Consider a consumer whose preferences over current consumption (c1) and future consumption (c2) may be represented by the following utility function:

u(c1,c2)=min{c1,2c2}.

The consumer receives income ofm1in the first period andm2in the second period. The price of consumption in both periods is $1, and the interest rate for both saving and borrowing isr.

1. Letm1=100.00andm2=105.00, and assume that the interest rate isr=25.00 The consumer's optimal level of future consumption is:
2. Suppose the interest rate rises tor=50.00.The consumer's optimal level of future consumption is now
3. As a result of the increase in the interest rate, the change in future consumption due to the income effect is:

Please provide step by step solution