A visitor to a recreational site has the utility function U(C, v) where v is visits...

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A visitor to a recreational site has the utility function U(C, v) where v is visits to the site and C is consumption of all other goods. For convenience, set the price of C equal to 1; the recreation site has an entrance fee P. Thus, the visitor's budget constraint is C + Pv s Io, where lo is exogenous income. (10 points) Show the visitor's objective, write the Lagrangian, and find the first-order and second-order conditions for the visitor's utility maximization problem. b. (5 points) Draw a generic graphical solution for this problem-clearly mark your axes, slopes etc.) and interpret the first-order conditions. c. (10 points) Using the implicit function theorem (by deriving the total differential) sign the effect of P on v if visits are a normal good (that is, visits v increase when income lo increases). d. (5 points) Using the envelope theorem, precisely interpret the Lagrange multiplier. A visitor to a recreational site has the utility function U(C, v) where v is visits to the site and C is consumption of all other goods. For convenience, set the price of C equal to 1; the recreation site has an entrance fee P. Thus, the visitor's budget constraint is C + Pv s Io, where lo is exogenous income. (10 points) Show the visitor's objective, write the Lagrangian, and find the first-order and second-order conditions for the visitor's utility maximization problem. b. (5 points) Draw a generic graphical solution for this problem-clearly mark your axes, slopes etc.) and interpret the first-order conditions. c. (10 points) Using the implicit function theorem (by deriving the total differential) sign the effect of P on v if visits are a normal good (that is, visits v increase when income lo increases). d. (5 points) Using the envelope theorem, precisely interpret the Lagrange multiplier.

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a The visitors objective is to maximize utility UC v subject to the budget constraint C Pv lo where ... View the full answer