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A product can be produced at either one of two quality levels: H (for high)or L (for low). The cost of production is zero for both quality levels. Consumers areinterested in having one unit of this product. There are two types of consumers.Consumers of type 1 are willing to pay up to $20 per unit of quality H and up to $10 perunit of quality L (i.e., the consumer's surplus of such a consumer is 20-p if he buys an Hunit for price p and it is 10-p if he buys an L unit for the price p); consumers of type 2 are willing to pay up to $8 per unit of quality H and up to $6 per unit of quality L. Let N1 and N2 denote the numbers of consumers of the two types respectively.
a) Find the price and quality chosen by a monopoly who is restricted to produce allunits at the same quality, when N1= 10, N2= 20 and when N1= 100, N2= 10
b) Suppose now that the monopoly can offer a menu of different quality levels at different prices. Find the profit maximizing menu that the monopoly will offer in each of the two cases considered in part (a) above.
c) For each of these cases compare the social welfare arising in scenario (a) to that arising in scenario (b).
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