Assume that the following equation quantifies the relationship between a countrys level of air pollution emissions (E) and its per capita income (I) E 5(I) 0 5 (I) 2 , where E is measured in thousands of tons of sulfur dioxide (SO 2 ) emissions, and I is measured in thousands of dollars a Graph the equation, and explain how it supports the theory of an environmental Kuznets curve (EKC) b If a countrys per capita income (I) increases from $2,500 to $3,500, what is the associated change in emissions (E) What do these changes suggest about where the country is operating on its EKC c Solve for the level of per capita income that maximizes the EKC What is the significance of this income level SO2 emission s (E) EKC Income per capita ( )

Question: Assume that the following equation quantifies the relationship between a countrys level of air pollution emissions (E) and its per capita income (I): E =

Assume that the following equation quantifies the relationship between a country€™s level of air pollution emissions (E) and its per capita income (I):

E = 5(I) ˆ’ 0.5 (I)²,

where E is measured in thousands of tons of sulfur dioxide (SO₂) emissions, and I is measured in thousands of dollars.

a. Graph the equation, and explain how it supports the theory of an environmental Kuznets curve (EKC).

SO2 emission s (E) EKC Income per capita (/)

b. If a country€™s per capita income (I) increases from $2,500 to $3,500, what is the associated change in emissions (E)? What do these changes suggest about where the country is operating on its EKC?

c. Solve for the level of per capita income that maximizes the EKC. What is the significance of this income level?

SO2 emission s (E) EKC Income per capita (/)

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