a. Does the market provide an efficient amount of effort?b. The teacher of the course is considering to implement a tax-cum-subsidy policy in order to enhance effort in the course. Suppose he seeks advice from you. He proposes to subsidize effort at the rates, meaning that putting G, units of time into working on the problem sets will feel less, concretely, only like putting (1-s)G, units of time. In order to subsidize effort, he will tax students' time at the rate t, so the total available time will become(1-1)W₁. What tax-subsidy combination would you propose in order to implement the social optimum while keeping budget balance? Maaike and Pim are VU students following the master course Advanced Microeconomics. Handing-inthe problem sets is obligatory and each group of students like the one formed by Maaike and Pim isrewarded with a common mark for their work. This implies that Maaike and Pim individual efforts onsolving the problems constitute public goods.Let us assume that Maaike and Pim derive similar utility from free time (F) and high marks (G) in thecourse according to the Cobb-Douglas utility function:UM(FM, G) = FG3,U (Fp, G) = F3G\!3where FM and Fp indicate the free time enjoyed by Maaike and Pim, respectively, and G is the jointeffort they put into the working of the problem sets.For simplicity let us assume that G is simply the outcome of giving up free time, so the productionfunction of G is simply:G = FG,where FG denotes the total amount of free time put in by the individuals (i.e. FGFG + F).Let us denote the total amount of time available to the individuals by W. Obviously,W = WM + W p.

A common mathematical representation of customer preferences in economics is the Cobb-Douglas…

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Chapter1: Making Economics Decisions

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a. Does the market provide an efficient amount of effort?

b. The teacher of the course is considering to implement a tax-cum-subsidy policy in order to enhance effort in the course. Suppose he seeks advice from you. He proposes to subsidize effort at the rates, meaning that putting G, units of time into working on the problem sets will feel less, concretely, only like putting (1-s)G, units of time. In order to subsidize effort, he will tax students' time at the rate t, so the total available time will become(1-1)W₁. What tax-subsidy combination would you propose in order to implement the social optimum while keeping budget balance?

Maaike and Pim are VU students following the master course Advanced Microeconomics. Handing-in
the problem sets is obligatory and each group of students like the one formed by Maaike and Pim is
rewarded with a common mark for their work. This implies that Maaike and Pim individual efforts on
solving the problems constitute public goods.
Let us assume that Maaike and Pim derive similar utility from free time (F) and high marks (G) in the
course according to the Cobb-Douglas utility function:
UM(FM, G) = FG3,
U (Fp, G) = F3G\!3
where FM and Fp indicate the free time enjoyed by Maaike and Pim, respectively, and G is the joint
effort they put into the working of the problem sets.
For simplicity let us assume that G is simply the outcome of giving up free time, so the production
function of G is simply:
G = FG,
where FG denotes the total amount of free time put in by the individuals (i.e. FG
FG + F).
Let us denote the total amount of time available to the individuals by W. Obviously,
W = WM + W p.

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