# Consumer Theory - Utility / Costs / Preference

I have the following question:

Violet buys two goods, toys and pens. We do not observe her preference but we know it satisfies the three assumptions, completeness, transitivity, and more is better. We also know her preference does not change with prices or income. Initially, Violet’s income is \$60, the price of toy is \$4 and the price of pen is \\$2, and Violet chooses to consume 5 toys and 20 pens to maximize her utility. Let A denote this basket. At basket A, Violet gets a utility of 40.

Now suppose the prices of toy and pen both change while Violet’s income remains the same. Given the new prices, Violet still gets a utility of 40 when she consumes her new optimal basket. What can you say about how much basket A costs Violet given the new prices?

I can concluded that the new optimal basket and basket A lie on the same indifference curve since they give the same amount of utility.

Based on my understanding*, I have considered 2 situations -

1. Basket A is the point in which the tangent line meets the indifference curve.
2. Basket A and the new optimal basket lie on the same kink of a particular curve.

Can i say that when the price change is an increment, then Basket A costs less than the new optimal basket? On the other hand, a decrease in prices will cause Basket A to cost more.

*Sorry if my understanding is flawed

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