Can somebody please explain this to me! Thanks! Suppose your life can be divided

Question

Can somebody please explain this to me! Thanks!

Suppose your life can be divided into two time periods: period 1 (working period) and period 2 (retirement period). The total income you get from working in period 1 is $2,000,000, while you know for sure that your total income from social security in the retirement period is $500,000. Your level of satisfaction from consuming goods in both periods is given by y = In C_x + (1/1+r) where C_x is the amount of money you spend for consumption in period 1, C_2 is the amount of money you spend for consumption in period 2, and r is the interest rate, which is assumed to be 5%.

Explanation / Answer

a) Marginal utility of C1 MC1= dU/dC1 = 1/C1

Marginal utility of C2 MC2= dU/dC2 = 1/(1+r)C2

MC1/MC2 = I1/I2

so (1+r)C2/C1 = 2000000/500000

so C2 = 4C1/(1+r) now r=0.05 so C2=3.81C1

b) If r=0.1 the C2 = 3.64C1 So consumption if first period is less

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