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QUESTION TITLE

Inverted U-Shaped Function

DESCRIPTION:

The Environment Kuznets Curve (EKC) postulates the relationship between per capita income and environmental degradation. It shows that initially as income rises, the degradation of the environment rises. But beyond some level of per capita income, the trend reverses. This situation can be interpreted simply as a very poor country with low industrialization that is not damaging the environment much and as a result, the environmental quality indicator is good. However, once a country starts the growth process, the environmental damage/ degradation increases. When income per capita increases, the demand for a cleaner environment will increase, environmental legislation will be enacted, and the environment will improve. This indicates that environmental impacts or emissions per capita have an inverted U-shaped function with per capita income. CO2 is taken as a function of GDP(per capita). In order to find out the effect of GDP(per capita) on CO2, the following model has been proposed: 

CO2 = BETA0 + B1GDP + B2GDP2 + u

From this model, discuss how we can get the inverted U-shaped of the Kuznet Curve and also discuss when this curve moves up and when it will move down.

SOLUTION:

The model suggests that the inverted U-shaped curve can be obtained by incorporating the quadratic term B2GDP2 into the relationship between CO2 emissions and GDP (per capita income). The curve moves up initially due to the positive linear effect of income on CO2 emissions, but it begins to move down once the negative quadratic effect becomes dominant, representing the environmental improvements associated with higher income levels.

OR

The proposed model, CO2 = BETA0 + B1GDP + B2GDP2 + u, suggests that the relationship between CO2 emissions and GDP (per capita income) follows an inverted U-shaped curve, which is similar to the pattern observed in the Environmental Kuznets Curve (EKC). Let's break down the components of the model and discuss how it can generate the inverted U-shaped curve.

CO2 represents the level of carbon dioxide emissions, which is a measure of environmental degradation. BETA0 represents the intercept term, which indicates the level of CO2 emissions when GDP (per capita income) is zero. B1 represents the coefficient for GDP, indicating the linear effect of income on CO2 emissions. B2 represents the coefficient for GDP squared, capturing the non-linear effect of income on CO2 emissions.

The quadratic term, B2GDP2, is what introduces the inverted U-shaped relationship. As GDP increases, the positive coefficient B1GDP captures the initial direct relationship between GDP and CO2 emissions. In other words, as income rises, there is typically an increase in industrialization, energy consumption, and production activities, which tend to generate more CO2 emissions. This corresponds to the ascending part of the curve.

It's important to note that the turning point of the curve, where the ascent transitions into the descent, can vary among countries depending on their specific circumstances, policies, and cultural factors. Therefore, the precise income level at which the curve shifts upwards or downwards may differ.

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