First, notice that you would pay for high effort if you could guarantee it. Profit from high effort at a salary of 70 is .8(200) + .2 (0) - 70 = 90. Low effort at the lower salary of 50 only yields .6(200) + .4(0) -50 = 70. But if you can't monitor your programmer, he will always choose low effort.
How about making the wage contingent on success? Let the wage be S if Wizard 1,0 is successful, and F if it fails. S and F will have to satisfy two conditions: a participation constraint and an effort- choice constraint.
The participation constraint is that
.8S + .2F >= 70. (where I am using >= to mean ``greater
than or equal to'')
If this is true, then the programmer will be willing to participate
in the development.
The effort-choice (or "incentive compatibility") constraint is
.8S + .2F >= .6S + .4F + 20,
where the 20 represents the extra payoff the programmer would get by
slacking off. If this inequality is true, then the programmer has no
incentive to slack off, because his payoff of .8S +. 2F
from high effort is as big as his payoff of .6S + .4F + 20 from low
effort.
We can rewrite the effort-choice constraint as
.2 S - .2F >= 20, so
S -F >= 100 and S >= 100+F.
Substitute S= 100+F into the participation constraint and we get
.8 (100+F) + .2F >= 70.
Making that an equality (so that we pay the minimum possible), 80
+.8F +
.2F = 70, so F = -10. We will give the programmer a negative wage of
-10 if
the product fails.
We still have to satisfy the participation constraint, though, so we need to pay a generous wage S if the product succeeds. Since .8S + .2 (-10) = 70, it must be that .8S = 72, and S =90.
These two constraints show the big problem in incentive contracts: getting the other side to participate, and getting them to exert the right effort. Much of the structure of wages and salaries can be explained by these two problems.