Question

The graph that accompanies this question illustrates two demand curves for a firm operating in a differentiated product oligopoly. Initially, the firm charges a price of \(60and produces 10units of output. One of the demand curves is relevant when rivals match the firm’s price changes; the other demand curve is relevant when rivals do not match price changes.

a. Which demand curve is relevant when rivals will match any price change?

b. Which demand curve is relevant when rivals will not match any price change?

c. Suppose the manager believes that rivals will match price cuts but will not match price increases.

(1) What price will the firm be able to charge if it produces 20units?

(2) How many units will the firm sell if it charges a price of \)70?

(3) For what range in marginal cost will the firm continue to charge a price of $60?

Short answer

. When rivals will match any price change, the demand curve${\mathrm{D}}_2$ is important.

b. When rivals will not match any price change, the demand curve$D_1$is important.

c.

1.Price the firm is able to charge if it produces 20 units is $20 per unit.

2. Number of units the firm sells if it charges a price $70 of is 0units.

3. For a range of 10 in marginal cost will the firm continue to charge a price of $60.

Step-by-step solution

Determining the curve representing the demand 

The goal of this task is to determine which curve represents the demand curve when rivals match the price changes and which curve represents the demand curve when rivals do not match the price changes based on the given graph.

Finding the demand curve that is relevant when rivals will match with price change

Note that demand is more inelastic when rivals match a price change than when they do not. That is because for a given price reduction, a firm will sell more if rivals do not cut their prices than it will if they lower their prices. In effect, a price reduction increases quantity demanded only slightly when rivals respond by lowering their prices. Similarly, for a given price increase, a firm will sell more when rivals also raise their prices than it will when they maintain their existing prices.

Observe that on the graph curve_{${\mathrm{D}}_2$} is more inelastic

Therefore, demand curve${\mathrm{D}}_2$ is relevant when rivals will match any price change.

Finding the demand curve which is relevant when rivals will not match any price change from the given graph

Observing that on the graph, curve$D_1$ is more elastic.

Therefore, demand curve$D_1$is relevant when rivals will not match any price change.

Observing from the graph for quantity

1. Observing from the graph that if the quantity_{$\left(x\right.-axis)$} is any number greater than 10 then the price should be read from the demand curve_{${\mathrm{D}}_2$}.

Reading from the graph that point on curve${\mathrm{D}}_2$ whose x coordinate is$20$ is obtained as:$\text{(20,20)}$

Therefore, the price charged at quantity of$20$ units is_$\$20$ per unit.

Observing from the graph for price

2. Observing from the graph that if the price_{$\left(y\right.-axis)$} is any number greater than$60$ then the price should be read from the demand curve_{$D_1$}.

Read that point from the graph on curve_{$D_1$,} whose y coordinate is_$70$ is:$(0,70)$

Therefore, when the price is$\mathrm{\$}70$ then the quantity of produced units is$0$

Observing from the graph for intersecting point

The Sweezy model of oligopoly presumes that the market behaves in a kink when competitor businesses match a price decrease to stop sales (and earnings) from declining but do not match a price rise. The top section of the demand curve$D_1$, (up to the point of kink), and lower portion of the demand curve$D_2$make up the kinked demand curve that has been created (from the point of kink).

(1) If a typical business in this market generates$20$units of output, it will be in the lower half of the demand curve$D_2$(from the point of kink).

At this quantity, the cost isper unit.

(2) The top component of the demand curve is the relevant portion of the kinked demand curve for price levels above$\$60$. (till the point of kink).

When the price isrole="math" localid="1658745955429" $\$70$, there is no production at all.

(3) There is a specific range in which, changes in the marginal cost do not affect the level of output that maximises profits (i.e., when a firm produces 10 units for $60 ).

Drawing the corresponding marginal revenue curves for the two demand curves reveals that the firm can continue to charge a price of $60 as long as it is within $20 to $50 of the marginal cost.