Ernie is a deeply committed lover of rubber duckies. Assume his preferences are CobbDouglas over rubber duckies (denoted by r on the xaxis) and a numeraire good (note: we use the notion of a numeraire good to represent a composite good of all other consumption goods in this example, that means everything other than rubber duckies its price is always $1]. El. Ernie earns a salary that provides him a monthly income of $90. Last month, when the price of a rubber duckie was $2, he bought 30 rubber duckies. Using what we know about the relationship between the parameters of the CobbDouglass utility function and expenditure shares, write down the specific utility function for Ernie (i.e. put in the appropriate numbers for a and 1 a: with a: denoting the weight put on rubber duckies}. Use your answer to part {a} to derive Ernie's Marshallian Demand for rubber duckies, his Compensated Demand for rubber duckies, his Compensated Demand for the numeraire good, and his expenditure function. Confirm your expenditure function is correct by taking the partial derivative with respect to rubber duckies you should get the compensated demand again. Imagine Governor Oscar T. Grouch sees Ernie as representative of the voting public. He is worried about being reelected, given that citizens like Ernie are about to be made unhappy by his new tax on rubber trees, which will increase the market price of rubber duckies from $2 to 54. Use the implied change in the Expenditure Function to compute Ernie's Compensating Variation for this price increase, that is, the amount that Ernie would need to be paid to maintain his original utility given the new price for rubber duckies. Draw a rough graph of the Marshallian Demand. Measure and show the loss of Consumer Surplus {565} that would be associated with this price increase using the Marshallian demand curve rather than the compensated demand curve. Now redraw your graph from part id] and add the Compensated Demand function for rubber duckies. Denote both CV and ACE on the graph Identify the difference between CV and 3C5 and clearly label it. Briefly provide intuition, using the Slutsky equation, for why CV and CS diverge. What factors cause the divergence between CV and CS to be large or small? Make sure your answer is no longer than 3 sentences