SOLUTION: Suppose the demand function for a monopoly's product is P=400-2Q and the average cost function is 𝐴𝐶=400/Q+4+0.2𝑄, where Q is the number of units and p is the price per un

Algebra ->  Finance -> SOLUTION: Suppose the demand function for a monopoly's product is P=400-2Q and the average cost function is 𝐴𝐶=400/Q+4+0.2𝑄, where Q is the number of units and p is the price per un      Log On


   

Question 1199609: Suppose the demand function for a monopoly's product is P=400-2Q and the average cost function is 𝐴𝐶=400/Q+4+0.2𝑄, where Q is the number of units and p is the price per unit. i) Write the Total Cost (TC) and Total Revenue (TR) functions. ii) Calculate the profit maximizing price and quantity. Determine the maximum profit.
Answer by ElectricPavlov(122) About Me  (Show Source):
You can put this solution on YOUR website!
**i) Find Total Cost (TC) and Total Revenue (TR) functions**
* **Total Cost (TC):**
* TC = (Average Cost) * Q
* TC = (400/Q + 4 + 0.2Q) * Q
* TC = 400 + 4Q + 0.2Q²
* **Total Revenue (TR):**
* TR = Price (P) * Quantity (Q)
* TR = (400 - 2Q) * Q
* TR = 400Q - 2Q²
**ii) Calculate Profit-Maximizing Price and Quantity**
1. **Find Marginal Cost (MC):**
* MC = d(TC)/dQ = 4 + 0.4Q
2. **Find Marginal Revenue (MR):**
* MR = d(TR)/dQ = 400 - 4Q
3. **Set MR = MC to find profit-maximizing quantity:**
* 400 - 4Q = 4 + 0.4Q
* 396 = 4.4Q
* Q = 90 units
4. **Find profit-maximizing price:**
* P = 400 - 2Q
* P = 400 - 2 * 90
* P = 220
5. **Calculate Maximum Profit:**
* Profit (π) = TR - TC
* π = (220 * 90) - (400 + 4 * 90 + 0.2 * 90²)
* π = 19800 - (400 + 360 + 1620)
* π = 19800 - 2480
* π = 17320
**Therefore:**
* **Profit-maximizing quantity (Q): 90 units**
* **Profit-maximizing price (P): $220**
* **Maximum Profit: $17,320**