Question
Suppose there are $n$ identical firms in a Cournot equilibrium. Show that the absolute value of the elasticity of the market demand curve must be greater than $1 / n .$ (Hint: in the case of a monopolist, $n=1,$ and this simply says that a monopolist operates at an elastic part of the demand curve. Apply the logic that we used to establish that fact to this problem.)
Step 1
The price elasticity of demand (E) is defined as \( E = \frac{dQ}{dP} \cdot \frac{P}{Q} \), where \( dQ/dP \) is the derivative of quantity with respect to price, \( P \) is the price, and \( Q \) is the quantity demanded. Show more…
Show all steps
Your feedback will help us improve your experience
Marcus Esteban and 63 other educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Suppose there are $n$ identical firms in a Cournot equilibrium. Show that the absolute value of the elasticity of the market demand curve must be greater than $1 / n$. (Hint: in the case of a monopolist, $n=1$, and this simply says that a monopolist operates at an elastic part of the demand curve. Apply the logic that we used to establish that fact to this problem.)
Suppose that a price-discriminating monopolist has segregated its market into two groups of buyers, the first group described by the demand and revenue data that you developed for question $5 .$ The demand and revenue data for the second group of buyers is shown in the accompanying table. Assume that $\mathrm{MC}$ is $\$ 13$ in both markets and $\mathrm{MC}=\mathrm{ATC}$ at all output levels. What price will the firm charge in each market? Based solely on these two prices, what can you conclude about the relative elasticities of demand in the two markets? What will be this monopolist's total economic profit?
Show that a profit-maximizing, unregulated monopolist will never operate in the price-inelastic region of its demand curve. Show how regulation can force the monopolist into the inelastic portion of its demand curve. What will be the impact of an increase in the regulated price of a monopolist upon revenues and profits when it is operating on $(a)$ the elastic portion of the demand curve, $(b)$ the inelastic portion of the demand curve, and $(c)$ the unit-elastic portion of the demand curve?
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD