A problem worked out

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A neat problem
On the next slide there is a problem that has the initial statement:
The town of Whoville has 100 identical consumers and 50 identical car washes. Each
consumer has income of $24. The diagram and chart below show the indifference
curves of a typical consumer and the marginal cost curve of a typical car wash.
Note the vertical axis should say All Other Goods.
To get the price of a car wash today:
Note in the graph if all $24 of the consumer is spent on car washes then we see 12 car
washes could be purchased. On this budget line it means the price of a wash is $2. We
see the typical individual would actually take 4 washes at a price of $2. The quantity
demanded would be 4 times 100 = 400 washes.
If the price is $2 the firm would have MC = MR at a Q less than 1. With 50 firms the
quantity supplied would be less than 50. With Qd > Qs price will rise.
If the price rises to $3, note if all $24 of the consumer is spent on car washes then 8 car
washes could be purchased. We see the typical individual would actually take 3 washes
at a price of $3. The quantity demanded would be 3 times 100 = 300 washes.
If the price is $3 the firm would have MC = MR at a Q = 1. With 50 firms the quantity
supplied would be 50. With Qd > Qs price will rise.
If the price rises to $6, note if all $24 of the consumer is spent on car washes then 4 car
washes could be purchased. We see the typical individual would actually take 2 washes
at a price of $6. The quantity demanded would be 2 times 100 = 200 washes.
If the price is $6 the firm would have MC = MR at a Q = 4. With 50 firms the quantity
supplied would be 200. With Qd = Qs we see the price in the market = 6.
Part b
If there is no entry or exit then it must be that economic profit = 0.
With revenue of $24 (which is $6 times 4 units) and variable costs of 3 + 4 + 5 + 6 =
$18,
The fixed cost must be $24 - $18 = $6.

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