Pmi?
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(221)331in rj=0. forqik<= 8k
(2b)21p_lxil+2knkqi,k- 11:k8k=0 forqg> 8k
The Lagrangen is the same as in the paper, except it becomes piecewise as described
by (2a) and (2b).
The rst order conditions

Pmi?
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Question 1
In the part of the article that is provided for this assignment, limitation of the paper is
not discussed in details. The paper assumes that the residential consumers are not
affected by the

dU/ngJ = dul/gl_y_1 + duZ/ngJ = dul/ngyl du2/dw2
If dul/gyyj - du2/L\y_2 > 0 (depending on the coefcients), then all wealth should go to consumer I
If dul/ghyj - du2/ 51352 < 0 (depending on the coefcients), then all wealth should go to consumer 2

Question 1
Take the derivative of the indirect utility function:
dV/dW = du/dxl *dxl/dW + du/dXZ *de/dW +
= 7L dB/dxl *Xm/dW + l dB/de *de/dW +
where B is the budget constraint B : pl *x1 + p2*x2 + : W
Simple algebra shows that the above
dV/dW = l ( dB/dx