The correct answer is -1.02. This is because the optimal allocation of consumption between current and future periods depends on the marginal rate of time preference, which is the rate at which people are willing to trade current consumption for consumption in the future. With a 2% interest rate and a €20,000 current income and €45,000 future income, the marginal rate of time preference between the two periods is -1.02.

## Supporting Explanation

The marginal rate of time preference (MRTP) is a measure of how much people are willing to trade current consumption for future consumption. It is calculated by taking the ratio of the present value of future consumption to the present value of current consumption. The present value of future consumption is equal to the future income divided by the interest rate. The present value of current consumption is equal to the current income.

## The Interest Rate and MRTP

The interest rate is an important factor in calculating the MRTP. It is the rate at which people are willing to trade current consumption for consumption in the future. When the interest rate is higher, the MRTP is lower, and when the interest rate is lower, the MRTP is higher.

## Calculating the MRTP

In this scenario, the interest rate is 2%, the current income is €20,000, and the future income is €45,000. The MRTP can be calculated by taking the ratio of the present value of future consumption to the present value of current consumption. The present value of future consumption is equal to the future income divided by the interest rate, or €45,000/2%, which is €2250. The present value of current consumption is equal to the current income, or €20,000. The MRTP is then equal to €2250/€20,000, which is -1.02.

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