Question 1 Consider consumer behavior in an economy with alcohol consumption x and all other goods y. Higher level of x means higher level of alcohol consumed. Let p denote the pre-tax price of x. Assume that x is subject to an ad valorem sale tax T. The total price of x is (1 + T)p. Assume that the price of y is equal to 1. Let p denote the salience parameter. If 0 1, tax is more salient than the regular price and consumers over-react to the tax. In the standard model, = 1, limited attention doesn't affect how people respond to tax and the regular price. A consumer with budget M maximizes her utility function from consuming alcohol x units and all other goods y units, subjecting to behavioral budget constraint. The behavioral budget constraint is: p(1 + pt)xty = M (a.) Consumer's utility function is: U = In(x)+y (b. ) [1] Write down consumer's utility maximization subjecting to behavioral budget constraint. Find first-order condition and derive optimal alcohol consumption x* as a function of p, t, p. Hint: In the utility function, substitute y out by using behavioral budget constraint. [2] Ceteris paribus, how does optimal alcohol consumption x* relate to the salience of alcohol tax $? Explain. 13] Apart from alcohol tax, if now there is also a social-norm nudge to "reduce" alcohol consumption to level r. The campaign turns consumer's utility function to: U = In(x) + v(x/r)+y (c.) where s (r - x)a if x Er v ( x/ r ) = 1 - 2 ( x - r)a if x>r (d.) x20,r20 1 2 1 is a coefficient of loss aversion From the utility function in equation (c.) and (d.), how will the effectiveness of the social norm nudge depend on the coefficient of loss aversion? Explain