Final answer:
The correct answer is B) Neither the slope nor the position of the budget line change. Since both income and prices double, the purchasing power and relative prices remain the same, keeping the budget line in its original position and maintaining its slope.
Step-by-step explanation:
When both the prices of two goods and the consumer's income double at the same time, the economic situation in question involves a change in the budget line on a consumer's budget constraint graph. The budget line represents all possible combinations of two goods that can be purchased given the consumer's income and the prices of the goods. If both income and prices double, the consumer can still purchase the same combinations of goods as before because their purchasing power remains the same. Hence, there will be no change in the slope of the budget line since relative prices have not changed, nor will there be a shift in the budget line's position as the consumer's real income remains constant.
The correct answer to the student’s question is B) Neither the slope nor the position of budget line change. This is because the budget line is determined by both the income and prices of goods. If both increase proportionally, the consumer's ability to purchase goods relative to each other remains unchanged, and thus the budget line will not shift nor change its slope. The consumption of goods will depend on the consumer's preferences as depicted by the indifference curves. If a consumer decides to alter their consumption, it would be reflected in a movement along the same budget line, not a shift of the line itself.