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ARE 100A PSI Due electronkcally: 10/11/2018, 10am C). She currently has volunteees signed up for seven houns of phone banking and one hour of canvusing ( canvasing every day, and the volunters are not willing to switch taks from what they sigeed up for Sonia’s preferences over the two activities are given by the following Us(B,C)-5.4 x B x C Assume B and C are easily divisible into fractions (don’t worry if your answers aren’ (a) Using monotonic transformations, rewrite Sonia’s utility function in Cobb- Douglas form. That i, write the utility as a function of the form UB,where the exponents surm to 1 (b) Draw the badget set given that volunteers are only willing to perform the task they signed up for. Remember free disposal.) Make this graph large, since we will use it again later. Clearly label the axes (c) What will be the quantity (d) On the sane graph, draw the indifference curve through the consumption point for Sonia. Iadicate in which direction on the graph utility s increasing. Name one other consumption bundle on the same indifference curve. (e) what is Sonia’s marginal rate of substitution between B and C? Now suppose Sonia meets up with other local candidates who are willing to trade their volunteers’ time. Volunteers are still only willing to perform the task they signed up for, but she can trade as much of her volunteers’ time as she likes. (() Let the market price initially be that one hour of phone banking and one hour of canvasing can ench be bought or sold for $10. What is Sonia’s total effective budget in dollars? ) Write an equation for the budget set and depict it on your graph from above (h) Using the Lagrange method, solve for Sonia’s optimal consumption bundle given the budget set. Show your derivations. Is she a net buyer or a net seller of canvasers? (0) Depiet the optimal bundle on the graph from above. Draw the indifference curve this bundle lies on. Gi) Define the share of budget spent on canvasers to be the amount spent on canvasers divided by the total budget. What is Sonia’s share of budget spent on canvasers? (k) Suppose as the election draws closer, the price of canvasing increases to $20 per hour, but the price of phone banking remains the same. Write a new expression for Sonia’s budget set. (You do not need to draw this on the graph.) (1) Solve for Sonia’s new optimal consumption bundle given the new prices. (m) Did the price change make Sonia better or worse off? How do you think this answer would be different if Sonia were a net seller of canvasers? (n) Suppose a second candidate, Tang, has preferences over the two campaign activities given by What is Tang’s MRS at Sonia’s optimal consumption bundle? How does this compare to Sonia’s MRS? Given these answers, which candidate would you say has a stronger relative preference for canvasing? (o) An angry anonymous commenter on an internet message board argues that, since the exponent on canvasing is the same for both Sonia and Tang in their original utility functions, they must have the 1 of 1 same relative preference for books. Do you agree or disagree with this comment? Explain why

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