00:01
Okay, guys, this is chapter 15, problem 9.
00:05
We're given this demand equation, total cost equation, marginal revenue, and marginal cost equations.
00:12
And we're told that international trade, at least to begin with, is prohibited.
00:18
The first part of the question asks us, what price the monopoly company in wickham charges for soccer balls? what quantity will they sell and how much profit the company makes? so as always, profit maximizing companies sets its price such that marginal cost equals marginal revenue.
00:41
And so we have the marginal cost and marginal revenue equations here.
00:45
So we're going to set them equal to each other.
00:47
10 minus 2q equals 1 plus q.
00:51
And so 9 equals 3q and 3 equals the quantity.
00:56
We then plug this into the demand equation.
01:03
Which is 10 minus q equals p, 10 minus 3 equals p, and so price is equal to seven.
01:14
So we see that the revenue, which equals quantity times price, equals three times seven equals 21.
01:25
And so then we just need to determine profits.
01:27
We need to know what the cost is.
01:28
Here we have the total cost equals 3 plus q plus 0 .5 q squared, which equals 3 plus 3 plus 0 .5 times 3 squared equals 6 plus half of 9, which is 4 .5 equals 10 .5...
