a monopolist can produce at a average cost of AC rs 5 . it faces market demand curve given by Q=52-P supose second firm enter the market let q1=output market of first firm and q2=output of seond firm , let q=q1+q2 . assume that the second firm has the identical cost as the first firm . calculate equilibrium output of both the form enter the market . what is the resulting market price and profit for each firm ?
Question
a monopolist can produce at a average cost of AC rs 5 . it faces market demand curve given by Q=52-P supose second firm enter the market let q1=output market of first firm and q2=output of seond firm , let q=q1+q2 . assume that the second firm has the identical cost as the first firm . calculate equilibrium output of both the form enter the market . what is the resulting market price and profit for each firm ?
Solution
The problem is about two firms in a monopolistic competition. Here are the steps to solve it:
Step 1: Identify the given information
- Average cost (AC) = Rs 5
- Market demand curve (Q) = 52 - P
- q1 = output of the first firm
- q2 = output of the second firm
- q = q1 + q2 = total market output
Step 2: Set up the equations Since the firms are identical and in a monopolistic competition, they will split the market equally. So, q1 = q2 = q/2.
Step 3: Substitute q1 and q2 into the demand equation Q = 52 - P q = 52 - P q/2 = 52 - P P = 52 - 2q
Step 4: Set up the profit maximization equation The firms will produce where marginal cost (MC) equals marginal revenue (MR). Since the average cost is constant, MC = AC = Rs 5.
Step 5: Solve for equilibrium output Set P = MC to find the equilibrium output: 5 = 52 - 2q 2q = 52 - 5 2q = 47 q = 47/2 q = 23.5
Since q1 = q2 = q/2, each firm will produce half of the total output. So, q1 = q2 = 23.5/2 = 11.75 units.
Step 6: Find the market price Substitute q into the demand equation to find the market price: P = 52 - 2q P = 52 - 2*23.5 P = 52 - 47 P = Rs 5
Step 7: Calculate the profit for each firm Profit = Total Revenue - Total Cost = (Price * Quantity) - (Average Cost * Quantity) = (5 * 11.75) - (5 * 11.75) = Rs 0
So, each firm will produce 11.75 units, the market price will be Rs 5, and each firm will make zero profit.
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