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:

mark me as brainliest

Step-by-step explanation:

Question 1. [Kuhn-Tucker] Answer all parts (a) – (d) of this question. An agent consumes x > 0 units of frankfurters and y > 0 units of vegetables to solve the program: (i) px + qy <M max a ln x + ß In y subject to x,y>0 (ii) h < 9 where a, ß, 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< show the optimal choice, denoted (x*, y*), is (a+b). BM αΜ ,* X BM (a + B)q: (a + B)p; * BM (c) [7 marks] Solve the necessary conditions for optimality when instead h > (a+Ba (d) [10 marks] Prove your answers above describe a global maximum.