Question

Mondi Company produces party boxes that are sold in bundles of 1000 boxes. The market is highly competitive, with boxes currently selling for R100 per thousand. The company has a total and marginal cost curve given by: TC = 3,000,000 + 0.001Q2 MC = 0.002Q Q is measured in thousand box bundles per year. [5] a. Determine Mondi's profit maximizing quantity. b. Calculate if the firm is earning a profit or a loss? c. Based on the analysis above, should Mondi Company operate or shut down in the shortrun?

Answer 1

Answer:

Given,

price of boxes per thousand = R100

Total cost function:

$TC=3,000,000+0.001Q^2\\MC=0.002Q$

(a). A firm in a perfectly competitive market maximizes its profit where the price is equal to the marginal cost.

$P=MC\\100=0.002Q\\Q=\frac{100}{0.002}\\Q=50,000$

At Q=50,000 the firm will maximize its profit.

(b). The formula to calculate profit or loss is given below:

$Profit=TR−TC\\Where\\,TR=P×Q\\TC=3,000,000+0.001Q^2\\Profit=100×50,000−(3,000,000+0.001×(50,000)^2)\\Profit=5,000,000−3,000,000−2,500,000\\Profit=5,000,000−5,500,000\\Profit=−500,000$

(c). To decide whether the firm should shut down or operate average variable cost is needed.

Note: if a firm's price is greater than the average variable cost then only it operates in the short run otherwise it will shut down operations.

$Variable cost=0.001Q^2\\=\frac{Variable\space cost}{Q}\\=\frac{0.001Q^2}{Q}\\=0.001Q\\=0.001×50,000\\=50$

Here, the average variable cost is less than the price (50<100) so the firm will shut down in the short run. The firm is neither covering its average total cost nor full average variable cost so it will shut down.