|Posted: 26 August 2006 at 8:58am | IP Logged
1. The production possibility frontier (PPF) for an economy is
g = 10-1/2x
Where g is the quantity of a pure public goods, and x is the private goods.The economy has two individuals: Pita and Jane. Their utility functions of Pita is given as follows
UPita = ln (x) + ln (g)
UJane = g
Note that Jane obtains no utility from private consumption.
(i) Sketch the PPF and indi”čerence curves for Jane and Pita .
(ii) Given the PPF, .nd the maximum utility that Pita could have. What
would Jane.s utility be in this case?
(iii) Given the PPF, what is the maximum utility that Jane can have? What would Pita.s utility be in this case?
(iv) Explain either graphically or numerically, why not all points on the PPF are Pareto Optimal.
2. The Government has recently announced legislation which willban smoking in all pubs. Many smokers enjoy smoking when they have a drink, and are therefore willing to pay more for a drink if they can smoke.
Aggregate demand from smokers is:
Psmoker = 20-q if smoking allowed, 20-2q if smoking banned
On the other hand, non-smokers hate the smell of smoke and are willing to pay less for a drink if there are smokers.
Pnon-smoker = 20-1/2q if smoking banned, 20-5q if smoking allowed
where q is the number of glasses of beer consumed. Pubs face constant marginal costs of $1.
(i) Draw the appropriate diagrams to show that if there was only one pub in town, it is Pareto e04 cient for it to be smoke-free. (Hint: calculate Consumer Surplus).
(ii) Assume that the pub has to charge all patrons the same price for the beer.that is, he cannot price discriminate between smokers and non-smokers, would a monopolistic pub be smoke-free?
(iii) In reality, pubs operate in a fairly competitive market place. Critically discuss the Government.s legislation to ban smoking in all pubs, from an efficiency point of view.