Dorothy lives in a city with high air pollution. Pollution is a bad, but she is able to avoid air pollution by wearing a face mask. Her preferences are given by
U(q1,q2 ) = (q1 - P)2q22
where q1 is the amount of time she spends wearing a mask, P is the amount of pollution and q2 is a composite of other goods (p2 = 1 ). Dorothy must decide how much to wear a mask and how much q2 to purchase. The price of masks is pM. Assume q1* > P when answering this question.
a. Derive Dorothy's demand for masks, q1*(p1,Y, P)
b. How does the quantity of pollution affect the demand for masks? That is, find q1*/P.
c. How does her income influence the quantity of masks she purchases? That is, find q1*/Y.
d. What condition must hold for the assumption q1* > P to hold?
a. q1* = (Y + p1P)/2p1
b. dq1*/dP = 1/2 > 0. She buys more masks when pollution increases
c. dq1*/dY = 1/2p1. She buys more masks as income increases (Normal)
d. We need (Y + p1P)/2p1 > P, so P < Y/p1
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