100 – 2Q, Suppose that the inverse demand for aloe juice in Greece is given by P vhere P is the price per bottle (1000ml) of aloe juice and Q is the total quantity, i.e., umber of bottles, supplied in the market. There are two aloe juice manufacturers in Greece, Aloe Health and Aloe Wealth, operating under similar cost conditions. Each nanufacturer's cost function is C(q) = 4qi, i =1,2, where q; is the manufacturer's ndividual quantity produced and Q = q1 + q2. a) Based on demand conditions every year, they decide, independently of each other, he quantity of aloe juice that will be supplied, letting the market determine the price ber bottle. Find the equilibrium price and each firm's profit in this market. %3D b) Consider that the above two manufacturers form a cartel, agreeing to fix their total

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Suppose that the inverse demand for aloe juice in Greece is given by P = 100 – 2Q,
where P is the price per bottle (1000ml) of aloe juice and Q is the total quantity, i.e.,
number of bottles, supplied in the market. There are two aloe juice manufacturers in
Greece, Aloe Health and Aloe Wealth, operating under similar cost conditions. Each
manufacturer's cost function is C(q) = 4qi, i =1,2, where q¡ is the manufacturer's
individual quantity produced and Q = qı + q2.
(a) Based on demand conditions every year, they decide, independently of each other,
the quantity of aloe juice that will be supplied, letting the market determine the price
per bottle. Find the equilibrium price and each firm's profit in this market.
%3D
(b) Consider that the above two manufacturers form a cartel, agreeing to fix their total
quantity in such a way that the market maintains a collusive price. For simplicity, the
eventual cartel directory will determine the target total-quantity and price pair, and
each firm will produce 1/2 of the total quantity decided by the directory. Find the total
quantity that maximizes cartel profits, the price that the cartel directory fixes, and
each firm's profit, assuming that both firms respect their cartel-imposed quota.
Transcribed Image Text:Suppose that the inverse demand for aloe juice in Greece is given by P = 100 – 2Q, where P is the price per bottle (1000ml) of aloe juice and Q is the total quantity, i.e., number of bottles, supplied in the market. There are two aloe juice manufacturers in Greece, Aloe Health and Aloe Wealth, operating under similar cost conditions. Each manufacturer's cost function is C(q) = 4qi, i =1,2, where q¡ is the manufacturer's individual quantity produced and Q = qı + q2. (a) Based on demand conditions every year, they decide, independently of each other, the quantity of aloe juice that will be supplied, letting the market determine the price per bottle. Find the equilibrium price and each firm's profit in this market. %3D (b) Consider that the above two manufacturers form a cartel, agreeing to fix their total quantity in such a way that the market maintains a collusive price. For simplicity, the eventual cartel directory will determine the target total-quantity and price pair, and each firm will produce 1/2 of the total quantity decided by the directory. Find the total quantity that maximizes cartel profits, the price that the cartel directory fixes, and each firm's profit, assuming that both firms respect their cartel-imposed quota.
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