Dwight works for a paper company. He has a two-year contract with his firm. This year the firm will pay himm1dollars. Next year, he will getm2dollars.

Dwight loves beets - in fact, beets are all he consumes. He would like to consume beets now, as well as in the future. Denote his current consumption of beets byc1and his next period consumption byc2. One tonne of beets costpdollars, whether he buys them this year or the next.

Dwight also has access to a savings bank account, where he can save money at the end of the first year. Denote his savings bys. He gets an interest of(100r) %i.e. for every dollar saved today, he gets(1 +r)dollars next year.

(a)Given that Dwight savedsat the end of the first period, what is his budget line in the second period?

(b)With the understanding that Dwight might be borrowing from his future in- come, what is his budget line for the first period?

Dwight is an upstanding citizen - he will not cheat the bank. Therefore, savings is just negative borrowing.

(c)Use this idea to combine the two budget lines into one budget line. [Hint: The combined "intertemporal" budget line should not have any terms containingbors.]

(d)What is the price consumption today, relative to consumption tomorrow?

(e)(Harder question) Suppose Dwight's contract lastedTperiods,T3. Denote consumption in periodtbyct, and the income in periodtasmt. Write down the budget line. [Hint: Use the same idea as above - net present value of consumption must equal net present value of income.]