<p>For a consumer deciding between goods A and B, with a budget of w:</p>
<ol>
<li>If A and B are the same price (or if A is cheaper), the consumer will spend their entire budget on A.</li>
<li>As the relative price of A rises, there is a threshold point at which the consumer will begin to spend some of their budget on B.</li>
<li>The proportion of B bought will continue to rise with the relative price of A, until a second threshold point is reached and the consumer is spending all of their budget on B.</li>
<li>Changes in wealth do not affect the proportion of goods bought. So for instance if w doubles, the consumer will buy twice as much of A and twice as much of B as they were buying before.</li>
</ol>
<p>These preferences appear to be rational, so what is a direct utility function that could represent them?</p>

CC BY-SA 4.0
2024-03-17T02:19:52.160Z
Wouldn't you just entirely buy the cheaper one, all other things being equal?
Scott Rowe
CC BY-SA 4.0
2024-03-17T16:20:08.277Z
In this case, the goods aren't perfect substitutes, and the consumer will always get more utility from A than the same amount of B. Even if A is more expensive, they'll still buy some A (unless A is a lot more expensive).
The example I'm thinking of is investment opportunities: imagine A is an investment that aligns with the investor's interests and values and B is an investment that doesn't. The investor will want to invest entirely in A, but if B is cheaper they'll also go for B.
H Rogers
CC BY-SA 4.0
2024-03-17T21:51:57.830Z
Ok, I guess I can visualize that. For most 'goods', people would not split it up like that. Normally I think of goods as consumables.
Scott Rowe
CC BY-SA 4.0
2024-07-27T13:40:32.433Z
@HRogers See the utility function provided in this problem: https://economics.stackexchange.com/a/58881/11824
Amit
<microeconomics><utility><preferences>
What is a utility function rationalizes these preferences?
H Rogers
# What is a utility function rationalizes these preferences?

(Asked by: username_0 on 2024-03-16)

For a consumer deciding between goods A and B, with a budget of w:

1. If A and B are the same price (or if A is cheaper), the consumer will spend their entire budget on A.
2. As the relative price of A rises, there is a threshold point at which the consumer will begin to spend some of their budget on B.
3. The proportion of B bought will continue to rise with the relative price of A, until a second threshold point is reached and the consumer is spending all of their budget on B.
4. Changes in wealth do not affect the proportion of goods bought. So for instance if w doubles, the consumer will buy twice as much of A and twice as much of B as they were buying before.

These preferences appear to be rational, so what is a direct utility function that could represent them?

**Tags:** microeconomics, utility, preferences
> **Comments:**
> **username_1**: Wouldn't you just entirely buy the cheaper one, all other things being equal?  
> **username_0**: In this case, the goods aren't perfect substitutes, and the consumer will always get more utility from A than the same amount of B. Even if A is more expensive, they'll still buy some A (unless A is a lot more expensive). The example I'm thinking of is investment opportunities: imagine A is an investment that aligns with the investor's interests and values and B is an investment that doesn't. The investor will want to invest entirely in A, but if B is cheaper they'll also go for B.  
> **username_1**: Ok, I guess I can visualize that. For most 'goods', people would not split it up like that. Normally I think of goods as consumables.  
> **username_2**: @HRogers See the utility function provided in this problem: https://economics.stackexchange.com/a/58881/11824  

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## 0 answers

