1) Kim is a salesperson at the PEAR computer company. The utility function of Kim is given by u(w,b,e) = w+b-c(e) where

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1 Kim Is A Salesperson At The Pear Computer Company The Utility Function Of Kim Is Given By U W B E W B C E Where 1 (61.27 KiB) Viewed 15 times

1 Kim Is A Salesperson At The Pear Computer Company The Utility Function Of Kim Is Given By U W B E W B C E Where 2 (35.98 KiB) Viewed 15 times

1) Kim is a salesperson at the PEAR computer company. The utility function of Kim is given by u(w,b,e) = w+b-c(e) where w E R is Kim's weekly wage, b is a bonus payment that is conditional on sales revenue, and c(e) is Kim's cost of effort where cle) = 2 if e<10 and cle) = (3x(e – 1012) if e 10. Michelle is Kim's boss, who is maximising PEAR's profits which are given by: Te(w,b,e) = R(e) - w-b. where R(e) is the firm's sales revenues and R(e) = 100e Michelle cannot observe Kim's effort (e) directly but observes R(e) and can set the bonus level dependent on sales revenues. a. If Michelle sets w=200 and b=0, what would be Kim's effort level (e) and PEAR's profits? (1 mark) b. If Michelle sets w=0 and b=1000 conditional on reaching a sales target of R(e) = 3000, what would be Kim's effort level (e) and PEAR's profits? (1 mark) c. If Michelle sets w=100 and a bonus payment of 20% of sales revenues (i.e. b = 0.2 x R(e)) what would be Kim's effort level (e) and PEAR's profits? (1 mark) d. What is the optimal wage (w) and bonus payment (b) that maximises PEAR's profits? (1 mark) i. Briefly discuss the potential challenges with implementing an employment contract as in d) in a real-world setting. (1 mark)
e. Dan is Kim's colleague. Michelle assigns Kim and Dan to work on a joint project, which can be described as a simultaneous move game with the following payoffs: Kim Work Hard Shirk 4, 12 Dan Work Hard Shirk y, y 12,4 X, X Suppose y=10 and x = 6. Find the Nash equilibria of this game. (1 mark) f. Suppose Michelle wants both Dan and Kim to Work Hard and plans to set x and y values accordingly. What values of x and y would ensure that both Dan and Kim to choose Work Hard? Interpret what such values of x and y could mean in reality. (1 mark)