Question

You run a company, GizmoNet, that produces gizmos. Gizmos hook onto iPhones, allowing users to access the internet via a virtual reality interface.

Your company hires software engineers, who are employed for three periods. In period one, they must train at GizmoNet. In this period their total productivity is $10 million, and training costs are $8 million. In periods two and three (after the training) productivity is $17 million and $19 million, respectively. An engineer who received no training would have productivity of $10 million at any other firm in all three periods.

Engineers can quit after training (and always get a job offer at other firms). If they do so, their productivity at other firms is $2 million lower than at GizmoNet in each of the last two periods. Assume no discounting.

b. (10 points) Suppose that the labor market is competitive, so that the firm

must earn zero profit from hiring an engineer. If so, what set of salaries

? , ? , ? must the firm offer to guarantee that the total return on the123

training investment is maximized? To choose an answer if you have more than one possibility, pick the feasible solution that maximizes ? (because

software engineers are impatient and risk averse, so ceteris paribus they prefer to be paid as soon as possible).
Hint: first figure out what has to happen to maximize the return on investment. The figure out any constraints on pay, etc. Only then figure out who should invest and get the return (worker or firm), and to what extent.

c. (5 points) In an economic sense (rather than accounting), who pays for the training investment, and who earns the return on the investment? Briefly explain.

Answer 1

a. If we look at the table below, it is clear that an engineer who joins other firms in period 1, can earn a maximum of 10M per year as salary (which is equal to their productivity each year). On the other hand the one who joins GizmoNet in period 1, can earn a maximum of 15M and 17M in periods 2 and 3, which is equal to the productivity at other firms after spending period 1 at GizmoNet. In other words, once GizmoNet employes an engineer in period 1, other firms cannot pay more than 15M and 17M to these engineers in periods 2 and 3, respectively. So GizmoNet can set period 2 and 3 salaries at 15M and 17M, respectively. For period 1 the salary would need to be 2M so that including the training cost GizmoNet earns at least equal to its cost. From an engineer's perspective earning 2M, 15M, and 17M is still better than joining other firms in period 1, where they would earn a maximum of 10M each year.

	At GizmoNet				At other firms (from period 1)			At other firms (from period 2)
Period	Training cost	Salary	Productivity	Profit	Salary	Productivity	Profit	Salary	Productivity	Profit
1	8	2	10	0	x	10	10-x
2		15	17	2	y	10	10-y	a	15	15-a
3		17	19	2	z	10	10-z	b	17	17-b
Total	8	34	46	4	x+y+z	30	30-x-y-z	a+b	32	32-a-b

b. Based on the above discussion it is clear that the cost of training is paid by the engineers themselves rather than the firm employing them.