Question

A purely competitive firm finds that the market price for its product is $20. It has a fixed cost of $100 and a variable cost of $10 per unit for the first 50 units and then $25 per unit for all successive units.

1. Does price exceed average variable cost for the first 50 units?
2. What about for the first 100 units?
3. What is the marginal cost per unit for the first 50 units? $ per unit.
4. What is the marginal cost for units 51 and higher? $ per unit for subsequent units.
5. For each of the first 50 units, does MR exceed MC?
6. What about for units 51 and higher?
7. What output level will yield the largest possible profit for this purely competitive firm?
8. Producing units will maximize profit.

Answer 1

Answer:

1. Yes, the price exceed average variable cost (AVC) for the first 50 units.

2. Yes, the price exceed AVC for the first 100 units.

3. Marginal Cost (MC) is $10 for the first 50 units.

4. MC is $25 per unit for subsequent units.

5. Yes, MR exceeds MC for each of the first 50 units.

6. MR is less than MC for units 51 and higher

7. The firm will produce 50 units to maximize profits.

Explanation:

1. Yes, the price exceed average variable cost (AVC) for the first 50 units. The price of $20 exceeds AVC for the first 50 units because AVC for the first  50 units is ($10 per unit x 50 units)/50 units

2. Yes, the price exceed AVC for the first 100 units.

The AVC for the first 100 units is $17.50 per unit: [($10 per unit x 50 units) ÷ $25 per unit x 50 units)/100].

3. Marginal Cost (MC) is $10 for the first 50 units.

4. MC is $25 per unit for subsequent units.

5. Yes, MR exceeds MC for each of the first 50 units.

since $20 > $10

6. MR is less than MC for units 51 and higher

Since $20 < $25

7. The firm will produce 50 units to maximize profits.

This is because the Marginal Cost (MC) of the 51st  unit exceeds Marginal Revenue (MR) and profit maximization is where MR=MC