Two rms (A and B) with unlimited capacity make identical widgets at zero cost and sell to a market of 300 buyers. Each buyer has a RP of $5 for one...
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Two firms (A and B) with unlimited capacity make identical widgets at zero cost and sell to
a market of 300 buyers. Each buyer has a RP of $5 for one widget and none is interested in
purchasing more than one widget. 200 of the buyers are uninformed, meaning that they are
unaware of the prices that A or B charge. Half the uninformed buyers choose A and the other
half choose B. As long as the chosen seller’s posted price is $5 or less, they buy the widget from
their chosen seller. The remaining 100 buyers are informed. They are aware of the prices that
each seller charges and patronize the one that gives them the largest surplus. In case of ties, the
informed buyers flip a fair coin to decide which firm to patronize. In the questions below assume
a ‘one shot game’. 1. Is each firm charging a price of $5 per widget an equilibrium? Explain. 2. Firm A continues to use a posted price (once set it is never changed), but firm B adopts a
‘beat-or-pay’ strategy. Specifically, firm B sets a. price and announces that if A has a price
that is equal to or lower than B’s price, it will either pay $10 to the buyer or sell them a
widget for at least a penny less than A. For example, if A posts a price of $3 and B posts a

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price of $4, then B must sell to each informed buyer at $2.99 (or less) or give each informed
buyer $10 (B can decide which of these to do). The announcement on B’s part is credible. Only informed buyers are aware of B’s announcement and therefore only they can take
advantage of it. Informed buyers are free to make multiple visits to each seller but make
only one purchase. Uninformed buyers do not receive the $10 in the event that A matches
or underprices B. In equilibrium What price will each firm set? Explain.

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