Suppose that a firm has a Total Cost curve of: Total Costs =...

Suppose that a firm has a Total Cost curve of: Total Costs = $9,000 + 3*Q^2 Giving it Marginal Costs determined by: MC = 2*3*Q Suppose also that the market price is equal to $380. At the profit-maximizing production quantity for this firm, what is the Average Total Costs at this Q? Note: round your answers to 2 decimal places.

Transcript

00:01 So here we're thinking about long -run equilibrium.

00:02 We have a demand curve of 6500 minus 100p.

00:07 We have a supply curve of 1200p.

00:11 And in equilibrium we know that quantity demanded has to be equal to quantity supplied.

00:17 So i'm going to set these equal to each other.

00:19 65 minus 100p is equal to 1200p.

00:23 That means 6500 is equal to 1300p.

00:28 That means that p is equal to 5.

00:31 And if p is equal to 5, you can plug back in, right? quantity demanded would be 6500 minus 100 outside of 5 is equal to 6000.

00:40 Quantity supplied would be 1200 outside of 5, which is equal to 6000, right? so there's my market equilibrium.

00:50 Now what we need to think about is the lowest price in the long run.

01:00 So here the idea is that in the long run we must have price is equal to minimum average total cost to ensure zero profit, right? that's the competitive idea, right? we know that in the long run zero profit is the competitive condition.

01:23 If the industry is making profit, firms will enter.

01:25 If the industry is losing money, firms will leave.

01:27 So zero long run means zero profit.

01:30 So here we have the total cost curve is 722 plus 2200.

01:38 So average total cost is equal to 722 over q.

01:45 Oh, sorry, this is q plus 2200.

01:49 And you see something is wrong here, right? i don't think this is right.

01:53 I think there's a small graphical error...

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