Ch8 Banks and Money

指 導 老 師：李 永 銘 老師學 生：李 珮 鈺 9464505 楊 仁 宏 9464518 黃 昭 容 9464521 李 淑 君 9564505日 期： 2006.11.16

Outline

Switching Costs and Competition A model of switching costs and fee competition Empirical estimations of switching costs

Automatic Teller Machines (ATMs) A model of banks competition with ATMs Incompatible ATMs Compatible ATMs One –way compatibility

Media of Exchange as Network Money and network effects Coexistence of different payment instruments

A model of switching costs and fee competition

Step1:Let:

:the fee charged by bank i

:the cost of switching from bank i to a new account in a different bank

:the utility of a consumer served by bank i

Step2:The profile of bank i ,as a function of fee charged and the number of accounts is:

A model of switching costs and fee competition

Step3:We index the banks so that 1 has the largest number of accounts, bank 2 has the second-largest number of accounts, and so on

Step4:

A model of switching costs and fee competition

Step5:The fees are observed, we can now solve for the unobserved switching costs of the customers of each bank.

Step6:The smallest bank assumes that it is targeted by bank 1, it maximizes

Step7:Since and are observed, we can solve for the unobserved remaining switching cost

Empirical estimations of switching costs-In the market for demand deposits

The Finnish banking industry 1997.All figures are in $U.S. Lifetime discounted sum of fees are based on a 4% real interest rate.

Empirical estimations of switching costs-In the market for demand deposits

•The large banks in general serve customers with high switching cost.•The smallest bank serves customer with no switching cost.•Switching costs account for between 0% to 11% of average balance a depositor maintains with the bank.

Empirical estimations of switching costs-In the market for loans

•Switching costs decline with the size of the bank as measured by the number of branches each bank maintains .

Deposit-account market, switching costs tend to rise with the size of the bank as measured by the number of accounts.

Market for loans, switching costs tend to decline with the size of the bank as measured either by the number of branches or the total loan size.

Empirical estimations of switching costs-Deposit accounts versus the market for loans

A model of banks competition with ATMs

Let::the fee charged to each bank i account holder

:the cost to a customer who switching from bank to another.

:the utility of a consumer served by bank i

:the number of ATMs of A bank

Incompatible ATMs

DefinitionBank i is said to be undercutting the fee set

by bank j if bank i reduces its fee so that all the customers of bank j switch to bank i .

Incompatible ATMs

Bank A sets the highest subject to the constraint that bank B will not find it profitable to undercut .Formally, is determined by

Similarly, is determined by

Incompatible ATMs

The equilibrium fee charged by each bank

Since each bank serves consumers, the profit levels are given by

Industry profit is given by

Incompatible ATMs

Proposition 8.1Each bank increases its fee when it increase

the number of installed ATMs relative to the competing bank.

Compatible ATMs

All customers of all banks are served by all ATMs

All ATMs are available to all consumers regardless of which bank maintains their account, undercutting is independent of the number of ATMs installed by each bank

The aggregate industry profit equals to

One-way Compatible

Suppose now that bank A males its ATMs available to all customers including the customers of bank B; however bank B installs incompatible ATMs so that only the customers of bank B can access its ATMs.

Bank A attempts to undercut the fee set by bank B and attract B’s customers it must set its undercutting fee to

Bank B attempts to undercut the fee set by bank A and attract B’s customers it must set its undercutting fee to

One-way Compatible

The profit levels are

The industry profit under one-way compatibility is

Banks competition with ATMs

Proposition 8.2The profile level of a bank declines when it

makes its ATMs available for the customers of a competing bank.

Media of Exchange as Networks- Money and network effects

Pure exchange economy： the effect of fiat money

Proposition 8.3 Suppose that there is no money in this economy any meeting between any two people will result in no trade. A barter economy cannot achieve a Pareto-optimal allocation

Media of Exchange as Networks- Money and network effects

Pure exchange economy： the effect of fiat money

AliceLikes applesHas bananas

BenjaminLikes bananas

Has carrots

CharlieLikes carrotsHas apples

$

$$

bananas

apples Carrots

Proposition 8.4 An introduction of fiat money into an economy supports trades that result in a Pareto-optimal allocation.

Proposition 8.5 It is sufficient that a relatively small number of individuals refuse to trade with money for having all individuals in the economy refusing to accept money in return for goods.

Proposition 8.6 even in states of public panic concerning the loss of value of the currency, currency could still serve as the main medium of exchange as long as governments accept tax payments and playsalaries using currency notes.

Money and network effects

Media of Exchange as Networks- Coexistence of different payment instruments

Two types of interacting agents： (1)Buyers

(2)Merchants

Three means of payment： (1)electronic-cash cards

(2)currency notes and coins

(3)charge cards

Merchants’s Costs for each means of payment

Assumptions on the non-fee costs merchants must bear when accepting each medium of payment

Currency： (1)Loss of time ΥM

(2)0 λ≦ M 1≦ (3)per-transaction cost of ΥM + λMPElectronic cash cards： no physical costs are associated with

electronic cash card transactionsCharge cards： from a consumer is required to get an

authorization that verifies that the customers has a sufficient credit to cover fro the purchase.Let φdenote the merchant’s credit verification per-transaction cost.

Merchants’ ranking of payment media

Buyers’ Costs for each means of payment

Currency： (1)The value of lost time ΥB

(2)Loss of money with probability λB

(3)per-transaction cost of ΥB + λB PElectronic cash card

(1)Loss of the card with probability λB

(2)Loss of e-cash due to magnetic errors

resulting in a loss of reading capability ,

with probability of γB

(3)per-transaction cost of (λB +γB) PCharge cards： assume that charge cards do not impose any p

hysical costs

Buyers’ ranking of payment media

Equilibrium usage of payment media

Equilibrium determination of payment media

Proposition 8.71. Let ΥB /γB<(φ-ΥM)/M ， three payment will coexist2. Small transactions will be paid for with electronic cash cards mediu

m-sized transactions with currency notes and coins large transaction with charge cards.

3. A reduction in the probability of magnetic errors, γB,in electronic cash cards,or a reduction in merchants’ credit verification cost, φ,can bring into the elimination of currency as a means of payment.

As soon as confidence is built around these cards,buyers will substitute electronic cash cards for notes and coins,which are extremely hard to handle.

Q & A