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In the second essay, I use an index based on Roemer [1998] to study the effect of education policies on health inequality in two exercises. First, I use the British Household Panel Survey to estimate the effect of compulsory schooling reform on health inequality. Second, I use NLSY79 to study the effect of the court-ordered education financing reforms in the United States. My results indicate that the British reform does not have any significant effect on equality of opportunity for health. The U.S. reform, however, appears to be equality enhancing under our framework. In the third essay, I discuss the optimal level of cigarette tax under the equal opportunity framework. Using cigarette taxation as policy instrument, I compute the level of health inequity under different tax rates. I estimate an empirical model in which return to smoking is allowed to vary across individuals. Policy simulations are performed to estimate the optimal cigarette taxation to equalize opportunity for health.