Suppose that your demand schedule for pizza is as follows: Price Quantity Deman

Suppose that your demand schedule for pizza is as follows: ...

Suppose that your demand schedule for pizza is as follows: $$\begin{array}{ccc} \text { Price } & \begin{array}{c} \text { Quantity Demanded } \\ \text { (income }=\$ 20,000) \end{array} & \begin{array}{c} \text { Quantity Demanded } \\ \text { (income }=\$ 24,000) \end{array} \\ \hline \$ 8 & 40 \text { pizzas } & 50 \text { pizzas } \\ 10 & 32 & 45 \\ 12 & 24 & 30 \\ 14 & 16 & 20 \\ 16 & 8 & 12 \end{array}$$ a. Use the midpoint method to calculate your price elasticity of demand as the price of pizza increases from $\$ 8$ to $\$ 10$ if (i) your income is $\$ 20,000$ and (ii) your income is $\$ 24,000$. b. Calculate your income elasticity of demand as your income increases from $\$ 20,000$ to $\$ 24,000$ if (i) the price is $\$ 12$ and (ii) the price is $\$ 16 .$

Suppose that your demand schedule for pizza is as follows:
$$\begin{array}{ccc}
\text { Price } & \begin{array}{c}
\text { Quantity Demanded } \\
\text { (income }=\$ 20,000)
\end{array} & \begin{array}{c}
\text { Quantity Demanded } \\
\text { (income }=\$ 24,000)
\end{array} \\
\hline \$ 8 & 40 \text { pizzas } & 50 \text { pizzas } \\
10 & 32 & 45 \\
12 & 24 & 30 \\
14 & 16 & 20 \\
16 & 8 & 12
\end{array}$$
a. Use the midpoint method to calculate your price elasticity of demand as the price of pizza increases from $\$ 8$ to $\$ 10$ if (i) your income is $\$ 20,000$ and (ii) your income is $\$ 24,000$.
b. Calculate your income elasticity of demand as your income increases from $\$ 20,000$ to $\$ 24,000$ if
(i) the price is $\$ 12$ and (ii) the price is $\$ 16 .$

Key Concepts

Price Elasticity of Demand

This concept measures the responsiveness of the quantity demanded of a good to a change in its price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price and is used to understand how consumers adjust their buying behavior in response to price changes. A higher elasticity indicates that consumers are more sensitive to price changes, while a lower elasticity suggests the opposite.

Income Elasticity of Demand

This concept quantifies how much the quantity demanded of a good changes in response to a change in consumers' income. It is calculated as the percentage change in quantity demanded divided by the percentage change in income. This measure helps to classify goods as normal or inferior; a positive income elasticity indicates a normal good, whereas a negative income elasticity indicates an inferior good.

Midpoint Method

The midpoint method is a technique used to calculate elasticity that involves taking the average of the starting and ending values as the base for percentage changes. By doing so, it minimizes the bias that occurs due to the direction of the change and provides a more accurate measure of elasticity when comparing differences between two points on a demand curve.

Demand Schedule

A demand schedule is a table that shows the quantity of a good that consumers are willing to purchase at various prices. It is a fundamental tool in understanding consumer behavior and market dynamics, and it serves as the basis for calculating elasticities and analyzing how factors like price and income affect the quantity demanded.

Transcript

00:01 Here we're going to be working on calculating elasticity, both price elasticity and income elasticity based upon this demand schedule that's been given to us.

00:11 This is the demand for pizza based upon two different income levels, an income of $20 ,000 and an income of $24 ,000.

00:19 Let's go ahead and start by calculating the price elasticity of demand as the price increases from $8 to $10 for price of pizza, and we're going to do this for each income level that we have here.

00:30 Start with our first one when our income is equal to 20 ,000.

00:34 Let's keep in mind here that what we're doing is calculating, so from 8 to 10, right? so we're going to be using these two quantities or prices and these are our quantities we're going to be using.

00:45 And you can see up top i've also given us the function or the formula that we can use here to calculate it, which makes it pretty straightforward.

00:53 So we can see that our, let's start with our q2.

00:56 So that's going to be our second quantity.

00:58 So we increase to 10.

01:00 So that's our, this is our second one and eight would be our first.

01:04 So the quantity, when the price is 10, is equal to 32.

01:09 And we can subtract that from our q1.

01:12 So when our price is $8, 40 pizzas were demanded, that gets divided by its midpoint.

01:21 So we do that.

01:22 We take 32 plus 40, and then divide it by two.

01:28 So we're calculating our elasticity here using the midpoint method, which is the most accurate way of doing it, to guarantee that we have the same base as we work through.

01:36 But either way, so that gives us our numerator.

01:39 Our denominator then is given by our second price minus our first price.

01:44 So we just said that our second price is $10, minus the first one of $8, and then that also gets divided by its midpoint.

01:52 So we have 10 plus 8 divided by 2 on our denominator.

01:58 We can go ahead and simplify this.

02:00 It'll give us negative 8 over 36 for a numerator divided by 2 over 9 for a denominator.

02:12 Simplifying that even further, we get price elasticity equal to negative 1.

02:21 Now we can go ahead and do the same thing for our second income bracket where our income is equal to $24 ,000.

02:27 So in this case, our numerator is going to be $45 ,000.

02:35 Minus 50 because you can see when our price is equal to 10 we there were 45 pizzas demanded and when our price is equal to 8 there are 50 pizzas demanded dividing that by its midpoint so 45 plus 50 divided by 2 all of this gets divided by our prices so this is actually going to be the same as what we found over in our first income right in here because our prices are still 10 and 8 so that's not going to really.

03:08 So i'm actually just going to go ahead and write on our denominator 2 over 9 because remember that's what we ultimately simplified this to was 2 over 9.

03:17 So that's just to save some space and some time on our end.

03:20 And now we can simplify what we have in our denominator or on our numerator.

03:25 And that ends up being negative 5 all over 47 .5 still over that 2 over 9.

03:34 And that gives us a price elasticity equal to negative 0 .47...

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