A business can produce its product in different versions: Version A has a basic
ID: 1209519 • Letter: A
Question
A business can produce its product in different versions: Version A has a basic design and a lower cost and Version B has an upgraded design and a higher cost of production. The business knows there are different types of customers, "High" demand (H) and "Low" demand (L), but cannot separate the different types of customers. The number of customers of each type and the maximum each type is willing to pay for the different versions of the product are illustrated in the table. In addition, the table gives the marginal cost of production for each version of the product. Assume the business offers the product in Version A only. Determine the optimal price (P_a) and compute the profit of the business. Assume the business offers the product in Version A and Version B. Determine the optimal prices (P_a and P_b) and compute the profit of the business.Explanation / Answer
(a)
A business will not keep p > 25, as there will be no buyers.
If he keeps p = 25, he will receive demand from only High Demand buyers, and his profit will be:
50*25 - 50*5 = 50*(25-5)
=1000
If he keeps 15 < p < 25, he will receive demand from only High Demand buyers, and his profit will be less than 1000 in the previous case as his price has declined, other things remaining same.
If he keeps p = 15, he will receive demand from both High as well as Low Demand buyers, and his profit will be:
150 * 15 - 150 * 5 = 150 * (15-5)
=1500
If he keeps p < 15, he will receive demand from both High as well as Low Demand buyers, and his profit will be less tahn 1500 in the previous case, as his price has declined, other things remaining same.
So, the optimal price for a business to make maximum profit is to keep price at 15, where he maximises profit (1500).
p*a = 15, Profit a = 1500
(b) For Version B
A business will not keep p > 35, as there will be no buyers.
If he keeps p = 35, he will receive demand from only High Demand buyers, and his profit will be:
50*35 - 50*10 = 50*(35-10)
=1250
If he keeps 25 < p < 35, he will receive demand from only High Demand buyers, and his profit will be less than 1250 in the previous case as his price has declined, other things remaining same.
If he keeps p = 25, he will receive demand from both High Demand buyers only for Version B as one would prefer higher quality version , and his profit will be:
50 * 25 - 50 * 10 = 50 * (25-10)
=750
If he keeps 20 < p < 25, he will receive demand from only High Demand buyers, and his profit will be less than 750 in the previous case as his price has declined, other things remaining same.
If he keeps p = 20, he will receive demand from both High as well as Low Demand buyers, and his profit will be
150 * 20 - 150 * 10 = 150 * (20-10)
= 1500
If he keeps 15 < p < 20, he will receive demand from both High as well as Low Demand buyers, and his profit will be less than 1500 in the previous case as his price has declined, other things remaining same.
If he keeps p = 15, he will receive demand from both High as well as Low Demand buyers for Version B, and his profit will be
150 * 15 - 150 * 10 = 150 * (15-10)
= 750
So, the optimal price for a business to make maximum profit is to keep price at 20 for Version B, where he maximises profit (1500).
p*b = 20, Profit b = 1500
p*a = 15, Profit a = 1500
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