Class 4 - Solutions 16 October 2002 Teaching Assistant: Mattia Makovec

1. Industrial Relations Labor Economics and Personnel Economics (code 5116) Academic Year 2002-2003 Class 4 - Solutions 16 October 2002 Teaching Assistant: Mattia Makovec Office Hours: Thursday, 14.30-16.30 Room 424, Via Gobbi 5, 4th floor email: mattia.makovec@uni-bocconi.it

2. Probelm 1 • a) Hire a secretary if they are the most cost effective input. A secretary costs $800*12=$9600 and produces 12000 copies so that their cost per output ratio is $9600/12000=0.8 The voice processor costs $500*12=6000 and it cost effective ratio is 1. So you should hire secretary. • b) The new word process for 6 months costs $250*6=$1500 and will produce 3000 pages with a cost per output ratio of 0.5. The firm should hire the secretary for the first 6 months and switch to the new word processor

3. Probelm 2 a)The firm should hire the most cost effective worker. To calculate the cost effective ratio we need to calculate total costs per day, which are obtained as the sum of daily labor costs (hourly wage times 8) plus capital costs. The following table shows that the most cost effective type of labor is high school workers, and the firm should hire high school labor b) with the new machine the cost output ratio increases (see Table) , so it is obviously optimal to stay with the old computer program c) following the wage increase, the lowest cost output ratio is with the college graduate d) With a new machine, it is optimal to hire master students (NB: there is a typo in the text of the exercise, the output of master students will be 13 instead of 12).

4. Probelm 2

5. Probelm 2

6. Probelm 3 • a) If they are hired only for a year, than it is optimal to hire the safe, since 6.3>6.2 • b) Also if they work for two years, it is instead optimal to hire the risky worker, since 12.8>12.6. NB: the expected profit for the risky worker is given by: 6.2 + 0.6*(12-1) = 12.8; remember that the contract is offered at the beginning of the first year for two years, so the firm’s decision is not taken at the end of the first year. • c) also if the horizon is 5 years the firm should hire the risky worker, and the profit differential widen. The expected profit from the safe worker is: 5*6.3=31.5, while for risky is: 6.2+(5-1)*0.6*(12-1) = 32.6 • d) If the termination costs are 2, than the firm should still hire the risky worker, since the expected profit is: 32.6 - 0.4*2= 30.6 < 31.5.

7. Probelm 4 a) The key condition for a piece rate scheme to work is that w_p*y_s>=w_s while simultaneously w_p*y_u<=w_u, where w_p is the piece rate wage, y_s is skilled production, w_s is the outside wage for skilled workers and w_u is the outside wage for unskilled workers. The w_p must then be larger than 7/9 but lower than 1. In other words Tomato must charge pay than a dollar per computer sold but more than 7/9 of a dollar. b) Out of the range specified in question a), Tomato should charge a wage that is just above the lowest bound (i.e. 7/9 of a dollar plus x, where x is as small as possible) c) There are now Unskilled workers, with an average expected production of 4.5. The range which is now acceptable is 7/9<w_p<8/9. The firm should still pay a salary as above, i.e. 7/9 plus x, where x is as small as possible. d) If unskilled sellers believe of having a productivity of 6 units per day, than Tomato should not set up a piece rate scheme since the key condition (w_s/y_s<=w_u/y_u) is not satisfied

8. Probelm 5 • a) w_1= small amount below 4000 (suppose 3900) and w_2=12200, would ensure that unskilled workers do not apply while skilled worker do • b) if the job last 3 years than the firm has some freedom over the wage in period 3. The firm must pay to the skilled workers 24100 over three periods. The first period wage should still be 3900, so as to discourage unskilled workers to apply. • c) In this case w_2=(2*w_s-(1+p)*w_u)/(1-p) while w_1=((1+p)*w_u-2p*w_s)/(1-p). W_2=28000 while w_1= -12000. In other words, skilled workers buy the job in period 1, since earn negative wage

9. Probelm 6a) Under complete ignorance, all players should be assigned in defense, since their average value is larger (78.75>62.5)b) With training costs, the firm can assign workers where they produce their best performance, in the specifi case 330 (output with training) is larger than (315), all in defense. So the firm should train the workersc) If there are two jobs in defense the firm should calculate the difference between defense and forward of each player, and assign in defense those workers with largest absolute differences, up to the point in which all slots are used up. IN the specific example, Golly and Carlos should be assigned in defense, while Ronaldo and Zidane forward.