Consider the market for roses in a small town.
The demand function is given by:
P = 20 - 0.25Q(D)
The supply function is given by:
P = 4 + 0.55Q(S)
The market equilibrium price for the roses is:
A) $15 per dozen roses.
B) $18 per dozen roses.
C) $5 per dozen roses.
D) $1 per dozen roses.
Indicate your specific subject in the "School Subject" box, so those with expertise in the area will respond to the question.
To find the market equilibrium price for roses in the small town, we need to equate the demand and supply functions and solve for the price (P).
The demand function is given by:
P = 20 - 0.25Q(D)
The supply function is given by:
P = 4 + 0.55Q(S)
Setting the two equations equal, we have:
20 - 0.25Q(D) = 4 + 0.55Q(S)
Now, we can solve for Q(D) and Q(S):
0.25Q(D) + 0.55Q(S) = 20 - 4
0.25Q(D) + 0.55Q(S) = 16
To determine the market equilibrium, we need to find the values of Q(D) and Q(S) that satisfy this equation. Unfortunately, we don't have specific information about the quantities demanded and supplied in this case. Therefore, we cannot find the exact market equilibrium price.
However, we can determine the possible equilibrium price range by substituting some values into the equations. Let's consider extreme cases:
1. If Q(D) = 0 and Q(S) = 0, the equilibrium price would be:
P = 20 - 0.25(0) = 20
2. If Q(D) is very high and Q(S) is very low, the equilibrium price would be lower:
P = 4 + 0.55(0) = 4
Based on these extreme cases, we can see that the market equilibrium price for roses in the small town would fall within the range of $4 to $20 per dozen roses.
Therefore, none of the given options (A, B, C, or D) accurately represents the market equilibrium price for roses in this scenario.