Consider a firm in an oligopoly in which a few sellers offer differentiated brands of widgets. Suppose that if Firm 1 were to cut its price in order to sell more widgets, its competitors would quickly lower their own prices to protect their market shares. If, however, Firm 1 were to raise its price, its competitors would not follow, and Firm 1 would lose market share. Under these (non-ceteris-paribus) assumptions, the demand curve faced by Firm 1 is, in effect, highly elastic at prices above the current price, and less elastic at prices below the current price. Suppose that Firm 1's current price is P* = $10 and it sells Q* = 4 widgets per day. If Firm 1 were to raise its price, it would face the demand: P = 12 – 2Q (P > 10) If Firm 1 were to reduce its price, it would face the demand: P = 14 - Q (P< 10) a) Write the firm's marginal revenue function for prices above and below $10. MR = (P > 10, so: Q* < 4) MR = (P < 10, so: Q* > 4) b) GRAPH Firm l's demand (D) and marginal revenue (MR) curves. Label point E (4, $10). c) Firm 1 has no incentive to change its price as long as: < MC < $_ d) Calculate the elasticity of demand for each demand function at E(4, $10). If Firm 1 raises price: ED = If Firm 1 lowers price: ED =

Consider a firm in an oligopoly in which a few sellers offer differentiated brands of widgets. Suppose that if Firm 1 were to cut its price in order to sell more widgets, its competitors would quickly lower their own prices to protect their market shares. If, however, Firm 1 were to raise its price, its competitors would not follow, and Firm 1 would lose market share. Under these (non-ceteris-paribus) assumptions, the demand curve faced by Firm 1 is, in effect, highly elastic at prices above the current price, and less elastic at prices below the current price. Suppose that Firm 1's current price is P* = $10 and it sells Q* = 4 widgets per day. If Firm 1 were to raise its price, it would face the demand: P = 12 – 2Q (P > 10) If Firm 1 were to reduce its price, it would face the demand: P = 14 - Q (P< 10) a) Write the firm's marginal revenue function for prices above and below $10. MR = (P > 10, so: Q* < 4) MR = (P < 10, so: Q* > 4) b) GRAPH Firm l's demand (D) and marginal revenue (MR) curves. Label point E (4, $10). c) Firm 1 has no incentive to change its price as long as: < MC < $_ d) Calculate the elasticity of demand for each demand function at E(4, $10). If Firm 1 raises price: ED = If Firm 1 lowers price: ED =

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Im a bit confused on how to figure this out could I have help.

Consider a firm in an oligopoly in which a few sellers offer differentiated brands of widgets.
Suppose that if Firm 1 were to cut its price in order to sell more widgets, its competitors would
quickly lower their own prices to protect their market shares. If, however, Firm 1 were to raise
its price, its competitors would not follow, and Firm 1 would lose market share. Under these
(non-ceteris-paribus) assumptions, the demand curve faced by Firm 1 is, in effect, highly elastic
at prices above the current price, and less elastic at prices below the current price.
Suppose that Firm 1's current price is P* = $10 and it sells Q* = 4 widgets per day.
If Firm 1 were to raise its price, it would face the demand:
P = 12 – 2Q (P > 10)
If Firm 1 were to reduce its price, it would face the demand: P = 14 – Q
(P< 10)
a) Write the firm's marginal revenue function for prices above and below $10.
MR =
(P > 10, so: Q* < 4)
MR =
(P < 10, so: Q* > 4)
b) GRAPH Firm l's demand (D) and marginal revenue (MR) curves. Label point E (4, $10).
c) Firm 1 has no incentive to change its price as long as:
$.
< MC < $
d) Calculate the elasticity of demand for each demand function at E(4, $10).
If Firm 1 raises price: ED =
If Firm 1 lowers price: ED =
|

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