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PROFESSOR: Hi, welcome back to the 14.01 problem solving videos. Today we're going to work on p-set 1 problem number 3 from Fall 2010. And we're going to work through all four parts of this problem. But to start off I'm just going to read through part A.

Consider the market for apple juice. In this market the supply curve is given by quantity supplied equals 10 pj minus 5 pa, and the demand curve is given by quantity demanded equals 100 minus 15 pj plus 10 pt, where j denotes apple juice, a denotes apples, and t denotes tea.

Part A asks us to assume that pa is fixed at $1 and pt equals 5. We need to calculate the equilibrium price and quantity in the apple juice market.

So to start off this problem, I wrote down both the supply and the demand functions. But before we get started with the algebra, I wanted to come over to this graph and I wanted to think about conceptually what we're going to be doing.

When we solve for an equilibrium price and the equilibrium quantity, all we're doing is we're finding the point at which the quantity supplied and the quantity demanded is equal. Looking at the graph, that point is going to be right here where the two curves intersect. So this will be q star, our equilibrium quantity, and this will be p star, our equilibrium price.

So for part A we're just solving for the equilibrium price and quantity. And they try to trip you up on this problem by throwing in the price of apples and the price of tea. But since they tell us what these prices are initially, we're just going to plug these into our supply and our demand functions. And once we do that, we'll have isolated the pj variable and the q variable so we'll be able to solve through for this problem.

So starting off with part A. We're going to go ahead and we're going to set the quantity supplied equal to the quantity demanded. And so for my supply function, I've already plugged in pa. And after plugging

in pa I found that 10 pj minus 5 is the supply curve. And the demand curve is equal to 150 minus 15 pj. Solving out for pj I find that the equilibrium price is equal to 6.2. And since I know this is an equilibrium price I'm going to go ahead and I'm going to label this with a star.

Solving through for the equilibrium quantity all we have to do is we have to take this equilibrium price we found and plug it back into either the supply curve or the demand curve. I'm going to go ahead and I'm going to plug it into the supply function. And that lets us solve for the equilibrium quantity denoted with the star. And that in this case is 57.

So looking at our graph, the equilibrium price and the equilibrium quantity, we can now label them. We can label the price, 6.2, and the equilibrium quantity 57.

Let's go ahead and move on to part B. Part B is going to be the exact same scenario as we started off with in part A, only what we're going to do now is we're going to shift the supply curve by changing the price of apples. Part B states, suppose that a poor harvest season raises the price of apples to pa equals 2. Find the new equilibrium price and quantity of apple juice and draw a graph to illustrate the answer.

Now what's happening in this scenario is that the demand curve is completely unaffected. The only thing that's changing is our supply curve is shifting. So when we look at our supply curve we have to think about conceptually what do apples represent. Well they're an input for the suppliers. It's something they have to use to make the apple juice.

Consider the market for apple juice. In this market the supply curve is given by quantity supplied equals 10 pj minus 5 pa, and the demand curve is given by quantity demanded equals 100 minus 15 pj plus 10 pt, where j denotes apple juice, a denotes apples, and t denotes tea.

Part A asks us to assume that pa is fixed at $1 and pt equals 5. We need to calculate the equilibrium price and quantity in the apple juice market.

So to start off this problem, I wrote down both the supply and the demand functions. But before we get started with the algebra, I wanted to come over to this graph and I wanted to think about conceptually what we're going to be doing.

When we solve for an equilibrium price and the equilibrium quantity, all we're doing is we're finding the point at which the quantity supplied and the quantity demanded is equal. Looking at the graph, that point is going to be right here where the two curves intersect. So this will be q star, our equilibrium quantity, and this will be p star, our equilibrium price.

So for part A we're just solving for the equilibrium price and quantity. And they try to trip you up on this problem by throwing in the price of apples and the price of tea. But since they tell us what these prices are initially, we're just going to plug these into our supply and our demand functions. And once we do that, we'll have isolated the pj variable and the q variable so we'll be able to solve through for this problem.

So starting off with part A. We're going to go ahead and we're going to set the quantity supplied equal to the quantity demanded. And so for my supply function, I've already plugged in pa. And after plugging

in pa I found that 10 pj minus 5 is the supply curve. And the demand curve is equal to 150 minus 15 pj. Solving out for pj I find that the equilibrium price is equal to 6.2. And since I know this is an equilibrium price I'm going to go ahead and I'm going to label this with a star.

Solving through for the equilibrium quantity all we have to do is we have to take this equilibrium price we found and plug it back into either the supply curve or the demand curve. I'm going to go ahead and I'm going to plug it into the supply function. And that lets us solve for the equilibrium quantity denoted with the star. And that in this case is 57.

So looking at our graph, the equilibrium price and the equilibrium quantity, we can now label them. We can label the price, 6.2, and the equilibrium quantity 57.

Let's go ahead and move on to part B. Part B is going to be the exact same scenario as we started off with in part A, only what we're going to do now is we're going to shift the supply curve by changing the price of apples. Part B states, suppose that a poor harvest season raises the price of apples to pa equals 2. Find the new equilibrium price and quantity of apple juice and draw a graph to illustrate the answer.

Now what's happening in this scenario is that the demand curve is completely unaffected. The only thing that's changing is our supply curve is shifting. So when we look at our supply curve we have to think about conceptually what do apples represent. Well they're an input for the suppliers. It's something they have to use to make the apple juice.

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