2. [14] Two scented candle vendors are located side-by-side at the artisanal crafts fair. As is customary in the industry, they are competing on price (they both have enormous chalk- board signs advertising their selling price for an 80-hour burn soy wax candle that smells like your fondest childhood memories). Vendor 1 has the cost function C(q₁) = 3q₁ and station 2 has the cost function C(q) = 5q2 where q1 and q2 are the number of candles sold by vendor 1 and vendor 2, respectively. The market demand for premium-scented soy wax candles is Q(p) = 50-p where Q = 91 + 92. a) [4] Write the demand functions of the two firms. b) [4] Are the two firms selling their wares at $5 per candle in a Bertrand-Nash equilibrium? Explain your why or why not. c) [6] Characterize a Bertrand-Nash equilibrium. How many candles will each firm sell in this equilibrium?

Economics (MindTap Course List)
13th Edition
ISBN:9781337617383
Author:Roger A. Arnold
Publisher:Roger A. Arnold
Chapter21: Production And Costs
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2. [14] Two scented candle vendors are located side-by-side at the artisanal crafts fair. As is
customary in the industry, they are competing on price (they both have enormous chalk-
board signs advertising their selling price for an 80-hour burn soy wax candle that smells like
your fondest childhood memories). Vendor 1 has the cost function C(q₁) = 3q₁ and station
2 has the cost function C(q) = 5q2 where q1 and q2 are the number of candles sold by
vendor 1 and vendor 2, respectively. The market demand for premium-scented soy wax
candles is Q(p) = 50-p where Q = 91 + 92.
a) [4] Write the demand functions of the two firms.
b) [4] Are the two firms selling their wares at $5 per candle in a Bertrand-Nash
equilibrium? Explain your why or why not.
c) [6] Characterize a Bertrand-Nash equilibrium. How many candles will each firm sell in
this equilibrium?
Transcribed Image Text:2. [14] Two scented candle vendors are located side-by-side at the artisanal crafts fair. As is customary in the industry, they are competing on price (they both have enormous chalk- board signs advertising their selling price for an 80-hour burn soy wax candle that smells like your fondest childhood memories). Vendor 1 has the cost function C(q₁) = 3q₁ and station 2 has the cost function C(q) = 5q2 where q1 and q2 are the number of candles sold by vendor 1 and vendor 2, respectively. The market demand for premium-scented soy wax candles is Q(p) = 50-p where Q = 91 + 92. a) [4] Write the demand functions of the two firms. b) [4] Are the two firms selling their wares at $5 per candle in a Bertrand-Nash equilibrium? Explain your why or why not. c) [6] Characterize a Bertrand-Nash equilibrium. How many candles will each firm sell in this equilibrium?
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