(Solved) Personnel Economics Exercise 1 Exercise 1: Hiring 1. A local snowboard firm wants to produce 200 snowboards next month. The firm must hire more labor...

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Personnel Economics Exercise 1 Exercise 1: Hiring
1. A local snowboard firm wants to produce 200 snowboards next month. The firm must
hire more labor in order to produce at this level (Q = 200), and is faced with the
option of hiring either skilled or unskilled workers (denoted S and U, respectively).
Should the firm always hire the most skilled workers? Under what conditions would
the firm hire unskilled workers? Under what conditions would the firm hire skilled
workers? Please formally derive your conclusions.
Assume the following:
Production function: Q = aS + U
Total Cost = WsS + WuU
Ws = wage of skilled workers
Wu = wage of unskilled workers
Now assume that Ws = 10, Wu = 8 and a = 2. Would the firm hire more skilled or
unskilled workers? Explain. Note: this problem can be solved either analytically or
using a spreadsheet: your choice.
2. Goleta Brewing Company hires only two types of labor, managers and brewing
assistants (denoted M and B, respectively). GBC has the following Cobb-Douglas
production function F(M,B) = M.5 B.5 and wants to produce 10 barrels of pale ale this
week. If the wage of managers is $50 per hour and the wage of brewing assistants is
$10 per hour, how many managers and brewing assistants should the firm hire (round
to nearest whole number)? How does your answer change when the wage of
managers decreases to $30 per hour and the wage of brewing assistants remains
constant. Is this result consistent with your intuition? Note: this problem can be
solved either analytically or using a spreadsheet: your choice.
3. A small consulting firm is only interested in hiring NIU graduates (denoted by S), but
it does not know how many it should hire in order to be profit maximizing. Assume
there is a competitive wage of $20 per hour and the production function is F(S)= 100S
– (1/8)S2 . Hiring additional workers will increase production F(S) over relevant
ranges of S. But is the 51st S more valuable than the 50th S in terms of her additions
to overall production? What quantity of NIU graduates should this firm hire and why
does it stop hiring at this level of S? How does your answer change if the production
function is F(S)= 200S –(1/8)S2 and the wage increases to $22? Note: this problem
can be solved either analytically or using a spreadsheet: your choice.
4. Solve the following problem using an excel spreadsheet. A tobacco company is
interested in hiring a salesperson to promote smoking cigarettes in nightclubs. The
position pays a flat salary of $50,000, regardless of sales levels. The firm has two
applicants, Predictable Patty and Risky Ricky. Predictable Patty can produce with
100% certainty $100,000 a year in sales. Risky Ricky, on the other hand, can produce
$300,000 with probability of 50%. But if he turns out to spend his time drinking and 1 Personnel Economics Exercise 1 dancing in the nightclubs instead of making sales, he could actually cost the firm $100,000 per year.
a) During their first year on the job, what are the expected sales of Patty and Ricky?
What are the firm’s expected profits on each worker?
b) Now assume both workers are currently 25, and they will work until the retirement
age of 65. The firm has the option to fire its new employee after one year based on
sales, but can only hire one employee. Assume that it takes only one year to discover
whether Ricky is productive or not, and that he will remain that way for his lifetime.
The firm’s discount rate for future profits is fixed at 10 percent over the life of both
workers. Which employee should it hire?
c) Now relax the assumption that each employee will stay with certainty until he or she
reaches age 65. Assume, instead, that each year the chances that a worker will leave
the firm, given he/she has not left to date, are 20 percent (i.e. the firm’s expected
turnover rate for these sales positions is 20 percent per year). Which employee should
it hire now?
d) Use your spreadsheet program to increase the firm’s discount rate higher and higher
above 10 percent. What happens to its expected present value of profits for each
worker? Do the same for the turnover rate. What happens in each case to the firm’s
decision regarding which of the two workers to hire? Why? 2

 


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