1. Using standard partial equilibrium analysis, show that technological progress that reduces production cost may not increase producer surplus. More precisely, imagine there is only one producer, and is a price taker.
(a) Using the graph of partial equilibrium, construct an example where reduction in marginal leads to reduction in producer surplus. (b) Suppose the firm is a monopolist who can choose price freely. Is there any instance that reduction in marginal leads to reduction in producer surplus?
2. Using Edgeworth box, prove that transfer paradox occurs only if there are multiple equilibria—there is an initial allocation that has multiple equilibrium.
3. Suppose there are two individuals and two goods. Preferences are given by u1(x,y) = max{x,y} and u2(x,y) = xy
Suppose that the initial endowments are
ω1 = (4,6)
and
ω2 = (6,4)
(a) Using Edgeworth box, argue there is no competitive equilibrium. (b) Now take a replica of this economy. That is, there are 4 individuals. Two of them have utility function max{x,y} and initial endowment (4,6)
The remaining two individuals have utility function
xy
and initial endowment
(6,4)
Now equilibrium exists. Derive one.
