Question

A consumer has an income of $90 and they face the following prices: Px​ =$5 and Py​

=$3. The consumer prefers good X three as much as good Y and is willing to trade good X and good Y at a constant rate. 1. Write the consumer's utility function that represents their preferences: U(X,Y)= 2. Using the information available, calculate the consumer's optimal consumption bundle. X∗ = units Y∗ = units - The consumer's total utility is U(X,Y)=

Answer 1

The consumer's utility function is U(X,Y) = 3X + Y. The optimal consumption bundle is X* = 15 units and Y* = 5 units. The consumer's total utility is U(X,Y) = 50.

Step-by-step explanation:

To find the consumer's optimal consumption bundle, we need to compare the ratio of the marginal utility to price of good X with the ratio of the marginal utility to price of good Y. Since the consumer prefers good X three times more than good Y, we can assign a utility function with a utility of 3 for good X and 1 for good Y. This can be represented as:

U(X,Y) = 3X + Y

Now, we can calculate the consumer's optimal consumption bundle by setting the ratio of the marginal utility to price of good X equal to the ratio of the marginal utility to price of good Y:

3/5 = 1/3

By solving this equation, we can find that X*=15 and Y*=5. This means that the consumer should consume 15 units of good X and 5 units of good Y to maximize their utility.

The consumer's total utility can be calculated by substituting the values of X* and Y* into the utility function:

U(X,Y) = 3(15) + 5 = 50