Diminishing marginal utility states that as a consumer consumes more of a good, the additional satisfaction (utility) gained from each additional unit of the good decreases. In other words, the marginal utility of consumption falls as consumption increases.

Diminishing marginal utility leads to convex-to-the-origin indifference curves. This is because as the consumer consumes more of one good, the additional satisfaction gained from consuming more of that good becomes less and less. Therefore, the consumer is willing to trade less of the good with diminishing marginal utility for the other good.

Diagram: (A diagram should be included here showing a convex-to-the-origin indifference curve. The axes should be labelled 'Good X' and 'Good Y'. The indifference curve should bow inwards towards the origin.)

Diminishing marginal utility has important implications for the demand curve. It explains why the demand curve is typically downward sloping. As the price of a good falls, consumers are willing to buy more of it because the additional satisfaction they gain from consuming each additional unit is relatively high (due to diminishing marginal utility). This leads to an increase in quantity demanded.

An indifference curve shaped like a straight line indicates that the consumer is perfectly content with any combination of the two goods, as they provide equal levels of satisfaction. This means the Marginal Rate of Substitution (MRS) is constant and equal to the ratio of the prices of the two goods (MRS = P_X/P_Y).

Diagram: (A diagram should be included here showing a straight-line indifference curve and a budget line that is parallel to the indifference curve. The axes should be labelled 'Good X' and 'Good Y'. The budget line should be parallel to the indifference curve.)

The consumer’s choices are determined by maximizing utility subject to the budget constraint. The consumer will choose the combination of goods on the budget line that is tangent to the highest possible indifference curve. This occurs where the MRS equals the ratio of the prices (MRS = P_X/P_Y).

If the price of one good falls, say good X, the budget line will rotate outwards, becoming steeper. The optimal consumption bundle will move along the new budget line to a point where it is still tangent to the highest possible indifference curve. Since the price of good X has fallen, the consumer can now afford more of good X and less of good Y, leading to a change in the optimal consumption bundle.

An indifference curve is a curve on a utility graph that shows combinations of two goods that provide the consumer with the same level of satisfaction. It represents all possible combinations of goods where the consumer is indifferent between them. A higher indifference curve indicates a higher level of utility. The slope of the indifference curve reflects the rate at which the consumer is willing to trade one good for another (the marginal rate of substitution - MRS).

A budget line is a line on a utility graph that shows all possible combinations of two goods that the consumer can afford, given their income and the prices of the goods. It is derived from the consumer's budget constraint: P_XX + P_YY = Income, where P_X is the price of good X, P_Y is the price of good Y, X is the quantity of good X, and Y is the quantity of good Y.

Diagram: (A diagram should be included here showing an indifference curve and a budget line intersecting at an optimal point. The axes should be labelled 'Good X' and 'Good Y'. The budget line should slope downwards from left to right.)

Changes in income affect the position of the budget line. If income increases, the budget line shifts outwards, moving further away from the origin. If income decreases, the budget line shifts inwards, moving closer to the origin. The slope of the budget line remains constant, reflecting the relative prices of the goods.