In a certain large city, hot dog vendors are perfectly competitive, and face a m

Question

In a certain large city, hot dog vendors are perfectly competitive, and face a market price of $1.25 per hot dog. Each hot dog vendor has the following total cost schedule: What is the profit-maximizing quantity (Q*) of hot-dogs for the typical vendor? What are the total profits at Q*? An increase in the number of vendors and a decrease in demand for hot dogs due to health concerns drove the price down to $1.00. What is the profit-maximizing quantity (Q*) and what are the total profits at Q* in this case?

Explanation / Answer

Working notes:

(1) MC = Change in TC / Change in Q

(a) In perfect competition, profit is maximized when P = MC. Here, the MC closes to P = 1.25 is MC = 1.12 when Q = 150.

So, Q* = 150

(b) Total profit at Q* = $34.5

(c) P = $1, so TR = $1 x Q = Q

Q* = 125, the level of output where loss is minimized (since at every output level there is a loss, the objective is to minimize loss).

Q TC MC TR = P x Q = 1.25Q Profit = TR - TC 1 63 0 -63 25 73 0.42 31.25 -41.75 50 78 0.20 62.5 -15.5 75 88 0.40 93.75 5.75 100 103 0.60 125 22 125 125 0.88 156.25 31.25 150 153 1.12 187.5 34.5 175 188 1.40 218.75 30.75 200 233 1.80 250 17

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