Guy has an income (Y)of $50 with which he can purchase DVDs (D)at $10 each and haircuts (H)at $20 each.Which one of the following represents Guy's budget line? A)Y = 10Q_D - 20Q_H B)50 = Q_D + Q_H C)Y = 50 + Q_D + Q_H D)20Y = Q_D + 10Q_H E)50 = 10Q_D + 20Q_H

Question

Quizplus · Accepted Answer

The budget line shows the different combinations of DVDs and haircuts that Guy can purchase with his $50 income. To calculate this, we can use the equation:

Y = 10D + 20H

where Y is Guy's income, D is the quantity of DVDs, and H is the quantity of haircuts.

We can rewrite this equation as:

10D + 20H = Y

or

10D = Y - 20H

Dividing both sides by 10, we get:

D = (Y/10) - 2H

This equation shows the relationship between the quantity of DVDs and the quantity of haircuts that Guy can purchase given his income. We can use this equation to plot the budget line.

If we set Y = 50, we get:

D = (50/10) - 2H

D = 5 - 2H

This equation shows that if Guy spends all his income on DVDs, he can purchase 5 DVDs (when H = 0). Alternatively, if he spends all his income on haircuts, he can purchase 2 haircuts (when D = 0). Plotting these two points and connecting them with a straight line gives us the budget line, which is represented by choice E:

50 = 10D + 20H

or

5D + 2H = 25

Guy Has an Income (Y)of $50 with Which He Can