Answer to Question #254807 in Microeconomics for Scott

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.