17 An oligopolist is currently charging a price of S170 and is selling 40 units

Question

17 An oligopolist is currently charging a price of S170 and is selling 40 units of output weekly. If the firm increases price above S170, its rivals tend not to follow and the firm thus faces a flatter demand curve P = 200-0.75Q. If the firm reduces price below $170, its rivals tend to follow and the firm thus faces a steeper demand curve P 250 - 2Q. At the current output level, within what range could marginal cost vary without giving the firm an incentive to change the current price? a. (110, 140). b. 90, 140). c. (200, 250) d. 170, 200). Answer Questions 18-25 based on the following information: A and B. Their cost functions are defined below, respectively: CA 1000010QA+0.5QA2 and CB 1200010QB+0.5QB The firms face the following market demand curve: P-610-Q, (where Q = QA + QB). 18 If the firms compete with price (Bertrand model), they should produce (QA, QB), allowing rounding errors: a. (120, 120). b. 150, 150). c. 171.43, 142.86) d (200, 200). 19 If the firms compete with price (Bertrand model), they can eam profits (RA, ), allowing rounding errors: a. (12500, 10500). b. 15250, 13250). c. (8000, 6000). d. 10000, 8000). 20 If the firms compete with the Cournot model, they should produce (QA, QB), allowing rounding errors: a. (120, 120). b. (150, 150). c. (171.43, 142.86) d. (200, 200). 21 If the firms compete with the Cournot model, they can earn profits (A,) allowing roundi a. (23750, 21750). b. (22734, 20734). c. (33571, 31571). d. (26250, 24250). ing errors:

Explanation / Answer

Question 17

At price above $170, demand function is as follows -

P = 200 - 0.75Q

Total revenue = Price * Quantity = (200 - 0.75Q) * Q = 200Q - 0.75Q2

Marginal revenue = dTR/dQ = d(200Q - 0.75Q2)/dQ = 200 - 1.5Q

At price below $170, demand function is as follows -

P = 250 - 2Q

Total revenue = Price * Quantity = (250 - 2Q) * Q = 250Q - 2Q2

Marginal revenue = dTR/dQ = d(250Q - 2Q2)/dQ = 250 - 4Q

The oligopolist will continue to charge $170 per unit, if the optimal output remains 40 units.

This value of Q = 40 units will remain optimal untill the marginal cost remains between two value of MR stated above.

Calculate MR when price is above $170 -

MR = 200 - 1.5Q = 200 - (1.5*40) = 200 - 60 = 140

Calculate MR when price is below $170 -

MR = 250 - 4Q = 250 - (4*40) = 250 - 160 = 90

So, if marginal cost is between $90 and $140, firm will have no incentive to change the current price.

The correct answer is the option (b).

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