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GREG HUTKO: Hi, welcome back to the 14.01 problem-solving videos. Today I'm going to be working on Fall 2010 Problem Set 5, Problem Number 4.

And I'm only going to be working the last few sections, E, F, G, and H in this video. But if you need help with the earlier sections, you should go ahead and should look at PSET Number 4, Problem Number 3.

And in that problem, we work through the production function, and we go through and we find conditional supply and the conditional demand curves.

But this problem is going to have us looking at aggregated supply in a market. We have to consider what production should be occurring in the market given a set number of firms in the market. And then we're going to think about the case of perfect competition where firms have to be operating at the absolute best efficiency possible. And we're going to look at how that affects the production level.

Part E is introduced by saying, consider now that r equals 4 and w equals 1.

And that the market demand for coffee is given by quantity demanded equals 20 minus p.

There are eight other companies operating in this market and all companies have the cost structures identical to Sebastian's company, the company that we've been dealing with earlier in the problem. Part E asks us, what is the aggregate supply in this market?

And if you look back earlier in this problem, the other piece of information that we're going to need is we're going to need this cost function that gives all of the cost in terms of the rental rate of capital or how much it cost to use each machine per hour, the wage rate or how much labor cost per hour, and q, the quantity, that's output by a specific firm.

Now, to find the aggregated supply, what we're first going to find is we're going to first find the supply curve for one firm within this market. And then we're going to set the demand or the supply curve in terms of quantity in terms of price. We're going to multiply by eight to aggregate it. And then we'll have our aggregated supply curve.

But before we do that, we also have to think of a limiting case as well. When we're representing the costs for a firm, we're going to represent both the marginal cost and the average cost.

The marginal cost is the cost of one single additional unit, while the average cost tells us all the costs including the fixed costs divided by the total that we're producing, what does that look like?

If the price in a market is below the minimum of the average cost of a firm in the market, they're not going to produce in the market. So if the price is below this critical p star, since the firm, even if they're producing right at the minimum of average cost, they can never recover their cost.

So a firm is only going to produce if this p where the price that's being charged is above the p star, the minimum of average cost. So we're going to find the supply curve in two cases, one where the price is above this minimum of average cost. And two, we're going to find it when the price is below that minimum.

Let's start off by finding the marginal cost to get our supply curve.

Taking the marginal cost, the derivative with respect to q. Or before we can take the marginal cost, sorry, let's plug-in for the variables w and r. We're going to find that our cost curve is given by 4 plus 4q squared.

Now we can find the marginal cost, which will be our supply curve for a single firm.

And I'm only going to be working the last few sections, E, F, G, and H in this video. But if you need help with the earlier sections, you should go ahead and should look at PSET Number 4, Problem Number 3.

And in that problem, we work through the production function, and we go through and we find conditional supply and the conditional demand curves.

But this problem is going to have us looking at aggregated supply in a market. We have to consider what production should be occurring in the market given a set number of firms in the market. And then we're going to think about the case of perfect competition where firms have to be operating at the absolute best efficiency possible. And we're going to look at how that affects the production level.

Part E is introduced by saying, consider now that r equals 4 and w equals 1.

And that the market demand for coffee is given by quantity demanded equals 20 minus p.

There are eight other companies operating in this market and all companies have the cost structures identical to Sebastian's company, the company that we've been dealing with earlier in the problem. Part E asks us, what is the aggregate supply in this market?

And if you look back earlier in this problem, the other piece of information that we're going to need is we're going to need this cost function that gives all of the cost in terms of the rental rate of capital or how much it cost to use each machine per hour, the wage rate or how much labor cost per hour, and q, the quantity, that's output by a specific firm.

Now, to find the aggregated supply, what we're first going to find is we're going to first find the supply curve for one firm within this market. And then we're going to set the demand or the supply curve in terms of quantity in terms of price. We're going to multiply by eight to aggregate it. And then we'll have our aggregated supply curve.

But before we do that, we also have to think of a limiting case as well. When we're representing the costs for a firm, we're going to represent both the marginal cost and the average cost.

The marginal cost is the cost of one single additional unit, while the average cost tells us all the costs including the fixed costs divided by the total that we're producing, what does that look like?

If the price in a market is below the minimum of the average cost of a firm in the market, they're not going to produce in the market. So if the price is below this critical p star, since the firm, even if they're producing right at the minimum of average cost, they can never recover their cost.

So a firm is only going to produce if this p where the price that's being charged is above the p star, the minimum of average cost. So we're going to find the supply curve in two cases, one where the price is above this minimum of average cost. And two, we're going to find it when the price is below that minimum.

Let's start off by finding the marginal cost to get our supply curve.

Taking the marginal cost, the derivative with respect to q. Or before we can take the marginal cost, sorry, let's plug-in for the variables w and r. We're going to find that our cost curve is given by 4 plus 4q squared.

Now we can find the marginal cost, which will be our supply curve for a single firm.

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