MRSxy stands for Marginal Rate of Substitution between two goods, x and y. It is the amount of one good that a consumer is willing to give up in order to obtain an additional unit of the other good while remaining at the same level of satisfaction.

Explanation:

A downward sloping linear IC (indifference curve) represents the relationship between the two goods, x and y, that provide the same level of satisfaction to the consumer. The shape of the IC depends on the MRSxy.

Diminishing MRSxy:
If the MRSxy is diminishing, it means that the consumer is willing to give up fewer units of good x to obtain an additional unit of good y as the quantity of good y increases. In other words, the consumer is becoming less willing to trade good x for good y as they acquire more of good y. This results in a downward sloping linear IC.

Increasing MRSxy:
If the MRSxy is increasing, it means that the consumer is willing to give up more units of good x to obtain an additional unit of good y as the quantity of good y increases. In other words, the consumer is becoming more willing to trade good x for good y as they acquire more of good y. This results in an upward sloping linear IC.

Constant MRSxy:
If the MRSxy is constant, it means that the consumer is willing to give up the same amount of units of good x to obtain an additional unit of good y, regardless of the quantity of good y. This results in a linear IC that is neither upward nor downward sloping, but rather a straight line with a constant slope.

Zero MRSxy:
If the MRSxy is zero, it means that the consumer is not willing to trade any units of good x for an additional unit of good y, indicating that the two goods are perfect substitutes. This results in a linear IC that is a horizontal line.

In conclusion, a downward sloping linear IC indicates that the MRSxy is diminishing, meaning that the consumer is becoming less willing to trade good x for good y as they acquire more of good y.