Consider the model of a vertical market shown in class. Suppose that the supplier sells each unit to the retailer for pw = c, but, in addition, requires the retailer to pay a fixed fraction of the retailer's profits, p. 2 Formulate the retailer's profit-maximization problem under this contract and show that this contract maximizes the total industry profit. That is, show that for any given p, the sum of the supplier's profit and the retailer's profit is equal to the profit made by a vertically integrated monopolist. (Hint: The retailer gets (1 − p) · Ã, rather than л₁. No need to re-do the vertically integrated monopolist's profit. Just take it from the notes.)

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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Consider the model of a vertical market shown in class. Suppose that the supplier sells each
unit to the retailer for pw = c, but, in addition, requires the retailer to pay a fixed fraction of the
retailer's profits, p.
2
Formulate the retailer's profit-maximization problem under this contract and show that this
contract maximizes the total industry profit. That is, show that for any given p, the sum of the
supplier's profit and the retailer's profit is equal to the profit made by a vertically integrated
monopolist.
(Hint: The retailer gets (1 − p) · Ã, rather than Ã₁. No need to re-do the vertically integrated
monopolist's profit. Just take it from the notes.)
Transcribed Image Text:Consider the model of a vertical market shown in class. Suppose that the supplier sells each unit to the retailer for pw = c, but, in addition, requires the retailer to pay a fixed fraction of the retailer's profits, p. 2 Formulate the retailer's profit-maximization problem under this contract and show that this contract maximizes the total industry profit. That is, show that for any given p, the sum of the supplier's profit and the retailer's profit is equal to the profit made by a vertically integrated monopolist. (Hint: The retailer gets (1 − p) · Ã, rather than Ã₁. No need to re-do the vertically integrated monopolist's profit. Just take it from the notes.)
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