The objective of this activity is to use data of a demand function faced by an o

Question

The objective of this activity is to use data of a demand function faced by an oligopolistic firm, and of its cost structure, in order to analyze pricing decisions. When Procter & Gamble (P&G;) planned to enter the Japanese market for Gypsy Moth Tape, it knew its production costs and understood the marked demand curve but found it hard to determine the right price to charge because two other firms - Kao soap, Ltd., and Unilever, Ltd. -were also planning to enter the market. All three firms would be choosing their prices at about the same time, and P&G; hat to take this into account when setting its own price. Because all three firms were using the same technology for producing Gypsy Moth Tape, they had the same production costs. Each firm faced a fixed cost of $480,000 per month and a variable cost of $1 per unit. From market research, P&G; ascertained that its demand curve for monthly sales was: Q = 3375(P)^-3.5 (Pu)^-.25 (P_k)^0.25 Where Q is monthly sales in thousands of units, and P, P_u, and P_k are P&G;'s, Unilever's, and Kao's prices, respectively. Assume that Unilever and Kao face the same demand condition. Write the equation of the total cost function of each firm Write the equation of the profit function of each firm Using the MS Excel tools, calculate the profit levels of the firms that correspond to the different combinations of prices of P&G;, Kao and Unilever using the following table. Assume that the price set by Kao and Unilever are equal. What is the best price that P&G; could set if the competitors set their price (P_u, and P_k) at $1.30? What is the best price that P&G; could set if the competitors set their price (P_u and P_k) at $1.50? What are the prices that you would expect to prevail in the market? Explain

Explanation / Answer

(2)Because all three firms were using the same technology for producing Gypsy Moth Tape, they had the same production costs. i.e C(Q) = 480,000 + Q.

(3)  Total profit is given by

pT = p1 + p2 = 24P - 4P2 + 2P2 - 40 = 24P - 2P2 - 40.

This is maximized when pT/P = 0. pT/P = 24 4P,

so the joint profit-maximizing price is P = $6.

Each firm’s profit is therefore p1 = p2 = 12P - P2 - 20 = 72 - 36 - 20 = $16.

(4)

(5)  In that case, P&G will lose money, but IT will lose the least amount of money ($6000 per month) by charging . $1.40. P&G's competitors would therefore not expect it to charge $1.30, and by the same reasoning, P&G would not expect them to charge a price this much low.

(6) In that case, it would beneficial for P&G to opt the best price i.e. $1.40.

(7) there are two possibilities :-

(a) given the prices of competitor firms, it would always be best for P&G to adopt the price $1.40. This is also the price at which all competitors are doing the best they can, so it is a Nash equilibrium.as, above table shows, all the firms would make the  make a profit of $12,000 per month.

(b) If all the firms in the market could collude , this collusion would make a larger profit. all firms would be agree to charge $1.50, and each of them would earn $20,000.

P&G price ($) 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.10 226 215 204 194 183 174 165 155 1.20 106 89 73 58 43 28 15 2 1.30 -56 -37 -19 2 15 31 47 62 1.40 -44 -25 -6 12 29 46 62 78 1.50 -52 -32 -15 3 20 36 52 68 1.60 -70 -51 -34 -18 -1 14 30 44 1.70 -93 -76 -59 -44 -28 -13 1 15 1.80 -118 -102 -87 -72 -57 -44 -30 -17

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