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Lecture 7

Lecture 7. Price Theory. Allocating Goods Over Time Chapter 17. Words to Know. bond coupon bond default risk discount dividends endowment face value maturity date nominal interest rate perpetuity present value real interest rate representative agent

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Lecture 7

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  1. Lecture 7

  2. Price Theory Allocating Goods Over Time Chapter 17

  3. Words to Know • bond • coupon bond • default risk • discount • dividends • endowment • face value • maturity date • nominal interest rate • perpetuity • present value • real interest rate • representative agent • Ricardian Equivalence theory • risk premium

  4. Introduction • Tools of consumer theory applied to borrowing and lending • Interest rates and relative pricing • Applications • Determining interest rates • Relax assumptions for a richer understanding

  5. Section 17.1 Bond and interest rates

  6. Bonds and Interest Rates • In a trade, you are simultaneously a seller and a buyer. • Bond • Promise to pay at some future date • Lender • Buy bond • Borrower • Sell bond

  7. Relative Prices • Interest rate • Measure of relative price of bond • Present value • Relative price in terms of current consumption (or current goods) • When interest rate is r, the relative price of tomorrow’s good is 1/(1+r) in terms of today’s goods, which is exactly the current value of tomorrow’s good.

  8. Relative Prices • Price of bond equal to present value of what promises to deliver. • So a bond that promises 1 apple tomorrow sells for a price of 1/(1+r). • Face value is the amount that a bond promises to pay (1 apple tomorrow) • Discount of a bond equals its face value minus its current price (1-1/(1+1)) • Maturity dateis the date on which a bond promises a delivery

  9. Relative Prices • Coupon bonds – a bond that promises a series of payments on different dates. • Perpetuities - a bond that promises to pay a fixed amount periodically forever.

  10. Bonds • Bonds usually promise to pay in dollars, so we need to consider inflation. • Nominal interest rate • Real interest rate • Approximately:

  11. Bonds • Default risk: The possibility that the issuer of a bond will not meet obligations. • Risk premium: Additional interest, in excess of the market rate, that a bondholder receives to compensate him for default risk

  12. Applications • Valuing productive asset • Corporate Stocks • Valuing durable assets • Cash or credit payment • Government debt • Planned Obsolescence • Artists’ Royalties • Land tax • Pricing exhaustible resources

  13. Land Tax • Coconino county imposed an annual tax of 10% per acre on all landowners 150 years ago. • Now the major claim that the tax is unjust so should be rescinded.

  14. Pricing exhaustible resources • Assuming that coal is sold at P0 now, and will be sold at P1 tomorrow. • The cost of digging out one unit of coal is MC. • The present value of the foregone opportunity for using up one unit of coal today is:

  15. Pricing exhaustible resources • The full marginal cost of removing the selling a unit of coal is equal to the sum of the marginal cost of digging it out and the present value of the foregone opportunity: • A competitive producer will choose a quantity where the current price is equal to this full marginal cost:

  16. Pricing exhaustible resources • A competitive producer will choose a quantity where the current price is equal to this full marginal cost:

  17. Market for Current Consumption • Consumer’s choice • Endowment is assumed • Time preference is assumed • Opportunities is represented by all feasible points alone the BC

  18. Market for Current Consumption • Consumer’s choice • Endowment is assumed • Time preference is assumed • Opportunities is represented by all feasible points alone the BC

  19. Demand for Current Consumption • Net borrowing or lending • Dependent on interest rate • Supply of current consumption • Fixed and vertical • Equilibrium

  20. Representative agent • An alternative way to the determination of equilibrium. • It refers to someone whose tastes and assets are representative of the entire economy. • Find the absolute slope of the representative agent’s indifference curve at the endowment point, and subtract one to obtain the market interest rate.

  21. Lower r is better? • An increase in interest rate hurts borrowers but benefits lenders. • But which one outweights the other?

  22. Comparative statics • An increase in future supply • An increase in current supply • A permanent productivity increase • Government debt – taxation or borrowing?

  23. Comparative statics • An increase in future supply • An increase in current supply • A permanent productivity increase • Government debt – taxation or borrowing?

  24. Comparative statics • An increase in future supply • An increase in current supply • A permanent productivity increase • Government debt – taxation or borrowing?

  25. Comparative statics • An increase in future supply • An increase in current supply • A permanent productivity increase • Government debt – taxation or borrowing?

  26. Recardian Equivalence • Neutrality of fiscal expansion: statement that government borrowing has no effect on wealth, consequently no effect on the demand for current consumption, and consequently no effect on the interest rate. • It depends on when government borrows today, whether the general public would expect that taxes will increase tomorrow.

  27. Production and Investment • In the previous model, we treated the number of apples available today and tomorrow as fixed and unchangeable. • A more complete model should take account of opportunities for current goods to be converted into future goods on an economy-wide basis. • Possible channels • Storage • Capital production

  28. Demand for Capital • Inputs to physical production process • Marginal product • Additional output available when one additional unit employed • Diminishing rate of marginal product of capital • Interest rate • Quantity of capital adjusts until interest rate equal to marginal product of capital (This statement is misleading, why?)

  29. Supply of Current Consumption • More capital demanded • Less current consumption supplied • Low interest rate • More capital demanded • Few resources available for current consumption

  30. Equilibrium • Derive demand for current consumption • Supply slopes upward • Relaxation of assumptions • No change from earlier conclusions • Brighter future, interest rate rises

  31. PriceInflation • Define the inflation rate by p where • For example,p = 0.2 means 20% inflation, andp = 1.0 means 100% inflation.

  32. Price Inflation • We lose nothing by setting p1=1 so that p2 = 1+ p . • Then we can rewrite the budget constraintas

  33. PriceInflation rearranges to so the slope of the intertemporal budgetconstraint is

  34. Price Inflation • When there was no price inflation (p1=p2=1) the slope of the budget constraint was -(1+r). • Now, with price inflation, the slope of the budget constraint is -(1+r)/(1+ p). This can be written asr is known as the real interest rate.

  35. Real Interest Rate gives For low inflation rates (p»0), r »r - p .For higher inflation rates thisapproximation becomes poor.

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