Chepa’s utility function is given by U (x, y) = ln x + 4 ln y....

Chepa’s utility function is given by U (x, y) = ln x + 4 ln y. Assume that Chepa has endowments (10, 10) and that Py = 10 throughout the problem. (h) This part of the question is to investigate Chepa’s welfare under different prices. We will do it step by step.

(i) By substituting out the M with the expression of Chepa’s endowment income (see part (g)), obtain Chepa’s gross demands as functions of Px.

(ii) Plug your answer to (i) into Chepa’s utility function (that is, replacing the general x and y in her utility function by the optimal x and y given Px) to obtain an expression of the maximal utility achieved by Chepa as a function of Px.

(iii) Find the value of Px that gives Chepa the lowest utility. (Hint: Take the answer to (ii), differentiate it with respect to Px, set the derivative to zero and solve for Px in that equation. It is a good practice to check the second order condition to make sure you are getting a minimum — but if you feel uninterested or that this is too hard, you can trust that I am giving you a “nicely behaved” minimisation problem and skip checking the SOC.)

(iv) Explain the economic meaning of your result in (iii).

Expert Solution

Rahul Sunny answered 7 months ago

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