The correct answer is d. become flatter. When the relative price (marginal rate of transformation, MRT) of a good (in this case, T) increases, the price line will become flatter. Let’s dive into the reasoning for this correct answer and then explore why the other options are not accurate.

Correct Answer (d): Become Flatter:

The price line, also known as the budget constraint or the opportunity cost line, represents the different combinations of two goods that a consumer can afford given their income and the prices of the goods. The slope of the price line reflects the relative prices of the two goods.

When the relative price (MRT) of good T increases, it means that more units of the other good (let’s call it G) must be given up to obtain an additional unit of T. This effectively indicates that T has become relatively more expensive compared to G.

To illustrate why the price line becomes flatter in this scenario, consider a simple example with two goods, T and G. If the relative price of T rises, it implies that the opportunity cost of acquiring an additional unit of T has increased. Therefore, to purchase more T, the consumer must give up more units of G.

Now, imagine the initial price line before the increase in the relative price of T. It shows the trade-off between T and G at the original prices.

If the consumer’s budget remains the same, but the price of T has increased in relative terms, the consumer can no longer afford to buy the same combination of T and G as before. In other words, the consumer has to consume less T and more G to stay within the budget constraint.

This change in consumption preferences means that the consumer will adjust their consumption bundle along the price line to a point where they are consuming less of the now more expensive good, T, and more of the relatively cheaper good, G. As a result, the price line will become flatter because it reflects the new trade-off between T and G at the changed relative prices.

Now, let’s explain why the other options are not correct:

a. Shift Out in a Parallel Fashion:

This option is not accurate. When the relative price of T increases, the consumer will not be able to afford the same combination of T and G as before. As explained above, they will need to consume less of the relatively expensive good (T) and more of the relatively cheaper good (G) to stay within their budget constraint. Therefore, the price line does not shift outward in parallel; it adjusts its slope and becomes flatter.

b. Shift In a Parallel Fashion:

This option is also not correct. A parallel shift of the price line would imply that the consumer’s budget constraint has changed uniformly for all levels of T and G consumption. However, when the relative price of T increases, the consumer’s choices change.

They will adjust their consumption to account for the change in relative prices, making the price line flatter but not shifting it in parallel.

c. Become Steeper:

This option is not accurate. A steeper price line would imply that the relative price of T has decreased. In this case, the relative price of T has actually increased.

When a good’s relative price increases, the price line becomes flatter to reflect the higher opportunity cost of acquiring that good. A steeper price line indicates a decrease in the relative price, which is not the scenario described in the question.

In summary, the correct answer is d. become flatter because when the relative price (MRT) of a good increases, the price line becomes flatter to reflect the change in the consumer’s choices, where they consume less of the relatively expensive good and more of the relatively cheaper good to stay within their budget constraint.

This adjustment aligns with the law of demand in economics, where consumers typically buy more of a good when its relative price falls and less when its relative price rises.