Closing Notes on Oligopolies Moving on
Day 22 (4/29/14)
Closing Notes on Oligopolies Safety Adds
American
Safety Ads No Safety Ads
A: Low D: Low A: Very Low D: Very High
Delta No Safety Ads A: Very High D: Very Low A: Medium D: Medium
It would make sense for each company to run safety ads. Yet this doesn’t happen because its agreed upon to “not go there”. It would be bad for both to get into competition over safety.
Moving on Present Value What is the “value” of $1,000 to be received in the future? Choice: a. 1,000 Now b. 1,000 1 Year from now You should prefer A because assuming there is positive interest rate you can convert it into more than a thousand in a year. Postponing is sacrificing interest. What is the number of dollars (“x”) received today that has the same value to you as $1,000 to be received I year from now? (Same as: What is the present value of $1,000 in 1 year?) Assume for now: 1. One interest rate in economy 2. You can borrow and lend at that interest rate
R = 10%
3. There is no uncertainty For x to be the PV of $1000 in one year, x(1+.10) = 1,000 x = 1,000/1.1 = $909.09 PV of $Y in one year = y/1+r
PV of $Y in two years = y/(1+r)2 Proof: y/(1+r)2 today y/(1+r)2 (1+r) in 1 year y/(1+r)2 (1+r)(1+r) in 2 years = y PV of $Y in “t” years =
$Y (1+r )t
PV gets smaller as: 1. $Y gets smaller 2. r gets larger 3. t gets larger Decision to Buy a Machine (or any physical capital) AANR – Additional Annual Net Revenue Net – Net of operating costs of the machine Example: suppose there is a machine which will last 3 years, each year it produces 50,000 in additional output per year. So 50,000 in additional gross revenue but the machine costs 15,000 per year to operate. AANR =$50,000 – $15,000 = $35,000 per year Suppose the purchase price of the machine = 100,000 Assume AANR comes at the end of each year, an r = 10% The present value of all future ANNR = (35,000 / 1.1) + (35,000 / 1.12) + (35,00 / 1.13) = 87,040 Doesn’t make sense to buy machine because present value is less than cost of machine If the present value of the future AANR < price of machine don’t buy it > price of machine buy it = price of machine INDIFFERENT Suppose r is now 2% PV of future AANR = (35,000 / 1.02) + (35,000 / 1.022) + (35,00 / 1.023) = 100,936 But the machine Critical interest rate rc is the interest rate which makes the PV of future AANR equal to the price of the machine In general if r < rc then do the project if r > rc then don’t do the project
Project
rc
Cost
A B C D E
8 6 4.56 3 2
109 209 75 1000 60
If interest is 5% - Projects A + B will be done investment = 100 + 200 = 300 If interest is 4% - Projects A + B + C will be done investment = 100 + 200 + 75 = 375
Financial Markets A market where financial assets are bought and sold A financial asset is a promise to pay in the future (IOUs)
Primary vs secondary market Households Businesses Government Agencies
Original Buyer
Primary Market
Someone Else
Secondary Market
Bonds vs Stocks Bonds: promise to money at various or Govt Agency Stocks: promise to profits of a company
pay out given future date
sums of Corporation
pay a share of Corporations
all future
A simple bond: a “Pure Discount Bond” 1 future payment only Amazon promises to pay owner of this bond $10,000 on April 29, 2015
Suppose r = 10% PV of bond = $10,000/1.1 = $9090
Closing Notes on Oligopolies Safety Adds
American
Safety Ads No Safety Ads
A: Low D: Low A: Very Low D: Very High
Delta No Safety Ads A: Very High D: Very Low A: Medium D: Medium
It would make sense for each company to run safety ads. Yet this doesn’t happen because its agreed upon to “not go there”. It would be bad for both to get into competition over safety.
Moving on Present Value What is the “value” of $1,000 to be received in the future? Choice: a. 1,000 Now b. 1,000 1 Year from now You should prefer A because assuming there is positive interest rate you can convert it into more than a thousand in a year. Postponing is sacrificing interest. What is the number of dollars (“x”) received today that has the same value to you as $1,000 to be received I year from now? (Same as: What is the present value of $1,000 in 1 year?) Assume for now: 1. One interest rate in economy 2. You can borrow and lend at that interest rate
R = 10%
3. There is no uncertainty For x to be the PV of $1000 in one year, x(1+.10) = 1,000 x = 1,000/1.1 = $909.09 PV of $Y in one year = y/1+r
PV of $Y in two years = y/(1+r)2 Proof: y/(1+r)2 today y/(1+r)2 (1+r) in 1 year y/(1+r)2 (1+r)(1+r) in 2 years = y PV of $Y in “t” years =
$Y (1+r )t
PV gets smaller as: 1. $Y gets smaller 2. r gets larger 3. t gets larger Decision to Buy a Machine (or any physical capital) AANR – Additional Annual Net Revenue Net – Net of operating costs of the machine Example: suppose there is a machine which will last 3 years, each year it produces 50,000 in additional output per year. So 50,000 in additional gross revenue but the machine costs 15,000 per year to operate. AANR =$50,000 – $15,000 = $35,000 per year Suppose the purchase price of the machine = 100,000 Assume AANR comes at the end of each year, an r = 10% The present value of all future ANNR = (35,000 / 1.1) + (35,000 / 1.12) + (35,00 / 1.13) = 87,040 Doesn’t make sense to buy machine because present value is less than cost of machine If the present value of the future AANR < price of machine don’t buy it > price of machine buy it = price of machine INDIFFERENT Suppose r is now 2% PV of future AANR = (35,000 / 1.02) + (35,000 / 1.022) + (35,00 / 1.023) = 100,936 But the machine Critical interest rate rc is the interest rate which makes the PV of future AANR equal to the price of the machine In general if r < rc then do the project if r > rc then don’t do the project
Project
rc
Cost
A B C D E
8 6 4.56 3 2
109 209 75 1000 60
If interest is 5% - Projects A + B will be done investment = 100 + 200 = 300 If interest is 4% - Projects A + B + C will be done investment = 100 + 200 + 75 = 375
Financial Markets A market where financial assets are bought and sold A financial asset is a promise to pay in the future (IOUs)
Primary vs secondary market Households Businesses Government Agencies
Original Buyer
Primary Market
Someone Else
Secondary Market
Bonds vs Stocks Bonds: promise to money at various or Govt Agency Stocks: promise to profits of a company
pay out given future date
sums of Corporation
pay a share of Corporations
all future
A simple bond: a “Pure Discount Bond” 1 future payment only Amazon promises to pay owner of this bond $10,000 on April 29, 2015
Suppose r = 10% PV of bond = $10,000/1.1 = $9090
