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Question: 2 sales tax with limited attention in class we saw...

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2 Sales Tax with Limited Attention In class, we saw evidence that consumers are not fully responsive to shrouded prices, like shipping costs and sales taxes. In this problem we will work through a model of rational limited attention. Consider a consumer whose income is $100. Her utility function is given by: U(X, Y, c) = ln(X) + Y-ve. In(-) is the natural logarithm. The derivative of the natural logarithm is dln(X)/dX 1/X The price of both X and Y is 1 but X is taxed at 10%. c equals 0 if the consumer does not pay attention to the sales tax and 1 if the consumer does pay attention. Therefore, ve is the psychic cost of paying attention. The consumers actual budget constraint is given by 100 -1.1x Y, but they perceive the price of X to be Px 1 + 0.1 c.Suppose the consumer pays attention to the tax (c= 1). How much X and Y should the consumer purchase? What is the consumers utility (this will depend on v)? 2.1 Suppose the consumer does not pay attention to the tax (c the optimal consumption choices in two steps. First, calculate the optimal relationship between X and Y assuming the prices are both 1. Second, use this derived relationship and the actual budget constraint to solve for the quantities. What is the consumers utility? 2.2 0). Solve for 2.3 For what values of v is it optimal for the consumer to pay attention to taxes? 2.4 Assume the consumer does not pay attention to taxes. Who pays for a sales tax now?

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