Based on the provided information about Darnell's income being cut in half, we can analyze the statements related to the budget constraint and the implications of such a change. Here's a breakdown of the potential causal relationships:
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A change in S causes a change in P.
- This statement implies that a change in one variable (S) affects another variable (P). In this context, S could represent the amount of money Darnell has to spend, and P could represent prices. However, this doesn't necessarily hold in the context of a budget constraint change resulting directly from a change in income.
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The relationship between S and P is not a causal relationship.
- This statement may hold true. The budget constraint is typically influenced by income (S) and prices (P), but a change in income does not directly cause changes in prices, hence the relationship might be better understood as correlated rather than causal.
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A change in E causes a shift of the budget constraint.
- If we interpret E as income (which Darnell's situation directly involves), this statement is accurate. A decrease in Darnell's income results in the budget constraint shifting inward (or downwards), reflecting less purchasing power.
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A change in P causes a change in S.
- This statement suggests that changes in prices (P) would lead to a change in Darnell's spending ability (S), which is not accurate in the context of income changes. Rather, a change in prices impacts how much goods can be bought with a given income.
Given this analysis, the best statements that summarize the causal relationships reflected in the graph would be:
- The relationship between S and P is not a causal relationship.
- A change in E causes a shift of the budget constraint.
The other two statements do not accurately describe the relationships in this scenario.