Question

An individual consuming two goods in a quasi-linear fashion as follows:

U(x,y) = x+alny

obtains utility from their quantities, x and y respectively

(for some positive constant a).

Let p and q be the prices of goods x and y respectively and m be the income of the consumer.

The individual always consumes the bundle of goods that maximizes his utility subject to the

budget constraint. a) Solve the individual's problem using Lagrange multiplier method and derive his demand

functions for the two goods. b) Verify the envelope theorem given the solution in part (a).

(3)

(3)

c) Find partial derivatives of demands, x and y with respect to p, q and m and discuss their signs. (6)

d) Let a = 1,p=2,q = 4 and m = 10 and check the second order sufficient conditions for your solution in part (a).

(4)

e) Represent the above problem (for values of parameters as given in part (d)) geometrically.

(4)

OR

2. Let the function g be defined for all x, y by

g(x,y) = ye-ay(x² + 2x)

a) Find all the stationary points of g (x, y) and classify them by using the second-order

derivative test. b) Does g have global maximum and global minimum points? Explain your answer. (2)

(5) + (6)

494

a

1.

c) Let S = ((x,y): 0≤x≤ 4,0 ≤ y ≤3). Prove that g has both global maximum and

minimum points in S and find them.

(2)+(5)​

Answer 1

Sorry I can't understand the question..

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Answer 2

Step-by-step explanation:

Let S = ((x,y): 0≤x≤ 4,0 ≤ y ≤3). Prove that g has both global maximum and

minimum points in S and find them.

(2)+(5)