A consumer receives income y in the current period, income y' in the future pe- riod, and pays taxes of t and t' in the current and future periods, respectively. The consumer can borrow and lend at the real interest rate r. Suppose con- sumer's utility is represented by a Cobb-Douglas function, U(c, c') = cªc′¹-α, where 0 < a < 1. For a Cobb-Douglas utility function, the marginal rate of substitution of current consumption for future consumption, MRSc,c', is ac' (1-a)c Part a Determine analytically consumer's optimal current consumption, c*, and future consumption, c'*. Draw a graph to show your results. Part b How an increase in the real interest rate, r, impacts optimal current consump- tion, c*, and future consumption, c'*? Again, show your results analytically and graphically.