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?

Question

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?

Quizplus · Accepted Answer

The Answer of 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?

Dorothy Lives in a City with High Air Pollution