Question

Two fishermen - McKenna (M) and Natasha (N) - fish in the Paradise Pond. They make their decisions simultaneously. The amount of fish, y, that each will catch (y^Mand y^N) depends on the amount of time, e, that each puts in each day (e^M and e^N) and on the amount of time that the other spends fishing each day.

Each player therefore has a production function for fish:

McKenna: y^M(e^M,e^N)=10e^M−1/2(e^M∗e^N)

Natasha: y^N(e^M,e^N)=10e^N−1/2(e^M∗e^N)

Additionally, each player derives utility from the amount of fish that they consume while disliking the effort that they need to exert:

McKenna: u^M=y^M−(e^M)^2

Natasha: u^N=y^N−(e^N)^2

Let us define social welfare as total utility: W = u^M+u^N. The socially optimal outcome is the Pareto-efficient outcome that maximizes social welfare.

How big should the tax τ be, in order to make each player choose the socially optimal level of effort? (Round off to two decimal places.)

Answer 1