Please do all parts for upvote Janice U and Kelly K like fi

Please do all parts for upvote :)

Janice (U) and Kelly (K) like fireworks displays. The marginal benefit curve for Janice is MBj-9-q. Kelly\'s MBk-27-3q. q is the total amount of fireworks consumed. The cost of every unit of fireworks is 4. Any fireworks one purchases can be enjoyed by the other at no cost to the other. a. What is the efficient number of fireworks for this society? b. Suppose the government decides to provide the efficient level of output found above. To pay for the fireworks, the government taxes J and K, using a Lindahl pricing scheme. What are the Lindahl prices? c. If J and K pay their Lindahl prices, what is the consumer surplus for J and K, respectively? What is the total consumer surplus for this society from consuming fireworks d. Instead of their Lindahl prices, suppose J and K are each charged 2 per unit. How does this change the total consumer surplus for the society?

Solution

Solution: Social marginal benefit = MBj + MBk

SMB = 9-q + 27-3q = 36 - 4q

Marginal cost, MC = 4

a) Efficient no. of fireworks, q = ?

SMB = MC

36 - 4q = 4

q = 32/4 = 8 units.

b) Lindahl pricing scheme is charging the consumers with proportionality of the benefit they derive. At efficient level of output, q=8 the marginal benefits derived by Janice and Kelly are (9-8=)1 and (27-3*8=)3 respectively. So, proprtional benefits are 1/4 = 25% and 3/4=75%, and thus the marginal cost burden is shared in this proportionality, so the Lindahl prices(LP) are $1 and $3 for Janice and Kelly.

c) Maximum willingness to pay(maxP) for fireworks for J and K is 9 and 27, respectively.

So, the consumer surplus for J, CSj = 1/2*(maxP - LP)*q

= 1/2 *(9-1)*8 = $32

And the consumer surplus for K, CSk = 1/2*(maxP- LP)*q

= 1/2 *(27 - 3)*8 = $96

Thus, total consumer surplus in the society = CSj +CSk

CS = 32 + 96 = $128

d) Now, CSj\' = 1/2*(9-2)*8 = 1/2*7*8 = $28

CSk\' = 1/2*(27-2)*8 = 1/2*25*8 = $100

Total consumer surplus,CS\' = CSj\'+CSk\'

CS\' = 28 +100 = $128

Hence, with such change in pricing, total consumer surplus hasn\'t changed (though the individual CS have changed: for Janice it has decreased while for Kelly it has increased by same amount)