Question

A country’s individuals each creates income worth a * e, where a is the individual’s ability and e the individual’s effort. Effort creates costs of 8 * e² for each individual. The country is corrupt and corrupt officials will confiscate every income above 32. How much effort does an individual with ability a = 32 choose?

Answer 1

Income of an individual is represented by= ae

cost of effort to the individual = 8e²

Every income above 32 will be confiscated so the individual will not want to put anymore effort after he has earned an income of 32.

Let's maximize the profit of individual:

Profit= total money earned - total cost incurred

= ae - 8e²

differentiating with respect to e:-

dp/de = a - 16e = 0 ( First order condition )

a = 16e

Now given in the question, the individual has a=32. Putting this value of a in the above equality we get,

32 = 16e

e = 2.

The individual will choose an effort level of 2.