Sonia is running for office and must allocate her volunteers' time between time phone banking (B) and canvasing (C). She currently has volunteers signed up for six hours of phone banking and two hours of canvasing every day, and the volunteers are not willing to switch tasks from what they signed up for. Sonia's preferences over the two activities are given by the following:
Sonia is running for office and must allocate her mlIJJltEETS1 time between time phone banking {B} and canvasing {C}. She currently has volunteers signed up for six hours of phone banking and two hours of canvasing every day, and the volunteers are not willing to switch tasks from what they signed up for. Sonia's preferences over the two activities are given by the following: Wise} = 5.4 x 32 x C Assume B and C are easily divisible into fractions {don't 1Iliazlrry if your answers aren't always integers]. {a} Using monotonic transformations, show that Sonia's utility function can be rewritten in Cobb-Douglas form {1.3. U = snarl-u} as was; = siei. 1I'ou can solve the rest of this problem using either the original or Cobb-Douglas utility function, since they represent the same preferences, but it will be easier to solve in Cobb-Douglas form. b On a a , draw Sonia's initial endowment. Make this h lar because we will use it ' later 5" Ell-3P HE 3534-11 on. l[Nearly label the axes. {c} On the same graph, draw the indifference curve through the endowment point for Sonia. It does not need to be to scale. Indicate in which direction on the graph utility is increasing. Name one other consumption bundle that lies on the same indiiference curve. {d} What is Sonia's marginal rate ofsubstitution between B and C at this initial endowment point? 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 for1 but she can trade as much of her molunteers" time as she likes. {e} Let the market price initially be that one hour of phone banking and one hour of canvasing can each be bought or sold for $10. 1What is Socnia's total effective budget in dollars? if} Write an equation for the budget set and depict it on your graph from above. {g} Using the Lagrange method, solve for Socnia's optimal consumption bundle given the budget set. Show your derivations. Is she a net buyer or a net seller of canvasers'? {h} Depict the optimal bundle on the graph from above. Draw the indifference curve this bundle lies on. i Su ose as the election draws closer, the rice of canvasin increases to $15 er hour, but the rise of PP P E P P phone banking remains at $10. Calculate Socnia's new budget set. {You do not need to graph this.) } Solve for Socnia's new optimal consumption bundle given the new prices. {it} 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 oanvasers? {1} Suppose a second candidate. Tang1 has preferences over the two campaign aotities given by UT{B1C} = g X Elli X C What is Tang's MRS at the bundle in L1]? How does this compare to Sonia's LIES? {m} A TV pundit argues that, since the exponent on eanvasing is the same for both Sonia and Tang in their original utility functions, they must have the same preference for canvasing. Do you agree or disagree with this comment? Explain why. Sonia and Tang meet two strategists, lQuentin and Raidah, who have diHering opinions about the optimal campaign strategy. Their strategies are given, respectively, by Wise} = mines. so} URI-EC} = as+2o l of? Both advocate spending all campaign money on B and C. (n) Which strategist considers the two activities to be perfect substitutes, and which considers them perfect complements? (o) On two separate graphs, draw the shape of the indifference curves for each strategist. (p) On each graph, draw the original budget set at the price level (10,10). (q) Using the graph, solve for each strategist's optimal consumption bundle
