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(b) Suggest two distinct utility functions that represent such preterences. (Hint: Think about monotonic transformations.) (c) Find MRS analytically. How does MRS depend on the values of (1, 72). Intuitively explain why (d) She spends her total income of $100 paying pi $2 for each Red Delicious and p2 $1 for each Gala. Find her optimal demand and show it on the graph. (e) Describe Kates optimal choice(s) when p $1. Consumer Demand 5. For each of the following utility functions, write down a transformation that would turn it into a Cobb-Douglas utility function of the form U(x,y) = xgp where α+ β = 1. (a) U(z,y)-γιyi-a where γ is a constant. (b) U(x,y)=x2y4 6. For each of the following utility functions, write down 2 monotonic transformations th would preserve the same underlying preferences as the original utility function. (a) U(x, y) riy (b) U(x, y) = (49x + 7y)2 7. A consuners utility function is given by

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?ues-hon no.s Solubon Cob- douglas suncion V(X,y) and V(Zyl is you Cob Douglas-fand İor

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