Every consumer has a red-money income and a blue-money income and each commodity has a red price and a blue price.You can buy a good by paying for it either with blue money at the blue price or with red money at the red price.Harold has 40 units of red money to spend and 35 units of blue money to spend.The red price of ambrosia is 4 and the blue price of ambrosia is 5.The red price of bubble gum is 1 and the blue price of bubble gum is 1.If ambrosia is on the horizontal axis, and bubble gum on the vertical axis, then Harold's budget set is bounded by
A)two line segments one running from (0, 75)to (7, 40)and the other running from (7, 40)to (17, 0).
B)two line segments, one running from (0, 42)to (10, 35)and the other running from (10, 35)to (50, 0).
C)a vertical line segment and a horizontal line segment, intersecting at (10, 35).
D)two line segments, one running from (0, 75)to (10, 35)and another running from (10, 35)to (17, 0).
E)a vertical line segment and a horizontal line segment, intersecting at (7, 40).

Question

Quizplus · Accepted Answer

To find Harold's budget set, we need to first determine how much of each good he can buy with his red and blue incomes separately.

With his red income, Harold can afford: 
- 10 units of ambrosia (40 red money ÷ 4 red price per unit of ambrosia)
- 40 units of bubble gum (40 red money ÷ 1 red price per unit of bubble gum)

With his blue income, Harold can afford:
- 7 units of ambrosia (35 blue money ÷ 5 blue price per unit of ambrosia)
- 35 units of bubble gum (35 blue money ÷ 1 blue price per unit of bubble gum)

Now, we can plot these points on the graph with ambrosia on the horizontal axis and bubble gum on the vertical axis:
- Red income: (10, 40)
- Blue income: (7, 35)

We can then connect these two points with a straight line to create Harold's budget set. However, we need to pay attention to which price we use for each good. Since the red price of ambrosia is lower than the blue price, Harold can buy more ambrosia with his red income than with his blue income. Therefore, we need to split the line at the point where Harold switches from buying ambrosia with his red income to buying ambrosia with his blue income.

This point occurs when Harold has spent all of his red income on ambrosia and is left with only blue income. We can calculate that this occurs after he has bought 10 units of ambrosia (his entire red income) and 5 units of bubble gum (35 - 5 = 30 units of blue money remaining). Therefore, the point where he switches from using red money to blue money is (10, 30).

This gives us two line segments for Harold's budget set:
- From (0, 40) to (10, 40) representing the portion where Harold is only using his red income to buy goods
- From (10, 30) to (17, 0) representing the portion where Harold is using his blue income to buy goods

Therefore, the correct answer is choice D.

Every Consumer Has a Red-Money Income and a Blue-Money Income