Some economists say that economic growth involves a trade-off between current generations and future generations. If a current generation raises its saving rate, what does it sacrifice? What will be gained for future generations?

Current consumption.

More output & More capital.

Explanation:

Economic growth is the increase in the productive base of a country within a period of time. It can also be seen as the increase in the production of goods and services produced by a country within a period of time, it is simply increase in the gross domestic product (GDP)

Savings is that part of disposable income that is not consumed. That is, that part of income that is not spent on current consumption is what we called savings, the simple equation is:

S = Yd - C

Where: S = Savings, Yd = Disposable income and C = Consumption.

When the current generation raises its savings rate, it sacrifices current consumption which is alternative forgone or opportunity cost of savings.

The gain for future generation is the accumulation of capital that will be available to them to produce more goods and services.