1. Consider the single-good utility function U{x) = 3x*, with a marginal utility given by MUx = &x. Plat the utility and marginal utility functions on two separate graphs. Does this utility function satisty the principle of diminishing marginal utility? Explain. 2. Alexa likes ice cream, but dislikes yogurt. If you make her eat another gram of yogurt, she always requires two extra grams of ice cream to maintain a constant level of satisfaction. On a graph with grams of yogurt on the vertical axis and grams of ice cream on the horizontal axis, graph some typical indifference curves and show the directions of increasing utility. 3. Andrea Zunov has $20 per week to spend on any combination of pineapples and green tea. The price of a pineapple is $4 and the price of a bottle of green tea is 2. The table below shows Arnie's utility values. Use the table to answer the questions that tollow the table. Marginal Marginal Quantity of | Total Marginal | Utility per |Quantity of| Total Marginal | Utility per Pineapples | Utility Utility Dollar Green Tea | Utility Utility Doll a. Complete the table by filling in the blank spaces. b. Suppose Arncld purchases 4 pineapples and 2 bottles of green tea. Is he consuming the optimal consumption bundle? If so, explain why. If not, what combination should he buy and why? 4. Explain how the listed events (a-d) would affect the following at Hilton Hotels. .. Marginal cost & Average variable cost #. Average fixed cost v, Average totfal cost a. Hilton decides on an across-the-board 5 percent increase in executive salaries. b. Hilton decides to eliminate all print advertising. c. Hilton signs a new contract with the Culinary Workers Union that requires the company to increase wages for all its kitchen workers. d. The federal government starts to levy a $5 room tax on all hotel rooms