3. Consider a household with well-behaved preferences over two goods represented by a general utility function "(C, ), with each good priced at P, and P2. The household receives an exogenous amount of income, Y . The government levies a proportional sales tax at a rate off On G, resulting in a tax-inclusive price of (1 4)P: (a) Write down the budget constraint for this household. (b) Using indifference curve analysis, graphically locate the optimal choice (i, ), given the budget constraint from part (a). Label slopes and intercepts on your graph. (e) Explain why no other point than the one you choice in part (b) could be the optimal choice. Use some examples of suboptimal points to aid your answer. (d) Express the consumer's optimality condition in terms ofu(c , (2)- (e) Use economic logic with your answer from part (d), and your graph from part (b), to explain whether or not the presence of the sales tax rates > 0 affects the optimal choice (c, o) relative to the case where n = 0