The applicable formula is;
A = P(1-r)^n
Where;
A = Final purchasing power
P = Current purchasing power
r = inflation
n = Number of years when P changes to A
Confirming the first claim:
A = 1/2P (to be confirmed)
P = $3
r = 7% = 0.07
n = 10.25 years
Using the formula;
A = 3(1-0.07)^10.25 = 3(0.475) ≈ 3(0.5) = $1.5
And therefore, A = 1/2P after 10.25 years.
Now, give;
P = $9
A = 1/4P = $9/4 = $2.25
r = 6.5% = 0.065
n = ? (nearest year).
Substituting;
2.25 = 9(1-0.065)^n
2.25/9 = (1-0.065)^n
0.25 = (1-0.065)^n
ln (0.25)= n ln(1-0.065)
-1.3863 = -0.0672n
n = (-1.3863)/(-0.0672) = 20.63 years
To nearest year;
n = 21 years
Therefore, it would take approximately 21 years fro purchasing power to reduce by 4. That is, from $9 to $2.25.
Competitive price taker firms always earn zero economic profit in long-run equilibrium because of the following reasons which include easy entry & exit, small player etc.
Perfect competition exists when there are many sellers, firms can easily enter and exit, products are identical from one seller to the next, and sellers are price takers.
A perfectly competitive firm must accept the equilibrium price at which it sells goods because it is a price taker.
A perfectly competitive firm will be unable to make any sales if it charges even a small amount more than the market price.
Furthermore, a perfectly competitive firm must be a very small player in the overall market, allowing it to increase or decrease output without affecting the overall quantity supplied and price in the market.
Hence, Competitive price taker firms always earn zero economic profit in long-run equilibrium.
Learn more about Long-run equilibrium:
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A fee paid by a borrower to the lender for the use of borrowed money; typically interest is calculated as a percentage of the principal (original loan amount). A debt evidenced by a "note," which specifies the principal amount, interest rate and date of repayment.