Lentz's Incorporated sells paper in a perfectly competitive market at a price of $2 per ream. At the profit-maximizing (cost-minimizing) level of output, average total cost is $2.50 per ream and average variable cost is $1.95 per ream. Should the firm continue to operate in the short run? Explain.
To determine whether the firm should continue to operate in the short run, we need to consider its profitability. In a perfectly competitive market, profit maximization occurs at the point where marginal revenue (MR) equals marginal cost (MC). In this case, we are given the market price of $2 per ream.
First, let's calculate the firm's average variable cost (AVC). AVC is the total variable cost (TVC) divided by the quantity of output. Since we are given the AVC as $1.95 per ream, we can assume that the TVC is also $1.95 per ream.
Profit is calculated as the difference between total revenue (TR) and total cost (TC). TR is obtained by multiplying the market price ($2) by the quantity of output. TC consists of the sum of total fixed cost (TFC) and total variable cost (TVC).
In this case, we are not explicitly provided with TFC or TVC, but we can deduce the information we need by working backwards. If the average variable cost (AVC) is given as $1.95 per ream and the average total cost (ATC) is given as $2.50 per ream, we can infer that the difference between ATC and AVC ($2.50 - $1.95 = $0.55) represents the average fixed cost (AFC) per ream.
Let's say the quantity of output is q reams. We can use this information to calculate the total cost (TC) as the sum of TFC and TVC. Since AFC is fixed (it doesn't change with the quantity of output), it can be found by multiplying AFC by q.
TC = TFC + TVC
TC = AFC * q + AVC * q
TC = (AFC + AVC) * q
TC = $0.55 * q + $1.95 * q
TC = $2.50 * q
Now, let's calculate the total revenue (TR) at the given market price of $2 per ream.
TR = Price * Quantity
TR = $2 * q
To determine the profit (π), we subtract TC from TR.
π = TR - TC
π = $2 * q - $2.50 * q
π = -$0.50 * q
If the profit (π) is negative, it means that the firm is experiencing losses. In this case, the profit is -$0.50 * q, which is negative for any positive quantity of output (q). Therefore, the firm is making losses at the profit-maximizing level of output.
In the short run, a firm should continue to operate if it can cover its variable costs, as shutting down would still incur fixed costs. In this case, the firm's AVC is $1.95 per ream, which is less than the market price of $2. Therefore, the firm should continue to operate in the short run, even though it is making losses. By doing so, it can cover its variable costs and contribute towards covering some of its fixed costs.
However, it's important to note that in the long run, firms in a perfectly competitive market will exit if they continuously make losses. This is because in the long run, all costs are variable, and firms cannot sustain losses indefinitely.