Final answer:
The price-to-earnings (P/E) ratio is calculated by dividing the market value per share by earnings per share, not by dividing the cost of sales by average inventory. The elasticity of supply for the supply curve 4P = Q is 1 for both price increases from 3 to 4 and from 7 to 8, indicating unitary elasticity where the percentage change in quantity supplied equals the percentage change in price.
Step-by-step explanation:
When examining the price-to-earnings (P/E) ratio, it's important to recognize that this financial metric is not calculated by dividing the cost of sales by average inventory. Instead, the P/E ratio is determined by dividing the market value per share by the earnings per share (EPS). For instance, if a company has a market value per share of $100 and EPS of $5, the P/E ratio would be 20. Now, let's address the elasticity of supply for a given supply curve expressed as 4P = Q.
The elasticity of supply measures how the quantity supplied responds to price changes. To find elasticity, we need to calculate the percentage change in quantity supplied and percentage change in price, then divide the former by the latter. Let's do the calculations for the price increase from 3 to 4 and from 7 to 8.
For a price increase from $3 to $4:
- Original quantity supplied at P=$3: Q=4*3=12
- New quantity supplied at P=$4: Q=4*4=16
- Percentage change in quantity supplied: ((16-12)/12)*100%=33.33%
- Percentage change in price: ((4-3)/3)*100%=33.33%
- Elasticity of supply: 33.33%/33.33% = 1
For a price increase from $7 to $8:
- Original quantity supplied at P=$7: Q=4*7=28
- New quantity supplied at P=$8: Q=4*8=32
- Percentage change in quantity supplied: ((32-28)/28)*100%=14.29%
- Percentage change in price: ((8-7)/7)*100%=14.29%
- Elasticity of supply: 14.29%/14.29% = 1
The elasticity of supply is the same, 1 in both cases, as the straight-line supply curve represented by the equation exhibits constant unitary elasticity.