Analyzing Break-Even Pricing and Production Decisions

 

Analyzing Break-Even Pricing and Production Decisions

Given the information provided – selling 1,000 units per week, average variable cost of $20, average cost of $55, and a selling price of $5 per unit – we will determine the break-even prices for the short run and long run. We will also assess whether the firm should continue to produce or shut down in each scenario.

Calculating Break-Even Prices:

1. Short Run Break-Even Price:
In the short run, the break-even price covers only variable costs as fixed costs are considered sunk. The break-even price is equal to the average variable cost.
Short Run Break-Even Price = Average Variable Cost
Short Run Break-Even Price = $20

2. Long Run Break-Even Price:
In the long run, all costs, including fixed costs, must be covered for the firm to break even. The break-even price is equal to the average cost.
Long Run Break-Even Price = Average Cost
Long Run Break-Even Price = $55

Production Decision Analysis:

Time Continue to Produce Shut Down
Short Run If selling price > Short Run Break-Even Price ($20), continue to produce. If selling price < Short Run Break-Even Price ($20), shut down.
Long Run If selling price > Long Run Break-Even Price ($55), continue to produce. If selling price < Long Run Break-Even Price ($55), shut down.

Evaluation Based on Selling Price of $5 per Unit:

1. Short Run:

– Selling Price ($5) < Short Run Break-Even Price ($20): The firm should shut down in the short run as it cannot cover its variable costs.

2. Long Run:

– Selling Price ($5) < Long Run Break-Even Price ($55): The firm should also shut down in the long run as it cannot cover all costs, including fixed costs.

In conclusion, based on the given selling price of $5 per unit, the firm should shut down both in the short run and long run as it is unable to cover its costs and break even at this price level. Making informed production decisions based on break-even analysis is essential for ensuring profitability and sustainability in a competitive market environment.