Consumption: Part II

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2.5 Present value discount rate

  1. If you are given a chance to borrow money today so as to generate a total wealth of $10,000 one year after. How much at least do you think you need to borrow now?

If a present value discount rate for a person is \(d\), it means that: With every 1 dollar he/she sets aside, he/she is able to generate \(1+d\) dollars one period in the future.

  1. Is a higher present value discount rate good for a saver? How about for a borrower?
  1. What defines a person’s present value discount rate? A household’s present value discount rate? A nation’s present value discount rate?

2.6 Intertemporal budget constraint.

Consider an economy where borrowing interest rate \(i_{b}\) is different from saving interest rate \(i_{s}\). Construct a three-period intertemporal budget constraint for the following scenarios.

  1. The household is a saver for period one and two.

  2. The household is a borrower for period one and two.

  3. The household is a saver for period one, but a borrower for period two.

2.7 Financial asset and present value discount rate.

Assume that the only saving scheme in the economy is to buy a discount bond. For this type of bond, you pay a price of \(\$P_{B}\) for each dollar claim tomorrow. That is pay \(\$P_{B}\) now and get back \(\$1\) tomorrow. If you want ot get back $B tomorrow, you need to pay \(\$P_{B}\times B\) now. There is no explicit interest payment.

  1. What is the rate of return of the discount bond?

  2. What is the present value discount rate in this economy?

2.8 Default.

When borrowers fail to serve their debt, including missing interest payment, they are said to default.

  1. How does default affect a saver’s budget constraint?

  2. How does default affect a borrower’s budget constraint? His present value discount rate?

2.9 Technology of saving

In a self-production economy, a household can produce \(y_{1}\) and \(y_{2}\) amount of rice for today and tomorrow. Assume that no rice left unconsumed after tomorrow.

  1. Let \(c_{1}\) and \(c_{2}\) be its consumption today and tomorrow. If any unconsumed rice can be kept for tomorrow’s consumption and the only saving scheme is to keep the unconsumed rice under the bed for tomorrow, what is the intertemporal budget constraint for the household?

  2. If any rice kept under the bed would have \(\phi\) portion deteriorated tomorrow (0<\(\phi\)<1), what would be the intertemporal budget constraint?Suppose there is a rice borrowing-lending market. For any one unit of unconsumed rice lent out, you can get back 1+r units back tomorrow (assume r>0). What would be the intertemporal budget constraint?

2.10 Interest rate policy and the households

When the central bank lowers the interest rates i,

  1. How would it affect consumption today?

  2. How would it affect household’s portfolio?

  3. How would it affect capital investment?

2.11 the Economist


“Putting it all on red. The rules encourage public-sector pension plans to take more risk”, Jul 30th 2016, the Economist magazine.

Pension funds collect money from employees with a future payout promise after investors retire. The monetary obligation these funds need to fulfill is their future cost.

  • In order to access whether the funds are not bankrupt, we need to convert their revenues and costs to the same time point, usually current date. How would present value discount rate affect the cost assessment?

Private-sector pension funds in America and elsewhere (and Canadian public funds) regard a pension promise as a kind of debt. So they use corporate-bond yields to discount future liabilities. … American public pension funds are allowed (under rules from the Government Accounting Standards Board) to discount their liabilities by the expected return on their assets.

  • Why does the choice of discount rates make American public pension funds to take a riskier investment strategy?

  • For financial regulators, it is wise to set the discount rate at its upper bound or lower bound? Or depends? Why?