of sales revenues that maximize DM's profits? (1 mark)

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