3. (Lehr #8.6) The chapter claims that the standard model predicts the maximum willingness to pay (WTP) to buy a good equals the minimum willingness to accept (WTA) to sell the good. Let's explore this claim in the context of buying and selling coffee mugs. Assume that an individual, Willie, is a participant in the Monetizing Mugs Lab Experiment. He has preferences over mugs (M) and wealth (W) represented by a utility function u(M, W). Willie initially has no mugs (M=0) and $8 of wealth (W = 8). His WTP is the amount of money he can give up in exchange for gaining a mug that makes him indifferent to just keeping his initial endowments. Mathematically, his WTP is then defined by the following indifference condition: u(0,8) = u(Don't Buy) = u(Buy for $WTP) = u(1,8 WTP) If Willie is gifted a mug, then his WTA is the amount of money he can accept in exchange for losing the mug that makes him indifferent to just keeping the mug. Mathematically, his WTA is defined by: u(1,8) : = u(Don't Sell) = u(Sell for $WTA) = u(0,8 + WTA) a. Suppose that u^ (M, W) = 12M+1+W. Use equations (8.1) and (8.2) to predict Willie's WTP and WTA. Box each value. b. Now suppose that u (M, W) = (M + 1) W. Use equations (8.1) and (8.2) to predict Willie's WTP and WTA. Box each value. You should have found that WTA = WTP in one of these cases and that WTA > WTP in the other. This illustrates that WTA need not always equal WTP. But what accounts for the difference in results? With the utility function in part (a), Willie's valuation of a mug does not change if his income goes up or down (i.e., no income effect). Whereas with the utility function in part (b), Willie's valuation of a mug increases with his income (i.e., a positive income effect). c. Provide intuition for the connection between (i) income effects and (ii) the relationship of WTA to WTP. Hint: By virtue of being gifted a mug, sellers have higher "incomes" than buyers. d. Which utility function do you think is more likely in the mug exchange context? Why? Box either u or u.