If you have an income of $40 to spend, commodity 1 costs $4 per unit, and commodity 2 costs $8 per unit, then the equation for your budget line can be written

Question

Quizplus · Accepted Answer

Let x be the number of units of commodity 1 and y be the number of units of commodity 2. Then, the equation for the budget line can be written as:

4x + 8y = 40

Simplifying, we get:

2x + 4y = 20

Dividing both sides by 2, we get:

x + 2y = 10

This equation represents a straight line on a graph with x on the horizontal axis and y on the vertical axis. The slope of this line is -1/2.

To maximize the utility with a given budget, we must choose the combination of commodities that lie on the budget line and give the highest level of satisfaction. This would be the point on the line farthest away from the origin.

The intercepts of the line are x=10, y=5. This point is the farthest away from the origin among all the points that lie on the line.

Therefore, the best choice is to buy 10 units of commodity 1 and 5 units of commodity 2, which costs $40.

Thus, the answer is C.

If You Have an Income of $40 to Spend, Commodity