1. Imagine that you've just landed a job as a market analyst and your initial assignment is to analyze the market for gourmet chocolate spread, a treat beloved by the very rich. This market is dominated by two key firms: ChocoRich and NuttyDelight. ChocoRich's quantity is denoted by q₁ and the cost of production in its factory is summarized by a cost function C(q₁) = 72q₁. Nutty Delight's quantity is denoted by q2 and the cost of production in its factory is given by C(q2) = 24q2. The market price is given by the inverse demand equation: P = 4800 - 6Q, where Q denotes the market quantity of output from the two firms, i.e., Q = q₁ + 92. a) Write down the profit functions for ChocoRich and NuttyDelight as a function of q₁ & 92. b) Now find and graph the best response function for each firm. c) What is the Nash equilibrium level of output for each firm, market price, profit of each firm, and market quantity? d) Provide evidence that your answer to part c is consistent with the definition of a Nash equilibrium by showing ChocoRich cannot raise their profit by unilaterally deviating from the equilibrium. Do this by showing that their profit declines both if they were to increase their quantity by 10 or decrease their quantity by 10. Explain how your result is consistent with a Nash equilibrium with no more than two sentences. e) Suppose the owner of ChocoRich were to suggest to the owner of NuttyDelight that they cooperate, acting as a cartel and jointly agreeing on an amount to produce, and splitting the profits. How should the firms distribute output across their factories in this case? Explain why in one or two sentences. What would be the total quantity produced, and what would be the profits of the two firms? Would both firms be better off with this deal than in the Cournot equilibrium in part c? f) How will the cartel deal affect the welfare of consumers? Compare consumer surplus with the Cournot price and market quantity, to consumer surplus with the cartel price and quantity.
1. Imagine that you've just landed a job as a market analyst and your initial assignment is to analyze the market for gourmet chocolate spread, a treat beloved by the very rich. This market is dominated by two key firms: ChocoRich and NuttyDelight. ChocoRich's quantity is denoted by q₁ and the cost of production in its factory is summarized by a cost function C(q₁) = 72q₁. Nutty Delight's quantity is denoted by q2 and the cost of production in its factory is given by C(q2) = 24q2. The market price is given by the inverse demand equation: P = 4800 - 6Q, where Q denotes the market quantity of output from the two firms, i.e., Q = q₁ + 92. a) Write down the profit functions for ChocoRich and NuttyDelight as a function of q₁ & 92. b) Now find and graph the best response function for each firm. c) What is the Nash equilibrium level of output for each firm, market price, profit of each firm, and market quantity? d) Provide evidence that your answer to part c is consistent with the definition of a Nash equilibrium by showing ChocoRich cannot raise their profit by unilaterally deviating from the equilibrium. Do this by showing that their profit declines both if they were to increase their quantity by 10 or decrease their quantity by 10. Explain how your result is consistent with a Nash equilibrium with no more than two sentences. e) Suppose the owner of ChocoRich were to suggest to the owner of NuttyDelight that they cooperate, acting as a cartel and jointly agreeing on an amount to produce, and splitting the profits. How should the firms distribute output across their factories in this case? Explain why in one or two sentences. What would be the total quantity produced, and what would be the profits of the two firms? Would both firms be better off with this deal than in the Cournot equilibrium in part c? f) How will the cartel deal affect the welfare of consumers? Compare consumer surplus with the Cournot price and market quantity, to consumer surplus with the cartel price and quantity.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:1. Imagine that you've just landed a job as a market analyst and your initial assignment is to analyze the
market for gourmet chocolate spread, a treat beloved by the very rich. This market is dominated by two key
firms: ChocoRich and NuttyDelight. ChocoRich's quantity is denoted by q₁ and the cost of production in its
factory is summarized by a cost function C(q₁) = 72q₁. NuttyDelight's quantity is denoted by q2 and the cost
of production in its factory is given by C(q₂) = 24q2. The market price is given by the inverse demand
equation: P = 4800 - 6Q, where Q denotes the market quantity of output from the two firms, i.e., Q = q₁ + q₂.
a) Write down the profit functions for ChocoRich and NuttyDelight as a function of q₁ & q₂.
b) Now find and graph the best response function for each firm.
c) What is the Nash equilibrium level of output for each firm, market price, profit of each firm, and
market quantity?
d) Provide evidence that your answer to part c is consistent with the definition of a Nash equilibrium
by showing ChocoRich cannot raise their profit by unilaterally deviating from the equilibrium. Do
this by showing that their profit declines both if they were to increase their quantity by 10 or
decrease their quantity by 10. Explain how your result is consistent with a Nash equilibrium with no
more than two sentences.
e) Suppose the owner of ChocoRich were to suggest to the owner of NuttyDelight that they cooperate,
acting as a cartel and jointly agreeing on an amount to produce, and splitting the profits. How
should the firms distribute output across their factories in this case? Explain why in one or two
sentences. What would be the total quantity produced, and what would be the profits of the two
firms? Would both firms be better off with this deal than in the Cournot equilibrium in part c?
f) How will the cartel deal affect the welfare of consumers? Compare consumer surplus with the
Cournot price and market quantity, to consumer surplus with the cartel price and quantity.
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