Question

Question 1. [Kuhn-Tucker] Answer all parts (a) - (d) of this question.

An agent consumes x 0 units of frankfurters and y0 units of vegetables to solve the program:

max alna+ 3 ln y subject to

(i) px +qy < M

(ii) h≤ y

where a, 3, p, q, M, h are strictly positive constants and h describes the government guideline on minimum vegetable consumption. Assume h< M/q.

(a) [15 marks] Write down the necessary conditions for optimality.

(b) [8 marks] For the case h<

BM (a+B)q show the optimal choice, denoted (x*,y*), is

αΜ

= (a+B)p' y*

BM

(a + B)q²

(c) [7 marks] Solve the necessary conditions for optimality when instead h> BM (a+B)q

(d) [10 marks] Prove your answers above describe a global maximum.​

Answer 1

Answer:

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Step-by-step explanation:

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