Consider the following Cobb-Douglas utility function

P1= 10, P2= 5
Where x1 and x2 are the two goods and P1 and P2 are their respective prices.
(i) Determine the optimal choice of consumption of x1 and x2
(ii) Find the expression for Indirect Utility Function

To solve this problem, we'll use the principles of utility maximization and derive the optimal consumption quantities \(x_1\) and \(x_2\). We are given the Cobb-Douglas utility function and the prices of the two goods.

### Utility function:
\[
U(x_1, x_2) = x_1^2 x_2^2
\]

### Prices:
\[
P_1 = 10, \, P_2 = 5
\]

### Step (i): Determine the optimal choice of consumption of \(x_1\) and \(x_2\)

To find the optimal choice, we need to maximize the utility function subject to the budget constraint.

#### Budget constraint:
\[
P_1 x_1 + P_2 x_2 = M
\]
Where \(M\) is the consumer's income.

#### Cobb-Douglas utility functions usually result in demands that are proportional to the income spent on each good. First, we rewrite the utility function in a form where _______ ____ __________ ___ ____ _______ _____.
____ _____ ________ ______ _________ ______ _________.
________ _______ ______ ___ ______ _______ ______.
___ _____ _____ _________ __________ ______ ____ ______ ______ __________ _____.
___ ______ ________ ________ ____ ____ _______ ___ __________.
____ __________ ___ ______ __________ _________.
___ _______ ________ ___ __________ ________ ___ ____ ____.
_____ ____ ________ __________ _________ ____ ______.
____ ___ ___ ________ ______ _______ ___ ________ __________ ______ ______ _____.
______ ________ _________ _________ _______ ____.
____ ______ ___ __________ _________ ______ _________.
__________ _______ _______ _____ ______ ____ _________ ___ ______ __________ ______.
_________ ______ ___ _____ ______ __________ _______ ____.
______ ___ _________ ____ ____ _____ ____.
_______ _____ ____ ______ _____ ______ _______ ____ __________.
__________ ____ ______ __________ ____ _______.
__________ ____ _______ _______ _________ ________ ___ ______ _____ ____.
__________ __________ ___ ________ ______ __________.
___ ___ ____ ___ ____ ____ ________ __________ _______ _________.
_________ ___ ________ _____ _______ ________ ________ ________ ____ ___ ______.
__________ ________ _______ ______ ____ ______ ___ _________.
_____ ________ __________ __________ _______ _______ _______ _____ ___ __________ ___.
_______ ______ ______ ___ _________ ______ __________ __________ _________ _________ __________ ________.
____ __________ __________ __________ _______ ________ ____ ___ ______ ___.
___ ____ ________ _______ _____ ______ _________ _______ ____ ________ ____.
___ __________ __________ _____ ________ ________.
______ __________ ______ _______ __________ _______ ___ ______.
___ _________ __________ _____ ___ ________ ____.
___ ________ __________ ____ ___ ___ ____ ____ _____ ___ ____ ___.
____ ________ __________ ________ ____ ___ __________ _________ ___ ________ ______.
____ _____ ___ ______ ________ ___ __________.
__________ __________ ____ ____ ________ _______ _________ ________ ____.
__________ _______ __________ ____ ______.
______ _____ _________ ______ ___ _________ ________ _____ _____ _______ ______ ____.
____ ___ ___ ________ ____ ___ ______ __________ _________ _____.
_________ ____ ________ _________ ___.
__________ ___ ______ ______ ____ ____.
_______ _________ ________ ________ _______ ________ ____ __________.
_____ ___ _________ _______ __________ _________.
_______ _________ _________ _______ __________ ___ __________ ______ _______ _____ ___.
_________ _____ _____ ____ _____ __________ _____ _______.
________ _________ _______ __________ _________ ______ ___.
____ ___ _____ _________ ________ _________ _________ _____ _______ _________ _______.
_______ _________ __________ _______ __________ ___ ___ ________ ____ ____ _______.
__________ ______ ______ ____ ____ ________ ____ __________.
_______ _______ _________ _______ ______ ______ ____ _____ _________.
______ _______ ____ _________ _______ ___ __________ __________ ____ ______.
________ ____ ________ _____ ____ __________ _____ ____ ______ __________ _____.
_______ ___ ________ ________ __________ __________ _______ _____ ___ _________.
Get Full Answer on WhatsApp