3.2. Changes in Demand vs. Movements along the Demand Curve

As we just saw, when own-price changes, quantity demanded changes. This change is called a movement along the demand curve or a change in quantity demanded, and it comes only from a change in own price.

Recall that to draw the demand curve, though, we had to hold everything except quantity and own-price constant. What would happen if income were to change by some amount? Suppose that household income rose by $10,000 per year to a value of 60. Then the value of Equation 3 would change to

Equation (5) 

Qdx=8.4−0.4Px+0.06(60)−0.01(20)=11.8−0.4Px

and Equation 4 would become the new inverse demand function:

Equation (6) 

P_x = 29.5 – 2.5Q_x  

Notice that the slope has remained constant, but the intercepts have both increased, resulting in an outward shift in the demand curve, as shown in Exhibit 2.

Exhibit 2. Household Demand Curve for Gasoline before and after Change in Income

In general, the only thing that can cause a movement along the demand curve is a change in a good’s own-price. A change in the value of any other variable will shift the entire demand curve. The former is referred to as a change in quantity demanded, and the latter is referred to as a change in demand.

More importantly, the shift in demand was both a vertical shift upward and a horizontal shift to the right. That is to say, for any given quantity, the household is now willing to pay a higher price; and at any given price, the household is now willing to buy a greater quantity. Both interpretations of the shift in demand are valid.

EXAMPLE 2

Representing Consumer Buying Behavior with a Demand Function and Demand Curve

An individual consumer’s monthly demand for downloadable e-books is given by the equation

Qdeb=2−0.4Peb+0.0005I+0.15Phb

where Qdeb equals the number of e-books demanded each month, P_eb equals the price of e-books, I equals the household monthly income, and P_hb equals the price of hardbound books, per unit. Notice that the sign on the price of hardbound books is positive, indicating that when hardbound books increase in price, more e-books are purchased; thus, according to this equation, the two types of books are substitutes. Assume that the price of e-books is €10.68, household income is €2,300, and the price of hardbound books is €21.40.

1. Determine the number of e-books demanded by this household each month.

2. Given the values for I and P_hb, determine the inverse demand function.

3. Determine the slope of the demand curve for e-books.

4. Calculate the vertical intercept (price-axis intercept) of the demand curve if income increases to €3000 per month.

Solution to 1:

Insert given values into the demand function and calculate quantity:

Qdeb=2−0.4(10.68)+0.0005(2,300)+0.15(21.40)=2.088

Hence, the household will demand e-books at the rate of 2.088 books per month. Note that this rate is a flow, so there is no contradiction in there being a non-integer quantity. In this case, the outcome means that the consumer buys 23 e-books per 11 months.

Solution to 2:

We want to find the price–quantity relationship holding all other things constant, so first, insert values for Iand P_hb into the demand function and collect the constant terms:

Qdeb=2−0.4Peb+0.0005(2,300)+0.15(21.40)=6.36−0.4Peb

Now solve for P_eb in terms of Q_eb: P_eb = 15.90 – 2.5Q_eb

Solution to 3:

Note from the inverse demand function above that when Q_eb rises by one unit, P_eb falls by 2.5 euros. So the slope of the demand curve is –2.5, which is the coefficient on Q_eb in the inverse demand function. Note it is not the coefficient on P_eb in the demand function, which is −0.4. It is the inverse of that coefficient.

Solution to 4:

In the demand function, change the value of I to 3,000 from 2,300 and collect constant terms:

Qdeb=2−0.4Peb+0.0005(3,000)+0.15(21.40)=6.71−0.4Peb

Now solve for P_eb: P_eb = 16.78 – 2.5Q_eb. The vertical intercept is 16.78. (Note that this increase in income has shifted the demand curve outward and upward but has not affected its slope, which is still −2.5.)