Consider a 2*2 pure exchange economy (ie 2 goods & 2 consumers).
The endowments are – Individual 1 (8,8)
Individual 2 (2,2).
Utility functions are as follows:
(1) Individual 1 has lexicographic preferences with respect to X. That is
The bundle (x1 , y1) will be preferred to (x2 , y2) when x1>x2.
But if x1=x2, then the bundle (x1 , y1) will be preferred to (x2 , y2) if and only if y1>y2.
(2) Individual 2’s utility function is given by U(x,y) = x^2 + y^2
Now our task is to find the contract curve and the competitive equilibrium.
(I) CONTRACT CURVE
First convince yourself that we cannot construct indifference curve (IC) for individual 1’s preferences. Because there are no 2 distinct bundles between which individual 1 will be indifferent.
Now let’s figure out how 2nd individual’s IC looks like.
For example let’s plot IC that represents 4 utils. Ie x^2 + y^2 = 4. Note that this is actually the equation of a circle centered at (0,0), with radius 2. Also since we are bothered about only positive values of x & y, IC representing 4 utils will be represented as follows:
On extending the green line we get the following figure:
Convince yourself that:
• The extended green line is the budget line faced by individual 1.
• Given this budget line, individual 1 will consume the bundle P.
• This implies that in the economy there will be excess demand for good 1 as individual 1’s consumption is outside the edgeworth box.
Suppose the budget line is the RED line given below.