To calculate the elasticity of supply, we need to use the formula:
Elasticity of Supply = (% change in quantity supplied) / (% change in price)
Given the supply function Q = 10 + 2p, we can determine the quantity supplied at a price of $10:
Q = 10 + 2(10) = 10 + 20 = 30
Now, let's calculate the elasticity of supply at this price. We'll consider a small change in price to calculate the percentage change in quantity supplied.
When the price is $10:
Q = 30
Let's consider a small increase in price to $11:
Q' = 10 + 2(11) = 10 + 22 = 32
Now we can calculate the percentage change in quantity supplied:
Percentage change in quantity supplied = (Q' - Q) / Q * 100
= (32 - 30) / 30 * 100
= 2/30 * 100
= 6.67%
Next, we calculate the percentage change in price:
Percentage change in price = (11 - 10) / 10 * 100
= 1/10 * 100
= 10%
Finally, we can calculate the elasticity of supply:
Elasticity of Supply = (% change in quantity supplied) / (% change in price)
= 6.67% / 10%
= 0.67
Therefore, the elasticity of supply of apples when the price is $10 is 0.67.
The closest option to this value is option OD. 0.67.