Question

Consider the two-period model of consumption-savings decisions with a perfect credit market. An intertemporal consumption-savings decision implies an economic trade-off between current and future consumption, where the interest rate is used to identify the present value of future consumption goods. (a) Starting from the consumer’s current-period and future-period budget constraints, derive the consumer’s lifetime budget constraint. (b) Re-write the lifetime budget constraint in slope-intercept form, and draw a graph of the consumer’s lifetime budget constraint. (c) Suppose that you win the lottery, which offers a one-time large cash settlement. How would this change your (i) current consumption, (ii) future consumption and (iii) savings, as predicted by the model? Draw a graph and make reference to it when answering this question. (d) Suppose that instead of winning the lottery, you are offered a job that will begin immediately after you graduate from Brock University. How would this change your (i) current consumption, (ii) future consumption and (iii) savings, as predicted by the model? Draw a graph and make reference to it when answering this question.

Answer 1

a. The consumer's PVBC is the consumer's life time budget constraint. It says; the Present value (Pu) of lifetime consumption = the pv af lifetime escome- the pr of life time toxes. Present value means the value in terms of the Consumption goods in periodi, That is this is the relative price of future consumption in terms of current consumption. & One unit of consumption today is equivalent to sto units of consumption tomorrow.

Ct c+ 1 = y + 4 to 16 ty 1+ tr lifetime wealth Denote the listine wealth by we = y tu f tit which is the lifetime resource a consumer has for consumption today and tomorrow, * We can rewrite the PUBC as, c+ 1 tr = we e'= we (1+0),– (1+0) C y-intercept slope. b. The equation y= Pb Bt Pw W defines all the (BW) pairs that cost exactly yo The equation called Budget constraint. Any (BW) pair that lies below the Budget constraint is affordable.

All pairs (bundles) that lie on or below the Budget constraint are the Budget set. Any pair that lies above can't be purchared with y. * Put W on the vertical and B on the horizontal axis of a graph. The Budget constraint can also be written: W=y/Pw - Pb/Pw B. The vertical intercept is ylpw. the slope us - Pb/Pw - and the horizontal intercept is y/pb. Y/Pw= 100 0 5 10 is ab 25 Y/P=20. & we get Pw=1, P6=s and Y=100

C J o Lottery officials draw five white balls out of a drum with 49 balls and one red ball from drum with 42 red balls, Players win prizes when the numbers on theirs ticket match some or all of the numbers drawn (the order in which the numbers are drowon does not matter). There are aways to win. Hort dere for in - future - Consumption 80% You Match You win JACKPOT $100,000 $5,000 $100 Odds lin 80,089, 128 lin 1,953,393 lin 364,041 in 8879 1 in 8466 I in 206 I in 605 1 in 118 I in 74 5 white balls of the red ball 5 white balls but not red ball 4 white balls and the red ball 4 white balls but not red ball 3 white balls & the red ball 3 white balls but not red ball & white balls & the red ball I white ball & the red ball o white ball & the red ball $100 a tots $7 $7. $4 $3