The owner of an online gaming site has hired a programmer to write code. The resulting profit created for the owner is 9C². Net profit is 9C² - pC where pC is being paid to the programmer. The programmer incurs a disutility of C³for writing C lines of code. The programmer chooses how many lines to code.

a) Solve for the number of lines of code that the programmer will write.

b) Solve for how much the owner will pay. How many lines of code are written? What are the payoffs for each?

c) How does the total surplus compare if there was no moral hazard (if total surplus were maximized)?

Now suppose the owner changes the compensation scheme: the programmer gets paid z x C²

The additional pay from writing another line can be as such z (C'+1)² - z (C')² = 2zC' + z = z (1+2C')

d) Solve for the number of lines the programmer will now write.

e) Assuming z x C², solve for the owner's optimal compensation scheme.

f) Why does this compensation scheme perform better?