Econ 330

Week 3 Answers

Fall 2002

 

1.      I will not describe again how the bond and loanable funds graphs are derived since you have already seen that three times: in class, in section, and in your textbook.  I will, however, describe how these graphs change in each of the five scenarios listed:

 

i)                    In this case, when bonds become less liquid relative to other assets, it becomes more difficult or takes more time to convert bonds into cash without incurring large costs.  Since this makes bonds less attractive to hold, the demand curve for bonds shifts back to the left.  Equivalently, the supply curve for loanable funds shifts back to the left.  After the bond and loanable funds markets settle at new equilibria, the price of bonds is lower, the nominal interest rate is higher, and the quantities of bonds and loanable funds are lower.

 

ii)                   If there is a decrease in expected inflation, then for borrowers (the sellers of bonds or demanders of loanable funds), the real cost of borrowing rises at every nominal interest rate.  In other words, the real amount that a borrower must repay (the amount of purchasing power sacrificed) for a given nominal stream of interest payments on a bond has gone up because prices are expected to rise less over time.  Hence, the bond supply curve shifts to the left; at every bond price, borrowers are willing to issue fewer bonds.  This is the same thing as a leftward shift in the loanable funds demand curve.

 

As for lenders, lower expected inflation will lower the expected nominal capital gains (price appreciation over time) on physical assets such as cars and houses, which are alternative stores of wealth.  A decrease in expected inflation (e.g. from 5% to 3%) will lead to expectations of lower physical asset prices in the future.  The resulting lower expected returns on these assets will make bonds look more attractive in comparison.  Thus, the bond demand curve will shift out to the right (the loanable funds supply curve also shifts to the right). 

 

To summarize, a decrease in expected inflation will shift the bond supply curve and loanable funds demand curve to the left.  The bond demand curve and loanable funds supply curve will shift to the right.  The result is that bond prices are higher and the nominal interest rate is lower in the new equilibrium.  The change in the quantity of bonds/loanable funds exchanged cannot be determined without more information about the relative magnitudes of the supply and demand shifts.

 

iii)                 If the interest rate is above equilibrium, there is excess supply of loanable funds.  Since high interest rates are the same as low bond prices, we can also say that there is excess demand in the bond market.  This should cause bond prices to rise and, again using the inverse relationship between bond prices and interest rates, interest rates should fall.  This movement in bond prices and interest rates occurs until we return to the intersection of supply and demand in both markets.

 

iv)                 If the government is running a deficit (revenues minus expenditures is negative during a given period), then the government sells bonds to finance this deficit (it is a supplier of bonds/demander of loanable funds).  If the government deficit shrinks, then supply of bonds from the government shrinks at every bond price or nominal interest rate.  This is equivalent to a leftward shift in the bond supply curve and loanable funds demand curve.  The result is an increase in bond prices, decrease in nominal interest rates, and a decrease in the equilibrium quantity of bonds and loanable funds exchanged.

 

v)                  If the riskiness of bonds increases, they become less attractive to hold relative to other assets.  Hence, bond demand is lower at every bond price (loanable funds supply is lower at every nominal interest rate).  This is a leftward shift in the bond demand curve and loanable funds supply curve. 

 

An increase in expected profitability of capital investments increases firms’ demand for loanable funds to finance new investment expenditures.  This is equivalent to an increase in the supply of bonds.  Thus, the bond supply curve shifts right, as does the loanable funds demand curve.

 

The net result is a decrease in bond prices, an increase in nominal interest rates, and an indeterminate change in the quantity of bonds/loanable funds exchanged. 

