In a certain large city hot dog vendors are perfectly compet

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?

Solution

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