Can somebody help me on this plz.

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ZOOM 3. of 2 20 POINTS. A consumer maximizes her utility u(c, c'), by choosing c and c', where c is the amount of consumption in the current period, and c' is the amount of consumption in the future period. The utility function is log-log: u(c, c') = log(c) + log(c') , where the coefficient =0.9. The consumer's income is y = 100 in the current period andy' = 120 in the future period. The consumer pays LUMP-SUM taxes T = 20 in the current period and T' = 10 in the future period. The real interest rate at which the consumer can either lend or borrow is r = 0.1 (10% per period). a. b. c. d. e. f. Write down the budget constraints for each period. Combine them to derive the consumer's intertemporal budget constraint. Plug in the numbers and compute lifetime wealth. Plot the consumer's budget constraint in a diagram with consumption today on the x axis and consumption tomorrow on the y axis. Solve for the intercepts and the slope. Write the Lagrangian and take first order conditions to find expressions for the optimal levels of consumption in the current period, consumption in the future period, and saving in the current period: c* , c* ', and s*. Next, plug in the numbers into these expressions, to calculate the values of c*, c* ', and s*. Is the consumer a lender or a borrower? Show the consumer's optimal consumption levels in a diagram that plots her budget constraint, her indifference curves, and her endowment point (the point (y T, y' T')). Now suppose that the consumer gets a temporary 20-unit bonus at work, such that current income is higher, y = 120. Use the formulas from part c) to compute the new values for c*, c* ', and s*. Explain the effects of the temporary increase in income in words. Now suppose that current income is unchanged at 100, but the consumer learns that she will get 20-unit bonus next period, such that future income is higher, y' = 140. What are the new values for c* , c*' , and s* ? Explain the effects of the future increase in income in words.