Finn is in charge of decorations for an upcoming festival, and he is planning to decorate with clovers (C) and flags (F). Suppose his preferences over decorations can be represented by the utility function U(C, F) = C^(3/4)F^(1/4) For this problem, assume C and F are infinitely divisible so you don’t need to worry about restricting to whole-number answers. (a) Write Finn’s budget constraint as a function of the prices PC, PF , and his budget I. (b) Write Finn’s constrained optimization problem in Lagrangian form and derive the three first order conditions. (c) Use two of the first order conditions to show that Finn’s marginal rate of substitution (MRS) equals the marginal rate of transformation (MRT) at the optimum. (Note: You do not need to solve the constrained optimization any more than this.)
Finn is in charge of decorations for an upcoming festival, and he is planning to decorate with
clovers (C) and flags (F). Suppose his preferences over decorations can be represented by the
utility function
U(C, F) = C^(3/4)F^(1/4)
For this problem, assume C and F are infinitely divisible so you don’t need to worry about
restricting to whole-number answers.
(a) Write Finn’s budget constraint as a function of the
(b) Write Finn’s constrained optimization problem in Lagrangian form and derive the three
first order conditions.
(c) Use two of the first order conditions to show that Finn’s marginal rate of substitution
(MRS) equals the marginal rate of transformation (MRT) at the optimum. (Note: You
do not need to solve the constrained optimization any more than this.)
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