Bolan's Fabric Shop sells discount material.Its demand and cost functions are Q_D = 40 - 2P and TC = 0.5Q².Its profit-maximizing price is: A) P = $5. B) P = $10. C) P = $15. D) P = $20. E) P = $0.

Question

Quizplus · Accepted Answer

To find the profit-maximizing price, we need to find the marginal revenue (MR) and marginal cost (MC) functions. 
First, we find the inverse demand function: 
QS1U1B1DS1U1B0 = 40 - 2P 
2P = 40 - QS1U1B1DS1U1B0 
P = 20 - 0.5QS1U1B1DS1U1B0 
Next, we take the derivative of this with respect to quantity to get the marginal revenue (MR) function: 
MR = dP/dQ = -0.5 
Now, we find the marginal cost (MC) function by taking the derivative of the total cost function: 
TC = 0.5QS1U1P12S1S1P0 
MC = dTC/dQ = QS1U1P1S1S1P0 
Plugging in the demand function, we get: 
MC = QS1U1(20-0.5QS1U1B1DS1U1B0)S1S1P0 
MC = 20Q - 0.5Q^2 
To maximize profit, we set MR = MC and solve for Q: 
-0.5 = 20 - Q 
Q = 40.5 
Plugging this back into the demand function, we get: 
P = 20 - 0.5(40.5) = $15 
Therefore, the profit-maximizing price is $15.

Bolan's Fabric Shop Sells Discount Material