Amy has income of M4 and consumes onlyr two goods: composite good y with price $1 and chocolate (good 3:) that costs $10,, per unit. Her preference ordering can be represented by a utility function is Uta, y). Assume preferences are well behaved. 1. To derive Marshallian demand function for chocolate, state Amy's opti- mization problem. What is the objective function? 1What is a constraint? 2. Draw the Amy's budget constraint. Place chocolate on the horizontal axis, and \"expenditure all other goods" on the vertical axis. What is the oppor- tunity cost of the chocolate? How it is related to the slope of the budget constraint? Why? 3. On a graph indicate the solution to 1). What are the two conditions that must be satised for a consumption bundle to be optimal? Explain why each must be satised. 4. Assume that the price of chocolate increases from p, to p?" per unit, op. In the optimal choice diagram, illustrate this new optimal basket for Amy. Is Amy better off or worse off at this new optimal basket than at the basket found in part 3)? Explain. 5. Decompose graphically the total effect of chocolate price change into in- come and substitution effects. 6. Based on your graph, is chocolate normal or inferior good? Explain. ?. Is it possible that Amy's demand for chocolate is upward-sloping? Explain