Question

Atlas Construction wants to buy some custom equipment from Vulcan Manufacturing. Atlas’ maximum willingness to pay for the equipment is $420 (thousand). Vulcan is willing to sell the equipment as long as it gets at least $300 (thousand). The two companies bargain over the price, p. The net benefit to Atlas is 420-p and the net benefit to Vulcan is p-300. The Nash product is the product of these benefits.

a. Use Excel to create a spreadsheet with columns for the price, the benefit to Atlas, the benefit to Vulcan, and the Nash Product. Let the price go from 300 to 420 in increments of 20 and find the price that maximizes the Nash product. Explain

b. Now suppose that Atla’s maximum willingness to pay is only 400. What is the price that arises from Nash bargaining now? Explain why the price would change in this way.

Answer 1

a) Table below exihibits the benefits to Atlas (column 2) and to Vulcan (column 3) for prices ranging from 300 to 420. Column 4 computes the nash product and the same is maximum when the price is 360. This value is at 3600.

Prices (1)	Benefit to Atlas (2)	Benefit to Vulcan (3)	Nash product (4)	Benefit to Atlas (5)	Nash product (6)
300	120	0	0	100	0
310	110	10	1100	90	900
320	100	20	2000	80	1600
330	90	30	2700	70	2100
340	80	40	3200	60	2400
350	70	50	3500	50	2500
360	60	60	3600	40	2400
370	50	70	3500	30	2100
380	40	80	3200	20	1600
390	30	90	2700	10	900
400	20	100	2000	0	0
410	10	110	1100
420	0	120	0

b) In the second case where marginal willingness for Atlas falls to 400, his benefit is only 400 - p. Column  5 and 6 show that with fall in willingness, the bargaining price also falls from 360 to 350 and the benefit is also reduced. Nash product is smaller at 2500. When willingness to pay falls demand shifts left and bargaing power is reduced which reduces benefits and equilibrium prices.