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In the economy of Mungo there is a person called Ike
In the economy of Mungo there is a person called Ike. Ike has a red income of 40 and a blue income of 10. Blue prices are 1 bcu (blue currency unit) per unit of ambrosia and 1 bcu per unit of bubblegum. Red prices are 2 rcus (red currency units) per unit of ambrosia and 6 rcus per unit of bubblegum. You have to pay twice for what you buy, once in red currency, once in blue currency. If Ike spends all of his blue income, but not all of his red income, then it must be that:
(a) he consumes at least 5 units of bubblegum.
(b) he consumes at least 5 units of ambrosia.
(c) he consumes exactly twice as much bubblegum as ambrosia.
(d) he consumes at least 14 units of bubblegum.
(e) he consumes equal amounts of ambrosia and bubblegum
Expert Solution
The correct answer is (b): he consumes at least 5 units of ambrosia. Since Ike must pay both the blue price and the red price for either of the too commodities, the true price is the sum of the two prices. The combinations of commodity purchases that would exhaust Ike's blue income are set out in the first two columns of the following table. Ike's residual red income, after making those purchases, is calculated in the third column of the table. Note that Ike must consume more than 5 units of ambrosia in order for him to have any residual red income. So, (b) is a true statement. He must consume at least 5 units of that commodity.
Purchases that Exhaust Ike's Blue Income
| Ambrosia Purchases | Bubblegum Purchases | Residual Red Income |
|---|---|---|
| 1 | 9 | $40-((1)(2)+(9)(6))=-$16 |
| 2 | 8 | $40-((2)(2)+(8)(6)}=-$12 |
| 3 | 7 | $40-((3)(2)+(7)(6)}=-$8 |
| 4 | 6 | $40-((4)(2)+(6)(6)}=-$4 |
| 5 | 5 | $40-((5)(2)+(5)(6)}=$0 |
| 6 | 4 | $40-((6)(2)+(4)(6)}=+$4 |
| 7 | 3 | $40-((7)(2)+(3)(6)}=+$8 |
| 8 | 2 | $40-((8)(2)+(2)(6))=+$12 |
| 9 | 1 | $40-((9)(2)+(1)(6))=+$16 |
| 10 | 0 | $40-((10)(2)+(0)(6)=+$20 |
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