Let's solve this step by step:
### Step 1: Calculate Revenue for Each Output Level
First, we need to calculate the revenue for each level of output. Revenue (R) is given by the product of the market price (P) and the output (Q).
The market price is [tex]$\$[/tex]4[tex]$.
| Output (Q) | Total Revenue (R) |
|------------|-------------------|
| 0 | \( 4 \times 0 = 0 \) |
| 1 | \( 4 \times 1 = 4 \) |
| 2 | \( 4 \times 2 = 8 \) |
| 3 | \( 4 \times 3 = 12 \) |
| 4 | \( 4 \times 4 = 16 \) |
| 5 | \( 4 \times 5 = 20 \) |
### Step 2: Calculate Profit for Each Output Level
Profit (π) is given by the difference between total revenue (R) and total cost (C).
| Output (Q) | Total Cost (C) | Total Revenue (R) | Profit (π) |
|------------|-----------------|-------------------|-----------------------------|
| 0 | \$[/tex]5 | 0 | [tex]\( 0 - 5 = -5 \)[/tex] |
| 1 | \[tex]$10 | 4 | \( 4 - 10 = -6 \) |
| 2 | \$[/tex]12 | 8 | [tex]\( 8 - 12 = -4 \)[/tex] |
| 3 | \[tex]$15 | 12 | \( 12 - 15 = -3 \) |
| 4 | \$[/tex]24 | 16 | [tex]\( 16 - 24 = -8 \)[/tex] |
| 5 | \[tex]$40 | 20 | \( 20 - 40 = -20 \) |
### Step 3: Determine Short-Run Production
In the short run, the firm will produce at the output level where it has the highest non-negative profit. However, in this case, all profits are negative. Thus, the firm should choose the highest profit, even if it is less than zero.
The highest profit here is \( -3 \) when producing 3 units:
- Short-run output level: 3 units
### Step 4: Long-Run Decision
In the long run, if total revenue (TR) is less than total cost (TC), the firm will exit the market. Here's the evaluation for the chosen output level of 3 units:
- Total Revenue (TR) for 3 units: \$[/tex]12
- Total Cost (TC) for 3 units: \$15
Since TR < TC in the long run, the firm should exit the market.
### Conclusion:
1. Short-run decision: The firm will produce three units.
2. Long-run decision: The firm will exit the market.
Thus, the firm will:
- Produce three units in the short run and exit in the long run.
