Macro Sound's is a monopolistic firm of producing headphones. Fixed daily cost of production is $1800. The production of each extra headphone is a constant of $28. From the experiences, it is known that if the price of its headphones is set at $100, nothing is sold. And for each $12 cut in price, quantity sold increased by 60 a day. This relationship continues to hold until price reduces to $16.
(a) By referring to the above information, construct a table to show the demand schedule for the price level adjusted down from $100, and the corresponding average total cost of production and profit. Also draw
an appropriate diagram for Marco Sound's demand curve, average total cost curve, marginal cost curve and marginal revenue curve.
(b) What quantity of headphone Marco Sound's produces to maximize its profit? What price should it charge?
(c) With reference to (a) and (b), what is Macro Sound's short-run economic profit or loss?
(d) In the long run, what will happen (explain in words, and no need to present any calculation) to the demand for Macro Sound's (1) the quantity of headphone sold, (2) the price charged, and (3) the economic profit?
(a) To construct the demand schedule, we start with the given information that no headphones are sold at a price of $100 and for each $12 decrease in price, the quantity sold increases by 60 per day.
Price Quantity Sold
$100 0
$88 60
$76 120
$64 180
$52 240
$40 300
$28 360
$16 420
Next, we can calculate the average total cost (ATC) and profit for each price level using the given information. The ATC consists of the fixed daily costs of $1800 plus the production cost of each additional headphone at $28.
Price Quantity Sold ATC Profit
$100 0 - -
$88 60 1800 + (60*28) (88-28)*60 - (ATC*60)
$76 120 1800 + (120*28) (76-28)*120 - (ATC*120)
$64 180 1800 + (180*28) (64-28)*180 - (ATC*180)
$52 240 1800 + (240*28) (52-28)*240 - (ATC*240)
$40 300 1800 + (300*28) (40-28)*300 - (ATC*300)
$28 360 1800 + (360*28) (28-28)*360 - (ATC*360)
$16 420 1800 + (420*28) (16-28)*420 - (ATC*420)
For the diagram, we plot the demand curve, average total cost curve, marginal cost curve, and marginal revenue curve. The demand curve shows the relationship between the price and the quantity of headphones sold. The average total cost curve represents the average cost of producing each headphone at different price levels. The marginal cost curve indicates the additional cost of producing one more headphone. And the marginal revenue curve represents the additional revenue obtained from selling one more headphone.
(b) To maximize profit, Macro Sound's should produce the quantity of headphones where marginal cost (MC) equals marginal revenue (MR). From the table, we can observe that the MC is the same as the ATC since the production cost per additional headphone is constant at $28. The MR can be calculated as the change in total revenue when the quantity sold increases by one. So, we subtract the revenue at each quantity from the revenue at the previous quantity.
To find the profit-maximizing quantity, we compare the MC and MR values at different price levels. The price that corresponds to the quantity where MC = MR is the price Macro Sound's should charge.
(c) To determine the short-run economic profit or loss, we subtract the total cost from the total revenue at the profit-maximizing quantity. If the result is positive, there is an economic profit. If it is negative, there is an economic loss.
(d) In the long run, the demand for Macro Sound's will depend on various factors such as competition, changes in consumer preferences, and technological advancements. Generally, in a monopolistic market, competitors may enter the market, increasing competition and reducing the demand for Macro Sound's headphones. As a result, the quantity of headphones sold may decrease, leading to a decline in the price charged. In the long run, economic profit in a monopolistic market tends to be reduced or eliminated due to competition.