The Laffer Curve in General Equilibrium: Consider, as in exercise 16.11, an exchange economy in which I own 200 units of x1 and 100 units of x2 while you own 100 units of x1 and 200 units of x2.
A: Suppose again that we have identical homothetic tastes.
(a) In exercise 16.11, you illustrated the impact of a tax t (defined in A(c) of exercise 16.11) in the Edgeworth Box. Begin now with a graph of just my endowment and my budget constraint (outside the Edgeworth Box). Illustrate how this constraint changes as t increases assuming that equilibrium price falls for sellers and rises for buyers.
(b) Repeat (a) for you.
(c) True or False: As t increases, you will reduce the amount of x1 you buy, and—for sufficiently high to, you will stop buying x1 altogether.
(d) True or False: As t increases, I will reduce the amount of x1 I sell and, for sufficiently high to, I will stop selling altogether.
(e) Can you explain from what you have done how a Laffer curve emerges from it? (Recall that the Laffer curve plots the relationship of t on the horizontal axis to tax revenue on the vertical —and Laffer’s claim is that this relationship will have an inverse U-shape.)
(f) True or False The equilibrium allocation in the Edgeworth box will lie in the core so long as t is not sufficiently high to stop trade in x1.
(g) If you have done exercise 16.10, can you tell whether the same inverse U-shaped Laffer curve also arises when tastes are quasi linear?
B: Assume, as in exercise 16.11, that our tastes can be represented by the utility function u(x1, x2) = x1x2 and that our endowments are as specified at the beginning of the problem.
(a) If you did not already do so in exercise 16.11, derive the equilibrium pre- and post-tax prices as a function of t.
(b) Construct a table relating t to tax revenues, buyer price p, seller price (p −t), my consumption level of x1 and your consumption level of x1 in 0.25 increments. (This is easiest done by putting the relevant equations into an excel spreadsheet and changing t)
(c) Can you see the Laffer curve for this example within your table?
(d) Does the inverse U-shaped Laffer curve also emerge in the case where we assumed quasi linear tastes such as those in exercise 16.10?