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## Profit, Rent,& Interest

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**Sources of Economic Profit**• reward for assuming uninsurable risks (for example, unexpected changes in demand or cost conditions) • reward for innovation • monopoly profits**Transfer Earnings**the amount that an input must earn in its present use to prevent it from transferring to another use.**Rent**the difference between what an input is actually paid and its transfer earnings**Example: Suppose you are willing to do a job as long as you**are paid at least $8 per hour, and you are getting paid $10 per hour. What are your transfer earnings? 8 What is your rent? 10 - 8 = 2**Example: Suppose an input is earning $10 per hour, but**would be willing to do the job without pay. What are the transfer earnings? 0 What is the rent? 10 - 0 = 10 (All of its pay is rent.)**Capital**• also called physical capital. • a factor of production. • examples: buildings and machines.**To purchase capital, you would probably need to borrow**funds. What does the market for loanable funds look like?**Demand for loanable funds**People borrow less if the price of the funds is high. (The price of the funds is the interest rate.) So, there is an inverse relation between the interest rate and the quantity demanded of loanable funds. So, the demand curve for loanable funds slopes downward.**Demand for loanable funds**interest rate D loanable funds**Supply of loanable funds**People are willing to lend more money if the interest rate is high. So, there is a direct relation between the interest rate and the quantity supplied of loanable funds. So, the supply curve for loanable funds slopes upward.**Supply of loanable funds**interest rate S loanable funds**Combine the demand for loanable funds and the supply of**loanable funds. interest rate S D loanable funds**The equilibrium quantity of loanable funds and the**equilibrium interest rate. interest rate S i* D Q* loanable funds**real rate of interest**money rate of interest - inflation rate If the money rate of interest is 7% and the inflation rate is 3%, what is the real rate of interest? real rate of interest = 7% - 3% = 4%**Why are there different interest rates?**• differences in costs of processing It costs more to process a $100,000 loan than a $10,000 loan, but not ten times as much. • differences in risk Will the loan be paid back on time and in full? Some people are riskier than others. • different loan durations conditions such as the inflation rate may change during the period of the loan**Components of the Money Interest Rate**• inflation premium • cost premium covering processing and risk • pure interest - price of earlier availability**The pure interest component:People are willing to pay to get**money now rather than wait until later because...**1. People prefer to have goods now rather than to have to**wait for them.**2. People can use the money to buy something that will**increase their productivity, so they can make more later.**Suppose you put $100 in the bank with an annual interest**rate of 5%. How much will you have next year? 100 + .05(100) = 100 + 5 = 105 or 100 (1+.05) 1**Suppose you leave the money in the bank. How much will you**have 2 years from now? 105 + (.05)(105) = 105 + 5.25 = 110.25 or 100 (1+.05) 2**How much will you have 3 years from now?**110.25 + (.05)(110.25) = 110.25 + 5.51 = 115.76 or 100 (1+.05) 3**1 year from now: 100 (1+.05) 12 years from now:**100 (1+.05) 23 years from now: 100 (1+.05) 3 How much will you have n years from now? 100 (1+.05) n**With an interest rate of .05, n years from now, 100**dollars will become 100 (1+.05) n Suppose you put R dollars in the bank with an annual interest rate of 5%. How much will you have n years from now? R (1+.05) n**With an interest rate of .05, n years from now, R dollars**will become R (1+.05) n Suppose you put R dollars in the bank with an interest rate of i. How much will you have n years from now? R (1 + i) n**We have concluded that if you put R dollars in the bank with**an interest rate of i, in n years you will haveR (1 + i) n . An alternative way of writing this information emphasizes the present and future aspects. Let PV be the current or present value that you are putting in the bank now and FV be the future value that you take out later. Then, we have**Present Value (PV)**• calculated by discounting, which is the opposite of compounding • also called Present Discounted Value (PDV) or Net Present Value (NPV)**Suppose you are going to receive R dollars at some time in**the future. The PV of that R dollars is the amount you need to put in the bank today, to receive the R dollars n years in the future, if the interest rate is i.**If the annual interest rate is 5% and you want to have $100**next year, how much do you have to put in the bank now ? PV = 100 / (1+.05) 1 = 95.24**If the annual interest rate is 5% and you want to have $100**in 2 years, how much do you have to put in the bank now? PV = 100 / (1+.05) 2 = 90.70**1 year: 100 / (1+.05) 1 2 years:**100 / (1+.05) 2 If the interest rate is 5% and you want to have $100 in n years, how much do you have to put in the bank now? PV = 100 / (1+.05) n**If the interest rate is .05, to get $100 in n years,**we need to put in the bank now:100 / (1+.05) n If the interest rate is .05, to get R dollars in n years, how much do you have to put in the bank now? PV = R / (1+.05) n**If the interest rate is .05, to get R dollars in n years, we**need to put in the bank now: R / (1+.05) n If the interest rate is i, to get R dollars in n years, how much do you have to put in the bank now? PV = R / (1 + i) n**We have concluded that if the interest rate is i, to get R**dollars in n years, the amount you need to put in the bank now is Since, in this case, the R will be received in the future, let’s rewrite it as future value FV. Then, we have**Notice the similarities between our compounding and**discounting formulae. Compounding: Discounting: These formulae are actually equivalent, and one can be derived from the other simply by multiplying or dividing.**Stream of Income: How much should you put in the bank now,**with an annual interest rate of i, in order to take out FV1 one year from now, FV2 two years from now, and FV3 three years from now? PV =**Stream of Income: How much should you put in the bank now,**with an annual interest rate of i, in order to take out FV1 one year from now, FV2 two years from now, and FV3 three years from now? PV = FV1 / (1 + i)1**Stream of Income: How much should you put in the bank now,**with an annual interest rate of i, in order to take out FV1 one year from now, FV2 two years from now, and FV3 three years from now? PV = FV1 / (1 + i)1 + FV2 / (1 +i)2**Stream of Income: How much should you put in the bank now,**with an annual interest rate of i, in order to take out FV1 one year from now, FV2 two years from now, and FV3 three years from now? PV = FV1 / (1 + i)1 + FV2 / (1 +i)2 + FV3 / (1 + i)3**The present value of an amount of money received (or paid)**now is that same amount of money. example: The PV of $100 received now is $100.**The PV of future income increases**• when the interest rate decreases. • when the amount of income received increases. • when the time the income is received is closer to the present.**Present Value of an Annuity**An annuity pays a fixed amount R every year from now on into the future. The present value of an annuity paying R dollars every year with an interest rate of i is PV = R / i**How do you determine whether you should make an investment?**Compare the present value of the benefits with the present value of the costs.**>**If PV(benefits) PV(costs) INVEST**<**If PV(costs) PV(benefits) DON’T INVEST