00:02
Hello, let's start with part a.
00:04
We need to find the equilibrium quantities q1 and q2.
00:13
So let's start with the market 1.
00:16
So the revenue function is found.
00:24
We multiply the demand function by quantity.
00:29
And now we can find the marginal revenue.
00:32
Marginal revenue is the derivative of total revenue.
00:37
With respect to quantity and it will be 80 minus 5 quantity 1 and this should be equal to marginal cost which is given which is 40 and from here we can find that the quantity 1 would be equal to 8 if we solve this it will be 8 for the second market we have different marginal revenue marginal revenue will be equal to 180 minus 20 times q2 and it's also equal to the marginal cost which is 40 and from here we can find that quantity 2 is equal to 7 so we found quantities it's 8 and 7 now we can find prices so using the given demand functions the price 1 would be 80 minus 2 .5 times 8 and it will be 60.
02:05
Price 2 is 180 minus 10 times 2 which is 7 and 2 which is 7 and this is equal to $110.
02:29
Okay, now part c we can find the total profit.
02:37
Profit, pi, would be equal to total revenue from the first market plus total revenue from the second market and minus total cost.
02:53
We can find this.
02:55
The price is 60.
02:58
60.
03:01
We multiply this by quantity, it's 8.
03:04
For the second market price is 100 and 10, multiply by quantity which is 7.
03:14
And we subtract the cost from this quantity...