3. Suppose as a policy advisor to the governement you are deciding whether to im

Question

3. Suppose as a policy advisor to the governement you are deciding whether to implement a lump-sum tax instead of the existing taxes on electronic goods. Suppose the representative consumer consumes only two goods, food (F) and the electronic good (E) and you have data for the following three secnarios:

Your goal is the check whether a lump-sum tax that generates same revenue is better for the consumer compared to the existing tax on electronics.

(b) (3 points) Calculate the revenue of the government for the gas on electronics. Also what would be after tax income for the consumer if an equivalent (same revenue) tax is imposed on the consumer in scenario 1.

(d) (5 points) Which policy is better for the consumer?

(e) (2 points) Suppose the only type of electronic product available in this economy is video game player which is making young kids addicted to video games. Do you want to change your answer for part (d)?

Explanation / Answer

a) At prices (PF',PE') =(2,5), Bundle demanded is (480,170). This implies total income available to the representative consumer in third scenario is 2*480 + 5*170 = $1,810.

This is the purchasing power of consumer in scenario 3.

The total expenditure of the consumer on bundle of scenario 2, (550,140) at prices of scenario 3, (2,5) is 1,800 < 1,810. Thus, in spite of being affordable, bundle (550,140) wasn't chosen.

In scenario 2, after the imposition of taxes on electronics, now for every unit consumer has to pay 8 + 2= $10.

so prices in scenario 2 = (4,10)

Now income with the consumer in scenaio 2 was, 550*4 + 140*10 = $3,600

in scenario 2, total expenditure incurred by consumer, had bundle of scenario 3, (480,170) been chosen = 480*4 + 170*10 = $3,620 > $3,600. Thus, bundle chosen in scenario 3 was not affordable in scenario 2.

Hence, we can see from above that B3 was not affordable in scenario 2, while even on being affordable, B2 was not chosen in scenario 3, implying B3 is revealed preferred to B2.

b) With 140 units of electronics, and tax of $2 on each unit, total tax revenue earned by the government = 140*2= $280.

Total income with the representative consumer in scenario 1 = 4*500 + 8*200 = $3600. (ofcourse this would be same as in scenario 2, because there only price due to tax changed, and not the income).

If $280 revenue tax is imposed on consumer in scenario 1, after tax income with the consumer = 3600 - 280 =$3,320

c) Bundle, B3 with prices (4,8) means total expenditure = 480*4 + 170*8 = $3,280 < $3,320 (after lumpsum tax income). Thus, B3 is affordable in this case.

Any poosible bundle under lump-sum tax say (F,E), the income is $3,320 with prices (4,8)

Then our budget line equals, 4*F + 8*E = 3320. Clearly, as in part a), B3 was affordable in scenario 2 after lumpsum tax was imposed, yet it wasn't chosen.

At scenario 3 prices, (2,5), this bundle would have costed 2*F + 5*E. If this is greater than $1,810, (F,E) is not affordable in scenario 3 and (F,E) is revealed preferred to B3. If this is smaller than $1810, consumer is not rational.

d) With existing taxes on electronics, consumer chooses (550,140). With imposition of lumpsum tax of same amount, i.e $280, the budget line of the consumer shifts inwards ( as income changes from $3600 to $3320). So the new bundle preferred (F,E) < (500,200) or F<500 and E<200. If the consumer prefers both goods equally, in the sense he cares about the consumption of both goods at best (well defined preferences) such lumpsum tax reduces consumption of both goods but still provides higher utility or satisfaction than commodity tax. As a result the commodity tax reduces consumption of electronics by a lot more than in case of lumpsum tax, and results in such lower`satisfaction such that increase in consumption of another good, food under commodity tax cannot compensate for the utility loss, in spite of lower consumption of food under lumpsum taxation.

e) As a social player, the policy advisor cares for well being of the consumer not only in respects of consumption of commodities in economy, but overall health too. As kids get addicted to video games, the social planner will prefer lower consumption of electronics, and higher for food. Thus, in this case the answer changes from part d) as it will prefer commodity tax to lumpsum tax, thereby affecting consumption of electronics (video games) in the manner as desired and also earning the same amount of tax revenue i.e, $280.

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