Question

A consumer has $70 to spend on goods X and Y,PX=$5 and the PY=$1. Using the utility function below, answer the following questions: U(X,Y)=min{2X,Y} 1. Calculate the consumer's optimal consumption bundle. X= units Y= units

Answer 1

The optimal consumption bundle for the given utility function and budget constraint is 10 units of good X and 20 units of good Y, which maximizes the consumer's total utility.

Step-by-step explanation:

To find the consumer's optimal consumption bundle of goods X and Y, we need to examine the utility function U(X,Y)=min{2X,Y} and the budget constraint provided by the information that the consumer has $70 to spend, where the price of X (PX) is $5 and the price of Y (PY) is $1.

The budget constraint for the consumer is represented by the equation 5X + 1Y ≤ 70, where X and Y are the quantities of goods X and Y respectively. To maximize utility, the consumer should choose a bundle where the marginal utility per dollar is equal for both goods, as long as the utility function dictates the form of consumption. Given the utility function U(X,Y)=min{2X,Y}, for utility to be maximized, the following condition must be met: 2X = Y.

Applying this condition to the budget constraint leads to the following system of equations:

• 2X = Y
• 5X + Y = 70

Substituting 2X for Y in the budget constraint gives 5X + 2X = 70, which simplifies to 7X = 70. Solving for X gives us X = 10. Subsequently, Y = 2X, leading to Y = 20.

Therefore, the optimal consumption bundle for the consumer is 10 units of X and 20 units of Y.