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Homework answers / question archive / Question 1 Orient Bhd
Question 1
Orient Bhd. and Theta Bhd. are the only two companies in this industry. Both companies have equal market share with an annual total demand of 1,000,000 units for the industry. The current industry price per unit of goods A is RM100 and the average cost is RM45 per unit. The price elasticity of demand for goods A is 2.0. The companies are contemplating of reducing the price per unit by 20% (low discount) or 50% (high discount). Based on a research, it is estimated if both decrease their price by 20% or 50%, then the increase in quantity demanded will be split 50:50. It is expected that the increase in quantity demanded at industry level if both companies decided to lower the price by 50% is 2,000,000 units. But if one company decides to decrease the price by 20% and the other by 50% then, the company with low discount will capture 30% and the company with high discount will capture 70% of the expected increase in quantity demanded of 1,080,000 units. Required:
a. Calculate the expected demand and derive the increase in demand when both companies decide to decrease selling price by 20%. (4 Marks)
b. Analyze the pricing decisions of the two firms as a non-co-operative game and answer the following;
i. Construct the pay-off matrix, where the elements of each cell of the matrix are the two firm's profit. (10 Marks)
ii. Derive the equilibrium set of strategies. (6 Marks)
a.(i). The expected total demand will be 1,400,000
(ii). Demanded quantity increases by 400,000 (40%)
b.(i). In the matrix below, the figures are in millions. The matrix will be :
Firm 1
50%. 20%
Firm 2 50%. 5 , 5 3.78, 11.34
20%. 11.34, 3.78. 25.5 , 24.5
(ii). From the matrix, the equilibrium strategies will be:
a). When they both reduce the price by 20%.
b). When both reduce the price by 50%.
Step-by-step explanation
a.(i). We have been given that elasticity is 2
This means that when the price decreases by one unit, the quantity increases by 2 units. This is as good as the quantity demanded doubles the rate at which price decreases. This is why when the5price is reduced by 50% the quantity demanded increases by 100%. If they both reduce the price level by 20%, the quantity demanded will increase by 40%. The new demand will be given as :
(140%/100%) * 1,000,000 = 1,400,000
The expected total demand will be 1,400,000
(ii). The formula for change in demand given the elasticity is :
2*(Percentage of price reduction /increase).
Since this is a normal good, if the price increases, demanded quantity reduces but when the price is reduced, the demanded quantity increase.
When price is reduced by 20%
The quantity demanded increases by : 2*(20%) =40%
40% * 1,000,000 =400,000.
Demanded quantity increases by 400,000 (40%)
b.(i). We know that each firm commands a 50% market share.
If they both reduce the price by 50%
The new price will be : 50% * RM100 = RM50
Demanded quantity for each firm : 50% * 2,000,000 =1,000,000
Profit will be given as : quantity * (unit price - average cost per unit)
Profit = 1,000,000 * (RM50 - RM45) = RM5,000,000
If they both reduce the price by 20%:
The new price will be : (100%-20%) * RM100 = RM80
Demanded quantity for each firm : 50% * 1,400,000 =700,000
Profit will be given as : quantity * (unit price - average cost per unit)
Profit = 700,000 * (RM80 - RM45) = RM24,500,000
If one reduces by 20% and the other by 50%:
The one that reduces the price by 20% will have the following :
Demanded quantity : 30% * 1,080,000 = 324,000
Profit will be given as : quantity * (unit price - average cost per unit)
Profit = 324,000 * (RM80 - RM45) = RM11,340,000
The one that reduces the price by 50% will have the following :
Demanded quantity : 70% * 1,080,000 = 756,000
Profit will be given as : quantity * (unit price - average cost per unit)
Profit = 756,000 * (RM50 - RM45) = RM3,780,000
In the matrix below, the figures are in millions. The matrix will be :
Firm 1
50%. 20%
Firm 2 50%. 5 , 5 3.78, 11.34
20%. 11.34, 3.78. 25.5 , 24.5
(ii). From the matrix, the equilibrium strategies will be:
a). When they both reduce the price by 20%. This gives the highest level of profit to each firm. The profit is RM24.5million if they both reduce the price by 20% The strategy is identified as: 20%20%( 24.5, 24.5)
b). When both reduce the price by 50%. Each firm earns a profit of 5million. It is an. Equilibrium since none of the firms earns a disadvantageous profit of 3.78 Million. They as well command the same level of customers when they set the same prices. From the payoff matrix, the strategy is given as: 50%,50% (5, 5)
