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ECON 1100: Intermediate Microeconomics

Assignment #10

Due Friday 12/08/2023 by 11:59 PM

Answer the following two questions clearly and completely. Be sure to show enough of your work - I want to be able to see how you arrived at your answers so that I can understand your thought process and give partial credit if warranted. You are welcome and encouraged to work in groups as long as the work you hand in is your own! Do not hesitate to stop  by  my office  hours  if you  have any questions or  merely wish to talk through any aspect of the problems. Good luck!

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.