Question

A consumer has $400 in income. They consume two goods, X and Y. Use the information below to answer the following questions: U(X,Y)=2x⁻⁰.⁶y⁰.⁴

MUx =1.2x⁻⁰.⁴y⁰.⁴
MUy =0.8x⁰.⁶y⁻⁰.⁶
Px =$40
Py =$10
1. Write the individual's budget constraint:
2. Calculate the individual's optimal consumption bundle - X∗ = units Y∗ = units

Answer 1

The individual's budget constraint is given by 40X + 10Y = 400. The optimal consumption bundle can be calculated by equating the marginal utility of X divided by its price to the marginal utility of Y divided by its price.

Step-by-step explanation:

The individual's budget constraint can be written as:

40X + 10Y = 400

To calculate the optimal consumption bundle, we need to find the point where the marginal utility of X divided by its price is equal to the marginal utility of Y divided by its price. By setting up the following equation:

1.2X-0.4Y0.4/40 = 0.8X0.6Y-0.6/10

Solving this equation will give us the values for X* and Y*.