. Met\'s preferences over consumption is defined by the following utility functi

Question

. Met's preferences over consumption is defined by the following utility function: u(c1,c2) = min[c1,2c2] . Note, c1 is Met's consumption today and c2 is Met's consumption next period.

a. Derive Met's demand for consumption today and consumption next period (let the price equal one in each period and the interest rate be 25 percent).

b. Would you describe Met's preferences by: "Live for today," or, "Save for Tomorrow"?

c. Solve for Met's optimal consumption in each period if he has 500 income that he receives each period (note: Met can borrow against his future income or save income to use in period 2).

Explanation / Answer

1.

Let the demand functions of Met be as follows,

Met's Demand for consumption be comprised of demand for consumption today and consumption next period be ,

                                                             D = D ( A, P, Y, r )

where, A = Autonomous consumption

          Price of Commodities = 1 ( Constant )

          Income = Y

          Interest Rate = 0.25 (constant)

Thus, his demand for consumption function be,

                                                 DT = D ( A, 1, Y, 0.25 )

                                                        = D ( A, Y, 0.25 )                                     ( Since , P = 1 , in both period)

where, if only income and autonomous consumption of Met increases his demand for consumption will increase and vice versa. However, if interest rate increases his demand for future consumption will increase , i.e. his savings will increase.

Thus his demand for consumption today can be separately written as,

DT = D ( A , Y)

and demand for consumption next period can be separately written as,
DNP = D (Y, 0.25 )

2.

Met's preferences by "Live for today," or, "Save for Tomorrow" could be written as follows,

"Live for today" can be written as ,                         u(c1,c2) = max [c1, 0]

"Save for Tomorrow" can be written as,   u(c1,c2) = max [0, C2]

3.                                 Met's optimal consumption in each period be stated as, C1* and C2*

Where, we know    u ( c1, c2 ) = min [ C1, 2 C2 ]

                                                            subject to , 500 = C1 + C2    

We know, r = interest rate = 0.25, thus his consumption in the next period be,

                                                               C2 = (0.25 x 500) = 125

Thus, his consumption in this period be,    C*1 = 500 - 125 = 375

But in the next period his optimal consumption will be C*2, which is added up by his previous period savings for future. Thus, in the next period he will consume the previously saved money and use it to the the then present period consumption, C*2 as

                                                    C*2 = 125 + 500 = 625

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.