 

 

2.  (a) In this case the coin maker and coin buyer share the same level of uncertainty about the quality of coin to be exchanged:  neither individual can tell which of the two coins is high quality and which is low quality.  We expect the valuations of the buyer and seller in this transaction to reflect this uncertainty.  The two individuals do know, however, that there is one high quality coin and one low quality coin so they know that there is a 50% chance of getting a coin of either quality.  Hence, both the coin maker and coin buyer should weight there high and low quality valuations in line with these probabilities:

 

valuation of a coin = 0.50*(high valuation) + 0.50*(low valuation)

 

When I say “valuation of a coin” it does not matter which coin type I’m talking about because the parties to the transaction cannot tell which coin type is going to change hands.  Using the formula above, the valuations chart becomes:

 

Total # of coins available

Value to the Buyer/coin

Value to the Seller/coin

2

$6,400

$4,800

 

Now suppose that the coin buyer, who is exchanging goods for coins, has goods he would like to trade with the coin maker that have a value falling between his coin valuation and the coin valuation of the coin seller/maker (assume, for simplicity, that both the buyer and seller value the goods the same).  In this scenario, both the buyer and seller would be willing to exchange one coin for the goods, since each would be getting something in return valued at least as much as what is being given up, and at least one person would be strictly gaining.  For example, if both value the goods at $5300, then the buyer is giving up $5300 worth of goods in exchange for a coin that is worth $6400 to him, a gain of $1100.  The seller is giving up a coin worth $4800 to her in exchange for goods worth $5300, a gain of $500. 

 

(b) In this case, the buyer has less information than the seller.  The seller knows which coin is the high quality coin and which is low quality, so her valuations remain as in the original table.  The buyer cannot distinguish between the two coins, so his valuations are as in the table above for each coin (assuming both coins are being offered by the seller).  If the buyer is willing to offer goods worth at most $6400 for coin, however, the seller will never be willing to sell a high quality coin; he values a high quality coin at $9000 (remember: he knows when he has a high quality coin in his hand).  Given this fact, the buyer’s coin valuation will be only $800, since he knows that only low quality coins will be offered to him by the coin maker (the buyer knows what a high quality coin is worth and therefore knows the coin maker will never sell him a high quality coin in exchange for goods worth $6400).  Thus, high quality coins will be completely driven from the market due to this informational asymmetry between buyer and seller.  The buyer will never be willing to exchange goods worth at least $9000 for a high quality coin, so the coin maker hangs on to his high quality coins and only low quality coins are used in exchange for goods from the coin buyer.  Notice now that if the buyer is offering the same package of goods worth, say, $5300, the transaction requires more than one coin, which is more inconvenient than using a single high quality coin.

 

What is the issue here? Adverse selection in the market for coins.  I found a nice description of adverse selection in the Penguin Dictionary of economics which should help your understanding of the issue:

 

Adverse Selection

 

The problem that, in certain markets, the inability of one trader to assess the quality of the other makes it likely that poor-quality traders will predominate. Noted by Akerlof in 1970, adverse selection is sometimes referred to as the lemon problem. A popular example of the phenomenon is in the second-hand car market, where sellers know whether or not their car is a lemon (i.e. performs badly), but where buyers cannot make that judgement without running the car. Given that buyers can't tell the quality of any car, all cars of the same type will sell at the same price, regardless of whether they are lemons or not. The risk of purchasing a lemon will lower the price buyers are prepared to pay for any car and, because second-hand prices are low, people with non-lemon cars will be little inclined to put them on the market.

 

There are three ingredients in this problem. First, a random variation in product quality in the market; secondly, asymmetric information about product quality between traders in the market; and thirdly, a greater willingness for poor-quality traders to trade at low prices than for high-quality ones to. (Lemon car owners will still put their cars on the market when the prices drop; other car owners will not.) There are many important markets where adverse selection is held to be significant - notably insurance and the market for credit.

 

For interest sake, I have included the Penguin Dictionary’s definition of “bad money driving out good money”, which is similar to (though not exactly the same as) the example discussed above:

 

‘Bad Money Drives out Good’

 

The idea that an injection of a low-quality coinage into a monetary system will dissuade holders of high-quality coins from parting with cash. Before paper money became universally accepted as a means for settling debts, precious metals were the most common forms of money. Gold and silver coins were struck bearing a face value equivalent to the value of their metal content. Debasement of the coinage occurred when the face value was kept above the value of the metal content of the coinage. The holders of the correctly valued coinage became unwilling to exchange for the debased coinage because they would obtain less metal in exchange than if they bought direct. The result was that the `good', undebased coinage did not circulate. The process is referred to as Gresham’s Law, and is an early application of the idea of adverse selection.