2. Suppose you intend to buy xo units of a particular commodity. Presently the opportunity to buy it at a price of po per unit. But you expect that searching among other sellers will yield a lower price. Let p(t) denote the lowest price per unit you expect to find after searching the market for t hours. Assume that price per unit decreases with every additional hour of time spent in searching alternative sellers. Further, it is usually harder to find lower prices as the search progresses. Suppose your hourly wage is w. (a) Write the profit that is expected from searching for t hours. (b) What is the necessary condition for maximum profit? Provide an economic interpretation of this necessary condition. Is this also the sufficient condition? (c) How will your optimal search time respond to (i) an increase in the intended amount of the commodity (ii) an increase in the opportunity cost of the search?
2. Suppose you intend to buy xo units of a particular commodity. Presently the opportunity to buy it at a price of po per unit. But you expect that searching among other sellers will yield a lower price. Let p(t) denote the lowest price per unit you expect to find after searching the market for t hours. Assume that price per unit decreases with every additional hour of time spent in searching alternative sellers. Further, it is usually harder to find lower prices as the search progresses. Suppose your hourly wage is w. (a) Write the profit that is expected from searching for t hours. (b) What is the necessary condition for maximum profit? Provide an economic interpretation of this necessary condition. Is this also the sufficient condition? (c) How will your optimal search time respond to (i) an increase in the intended amount of the commodity (ii) an increase in the opportunity cost of the search?
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Transcribed Image Text:2. Suppose you intend to buy xo units of a particular commodity. Presently the
opportunity to buy it at a price of po per unit. But you expect that searching
among other sellers will yield a lower price. Let p(t) denote the lowest price per
unit you expect to find after searching the market for t hours. Assume that price
per unit decreases with every additional hour of time spent in searching alternative
sellers. Further, it is usually harder to find lower prices as the search progresses.
Suppose your hourly wage is w.
(a) Write the profit that is expected from searching for t hours.
(b) What is the necessary condition for maximum profit? Provide an economic
interpretation of this necessary condition. Is this also the sufficient condition?
(c) How will your optimal search time respond to (i) an increase in the intended
amount of the commodity (ii) an increase in the opportunity cost of the search?
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