2. Consider the following Ramsey pricing Lagrangian exercise. max (B1(91) + B2(q2) – C191 – c292 – F +A {p1(qı)qı + P2(92)q2 – c191 – c292 – F}] 91.92 Bi(qi) represents the area under the demand curve for i, and p¿(q.) is the demand for good i. a) Give the first-order conditions from the above maximization. b) Take the first-order condition for q1, and solve for the Ramsey pricing rule, in termns of the price-cost margin, and the elasticity of demand: Əqı Pı api 91 €1 c) Suppose the market is such that the demands for q1 and q2 are both relatively elastic. Would the associated Ramsey price outcome be less efficient than if both demands were relatively inelastic? Explain.

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Chapter1: Making Economics Decisions
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2. Consider the following Ramsey pricing Lagrangian exercise.
max [B1(91) + B2(q2) – C141 – c292 – F +A {p1(q1)q1 + p2(92)92 – C191 – c292 – F}]
91,92
Bi(qi) represents the area under the demand curve for i, and pi(q) is the demand for good i.
a) Give the first-order conditions from the above maximization.
b) Take the first-order condition for q1, and solve for the Ramsey pricing rule, in terms of
the price-cost margin, and the elasticity of demand:
Əqı pi
dpi 91
€1
c) Suppose the market is such that the demands for q1 and q2 are both relatively elastic.
Would the associated Ramsey price outcome be less efficient than if both demands were
relatively inelastic? Explain.
Transcribed Image Text:2. Consider the following Ramsey pricing Lagrangian exercise. max [B1(91) + B2(q2) – C141 – c292 – F +A {p1(q1)q1 + p2(92)92 – C191 – c292 – F}] 91,92 Bi(qi) represents the area under the demand curve for i, and pi(q) is the demand for good i. a) Give the first-order conditions from the above maximization. b) Take the first-order condition for q1, and solve for the Ramsey pricing rule, in terms of the price-cost margin, and the elasticity of demand: Əqı pi dpi 91 €1 c) Suppose the market is such that the demands for q1 and q2 are both relatively elastic. Would the associated Ramsey price outcome be less efficient than if both demands were relatively inelastic? Explain.
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