We now consider a duopoly model where the firms offer products with different qualities and consumers differ from each other in how much they care for quality. Suppose the firms offer their products with quality si ∈ [0,1] and consumers’ ‘location’ in terms of how much they care about quality is given by a parameter θ ∈ [0,1] and consumers are uniformly distributed over this interval. Suppose the firms first choose their quality s1 and s2 and then set prices p1 and p2. A consumer of type θ derives utility vi = r − pi + θsi from consuming a unit from firm i and where reservation price r is high enough that everyone purchases from one of the two firms. Suppose the marginal cost of producing increases with quality. There are no fixed costs and the total variable cost is C(qi,si) = csiqi so that marginal cost is csi and increases with quality. Further, let c = 1 so marginal cost is si. Consider the second stage where given a choice of qualities s1 and s2 with s1 < s2, the firms simultaneously choose their prices. 1. Compute θb, the location address of the indifferent consumer and derive demand for the two firms. Also, write down the profit function for each firm.
We now consider a duopoly model where the firms offer products with different qualities and consumers differ from each other in how much they care for quality.
Suppose the firms offer their products with quality si ∈ [0,1] and consumers’ ‘location’ in terms of how much they care about quality is given by a parameter θ ∈ [0,1] and consumers are uniformly distributed over this interval. Suppose the firms first choose their quality s1 and s2 and then set prices p1 and p2. A consumer of type θ derives utility
vi = r − pi + θsi
from consuming a unit from firm i and where reservation price r is high enough that everyone purchases from one of the two firms. Suppose the marginal cost of producing increases with quality. There are no fixed costs and the total variable cost is
C(qi,si) = csiqi
so that marginal cost is csi and increases with quality. Further, let c = 1 so marginal cost is si.
Consider the second stage where given a choice of qualities s1 and s2 with s1 < s2, the firms simultaneously choose their prices.
1. Compute θb, the location address of the indifferent consumer and derive
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could you explain step 2 more thoroughly please
by Bartleby ExpertShow that in equilibrium firms will go for a maximal quality difference. (Hint: take partial of equilibrium profits with respect to s2 − s1)
by Bartleby Expert- Compute the
equilibrium prices, quantities , and profits for both firms. Consider now the first stage.
by Bartleby Expert2. Compute the
Consider now the first stage.
3. Show that in equilibrium firms will go for a maximal quality difference. (Hint: take partial of equilibrium profits with respect to s2 − s1)
4. If you were a lobbyist for firm 1, as a business strategy would you argue to the policymakers to introduce legislation – in the name of safety and quality of course – that increases or decreases the value of c?
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