Asked by Minh Anh Tr?n Ng?c on Jun 11, 2024
Verified
suppose that the demand curve for antimacassars is p 51 Q/900.The firm's profit-maximizing output is closest to
A) 16,875 antimacassars.
B) 5,625 antimacassars.
C) 3,712.50 antimacassars.
D) 11,250 antimacassars.
E) 2,812.50 antimacassars.
Demand Curve
A graphical representation showing the relationship between the quantity of a good consumers are willing to buy and its price level.
Profit-Maximizing Output
The point of maximum profitability for a company is reached when its marginal cost is equal to its marginal revenue, indicating the optimal production level.
Antimacassars
Protective coverings used on the backs and arms of furniture to prevent them from soiling or wear, typically made of fabric or lace.
- Analyze the output volumes that ensure the highest profits for organizations within different market frameworks.
Verified Answer
AT
Andrea TovarJun 13, 2024
Final Answer :
D
Explanation :
To find the profit-maximizing output, we need to use the marginal revenue (MR) and marginal cost (MC) approach.
First, let's find the MR:
MR = dTR/dQ = p(1+dQ/dS)
where dQ/dS is the inverse of the demand equation:
dQ/dS = 1/900p
Substituting this into the MR equation:
MR = p(1+1/900p) = p + 1/900
Now, let's assume the cost of producing each antimacassar (MC) is a constant $10.
To maximize profit, the firm should produce at the output where MR = MC.
MR = MC
p + 1/900 = 10
p = 899/90
Substituting this back into the demand equation:
Q = 900p/(899)
Q = 11,250
Therefore, the firm's profit-maximizing output is 11,250 antimacassars.
First, let's find the MR:
MR = dTR/dQ = p(1+dQ/dS)
where dQ/dS is the inverse of the demand equation:
dQ/dS = 1/900p
Substituting this into the MR equation:
MR = p(1+1/900p) = p + 1/900
Now, let's assume the cost of producing each antimacassar (MC) is a constant $10.
To maximize profit, the firm should produce at the output where MR = MC.
MR = MC
p + 1/900 = 10
p = 899/90
Substituting this back into the demand equation:
Q = 900p/(899)
Q = 11,250
Therefore, the firm's profit-maximizing output is 11,250 antimacassars.
Learning Objectives
- Analyze the output volumes that ensure the highest profits for organizations within different market frameworks.