Hello, I'm really confused about how to approach this problem. I do not know how to start and am trying to figure out how to do part a- but I'm not
Question

# Hello,

I'm really confused about how to approach this problem. I do not know how to start and am trying to figure out how to do part a- but I'm not sure which equations to use?

The Optimal Bundle Trevor, a graduate student has preferences for home cooked meals (qCM) and dining out (qDO) summarized by the utility function U(qCM, qDO) = qCM0.5qDO0.5.

a) Write the expression of Trevor's marginal utility from home cooked meals. Is this declining in the number of home cooked meals?

b) Write the expression of Trevor's Marginal Rate of Substitution (MRS) of dining-out for home cooked meals as a function of qCM and qDO.

c) In a diagram measuring home cooked meals along the horizontal axis and dining out on the vertical axis, draw a couple of his indifference curves. Does Trevor consider home cooked meals a perfect substitute, an imperfect substitute, or a perfect complement to dining out? Trevor's budget for food and dining is $480. The average cost of a home cooked meal is$5 while the average cost of dining out is $16. d) Write the expression of Trevor's budget constraint. What is Trevor's opportunity cost of an extra home cooked meal (keep in mind that we assume meals are infinitely divisible, the answer is not a round number of meals consumed out of the house)? e) In a separate diagram measuring home cooked meals along the horizontal axis, draw Trevor's budget constraint. f) Use the Lagrangian method to find Trevor's optimal choice of home cooked meals and meals consumed out of the house. f.1) Write the expression of the Lagrangian function. f.2) Take the derivatives respect to qCM, to qDO, and to l (first order conditions of the Lagrangian problem) f.3) Solve for the endogenous variables qCM, qDO, and l. g) To your second diagram add an indifference curve to illustrate Trevor's optimal bundle. Suppose the price of home cooked meals increases to$8 per meal. The cost of dining out and Trevor's budget do not change.

h) Would you expect Trevor to consumer more or fewer home cooked meals? Would you expect him to dine out more, the same, or less often? Keep in mind we are just eliciting your opinion here. No wrong answer.

i) Now, solve Trevor's utility maximization problem at the new prices. What is Trevor's new optimal bundle?

j) In your second diagram, draw Trevor's new budget constraint. Then adding an indifference curve illustrate his new optimal bundle.

k) Does the result you found match your original intuition of the way a change in the price of home cooked meals would influence Trevor's consumption choices?

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