What is the equation for the budget constraint of a consumer with an income of $200, where the price of good X is $4, and the price of good Y is $8?

The budget constraint represents the combinations of goods that a consumer can buy given their income and the prices of the goods. In this scenario, the consumer has an income of $200, the price of good X is $4, and the price of good Y is $8.

The budget constraint can be formulated using the formula:

Income = (Price of X × Quantity of X) + (Price of Y × Quantity of Y)

By substituting in the values:

$200 = ($4 × X) + ($8 × Y)

This can be rearranged to isolate Y on one side:

$8Y = $200 - $4X

To solve for Y, divide all terms by 8:

Y = (200 - 4X) / 8

This simplifies to:

Y = 25 - 0.5X

This equation shows that for every additional unit of good X consumed, the consumer must give up 0.5 units of good Y to stay within their budget, illustrating the trade-off between the two goods.

Thus, this equation effectively captures the consumer’s budget constraint based on their income and the prices of goods X and Y, making it the correct choice.