Consider the relationship between monopoly pricing and price...

Consider the relationship between monopoly pricing and price elasticity of demand. a. Explain why a monopolist will never produce a quantity at which the demand curve is inelastic. ($Hint$: If demand is inelastic and the firm raises its price, what happens to total revenue and total costs?) b. Draw a diagram for a monopolist, precisely labeling the portion of the demand curve that is inelastic. ($Hint$: The answer is related to the marginal-revenue curve.) c. On your diagram, show the quantity and price that maximize total revenue.

Consider the relationship between monopoly pricing and price elasticity of demand.
a. Explain why a monopolist will never produce a quantity at which the demand curve is inelastic. ($Hint$: If demand is inelastic and the firm raises its price, what happens to total revenue and total
costs?)
b. Draw a diagram for a monopolist, precisely labeling the portion of the demand curve that is inelastic. ($Hint$: The answer is related to the marginal-revenue curve.)
c. On your diagram, show the quantity and price that maximize total revenue.

Key Concepts

Monopoly Pricing

Monopoly pricing refers to the ability of a sole supplier in a market to set prices above marginal cost due to the lack of competition. Unlike firms in competitive markets that are price takers, a monopolist chooses an output level where its marginal revenue equals its marginal cost, thereby maximizing profits. This pricing decision is critically linked to the market demand curve, as the monopolist must consider how changes in the quantity produced affect the price it can charge.

Price Elasticity of Demand

Price elasticity of demand measures how sensitive the quantity demanded is to a change in the price of a good. In the context of a monopolistic market, the elasticity of demand plays a crucial role because it determines the impact of price changes on total revenue. A more elastic demand implies that consumers are highly responsive to changes in price, while a less elastic (or inelastic) demand indicates that quantity demanded does not change significantly with price changes.

Inelastic Demand

Inelastic demand occurs when the absolute value of the price elasticity of demand is less than one, meaning that the percentage change in quantity demanded is less than the percentage change in price. For a monopolist, operating in the inelastic portion of the demand curve is suboptimal because any further price increases lead to a decline in total revenue, as the loss in quantity sold outweighs the benefit of charging a higher price.

Marginal Revenue

Marginal revenue is the additional revenue a firm gains from selling one more unit of its product. In a monopolistic setting, there is a direct relationship between marginal revenue and the price elasticity of demand, expressed as MR = P × (1 - 1/|?|). This formula illustrates that when demand is inelastic (|?| < 1), marginal revenue becomes negative, which signals that increasing output in such a region would be detrimental to total revenue.

Total Revenue Maximization

Total revenue maximization occurs at the point where the price elasticity of demand is unitary (|?| = 1), meaning that the percentage change in quantity demanded exactly offsets the percentage change in price. At this point, any small change in price does not change total revenue. For a monopolist, while profit maximization may not coincide with revenue maximization, understanding this concept is important for identifying the boundaries of the demand curve, particularly the region where the demand switches from elastic to inelastic.

Transcript

00:01 So while seeing the question let's put a move to the answer so let's see here that the first one is when demand is in elastic a decrease in price actually reduces tr in spite of the increased unit sales thus mr is negative and a firm will never produce where mr is negative so when demand curve is in elastic mr is negative tr is decreasing so let's let's move to the second point graph of monopoly showing elastic and inelastic portion of demand curve.

02:46 So let's see here that the graph is so here is y -axis and x -axis and on the x -axis is zero and quantity and on the second graph also here is y -axis and x -axis and on the x -axis is quantity.

03:37 And this side this side is cost and revenue so on the first graph we are going to draw that tr curve so let's see here that so this is tr and on the second graph we are going to draw the ar and mr line so let's see here that so here is price and here is quantity so this is ar line and now we are going to draw the mr and this is mr and we draw the line which connects tr to the arn mr.

05:33 So let's see here that from here to here it is relatively elastic and from here to here it is relatively inelastic and this line is unit elastic and this point is marked as a.

06:35 So here is the full graph.

06:38 So let's move forward to the third point.

06:51 So the point where mr equals 0 is the point of maximized tr.

07:20 In other words, where price elasticity of demand is unit elastic, the mr is zero, and tr is at its maximum.

08:02 On the graph point a represent the maximum tr the price is p and the quantity is q so here is the three points which are given in the quotient so the first point is when demand is inelastic a decrease in price actually reduces tr in spite of the increased unit sales does mr is negative and a firm will never produce where mr is negative so when demand curve is inelastic mr is negative tr is decreasing.

09:19 So let's move to the second point.

09:21 So the graph of monopolies showing elastic and inelastic portion of demand curve.

09:26 So here is the graph on the first graph, it is y axis and x axis.

09:31 Here is zero and on the x axis is quantity...

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