15.5. [Related to text problem 15.7.] Demand for bottled water is given by: W 10
ID: 1127400 • Letter: 1
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15.5. [Related to text problem 15.7.] Demand for bottled water is given by: W 1000-100P. Krystal Kleàr and Nature's Nurture can produce bottled water at a constant marginal cost of 10 cents (.10) per bottle. Consumers are indifferent between the two waters and will buy the one that has the lowest price. If both firms charge the same price, each gets half the sales. a. If KK charges 15 cents per bottle, what will NN's profit be if it also charges 15 cents? (1) Therefore, NN would choose a price of (3) profit would then be (4) If it charges 14 cents? (2) -_ so KK would then reduce its price to cents. KK's NN would retaliate by (6) and this process would continue until both had reduced their prices to (7) cents. This is-a (81 be (9) equilibrium. Each firm's profit would The outcome (1 areto efficient. b. NN discovers a new, more accessible source for its water. The effect of the discovery is to reduce NN's marginal cost to 8 cents per bottle. KK is stuck with its old source ànd marginal cost of 10 cents per bottle. If NN leaves its price at the equilibrium level from part a, their profit will now be -, and if they reduce it to 9 cents it will be. Therefore, NN will price its water at (3)Explanation / Answer
At p=.15
W=1000-100(.15)
W= 985
If both firms charge the same price then each wil get 985/2 = 492.5 the sales.
If both firm charge price .15 then profit of NN = TR-TC
Profit = (.15-.10)(492.5)
Profit = 24.625
If NN charge price=.14 then all sales go to NN because he is charging lower price.
Profit in this case= (.14-.10)(985)= 39.4.
Therefore NN would charge price of 14 cent.kK's profit in this case would be 0. Because KK's charging higher price than NN therefore no sales goes to KK'S. So, KK would then reduce its price to 14cent. NN would retaliate by charging price equal to 13 cent. And this process would continue until both had reduced their prices to 10 cent (equal to marginal cost). This is a price equilibirium.each firm's profit would be 0. Because firm charging price equal to marginal cost.
B) if NN'S marginal cost reduced to 8 cent. Then at equilibirium price i:e p=.10 profit of NN= (.10-.08)(492.5)=9.85
And if NN charge price =.09. Then profit=(.09-.08)(985)= 9.85
Therefore NN price its water at .09.
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