00:01
Yes, so for part a, for the market equilibrium price and quantity, so we can find the market supply function, given the cost function, vc is equal to 10q plus q squared.
00:13
For each firm, the marginal cost can be found as the first derivative of vc with respect to q.
00:20
So we have that marginal cost is going to be equal to 10 plus 2q.
00:26
And then in perfect competition, a firm will produce where p is equal to mc.
00:31
So we get that p is 10 plus 2q.
00:35
So and q is p minus 10 over 2.
00:39
So given 200 identical firms, the total market quantity supplied is going to be equal to 200 times q, which is 200 times p minus 10 divided by 2, giving us what the quantity supplied here is equal to 100p minus 2000.
01:00
And then setting quantity demand equal to quantity supplied to find the equilibrium, we get quantity supplied equal to quantity demanded.
01:12
So we get 100p minus 2000 equals 3000 minus 100p, giving us that 200p is equal to 5000.
01:22
Dividing by 200, we get p is 25.
01:25
And then plugging that into the demand function, we get the quantity would be 3000 minus 100 times 25.
01:38
So 3000 minus 2500 is 500.
01:42
So for a, the equilibrium price is going to be 25.
01:48
Goes in the first blank and the second blank.
01:50
We have that the market equilibrium quantity is going to be 500 units...