Extra Material for Chapter 4

Extra Material for Chapter 4 • “Midpoint” convention for calculating elasticity • Rules for tax-shifting (a jump ahead to chapter 7). Chapter 4: Elasticity

Calculating Elasticity Using the Midpoint Convention For changes in demand or supply that are relatively large, we use the midpoint of the arc in the formula. Chapter 4: Elasticity

Calculating Elasticity of Demand Example Price rises from 90 to 110 Quantity demand falls from 240 to 160 units. P B A D Q Chapter 4: Elasticity

Example, continued How much has price increased? 110-90 = 20 To find the percentage change, divide the absolute increase (20) by the midpoint of the old and new prices, 100. Price increased 20% This is the “midpoint convention.” Chapter 4: Elasticity

Example, continued How much has quantity demanded decreased? 240-160 = 80 To find the percentage change, divide the absolute decrease (80) by the midpoint of the old and new quantities, 200. Quantity decreased 40% using the midpoint convention. Chapter 4: Elasticity

What is a “midpoint”? The midpoint of two points on a line can be found in this way: midpoint price: (P1+P2)/2 midpoint quantity; (q1 + q2)/2 So in this example midpoint price: (110 + 90)/2 = 100 midpoint quantity; (240+160)/2=200 Chapter 4: Elasticity

Example, continued ED = 40%/20% = 2. The final step is the same as before, putting these together. The only difference in this formula and the one you learned earlier is that we use the midpoint values for p and q, not the initial values. Chapter 4: Elasticity

“Tax Shifting” • An excise tax is a “sales tax” that sellers must pay the government on every item sold. • It may be “ad valorem,” a specific percentage of value. • It may be “specific,” a fixed amount. • Although the seller hands over the money to the government, the “burden” of the tax is generally shared between producers and consumers. Chapter 4: Elasticity

Sales Tax and Supply and Demand • Putting a sales tax on a product shifts supply upward by the amount of the tax. • If sellers were willing to sell 100 items for $1.00 each before a $.10 tax was added, they would now only be willing to sell 100 items if they could collect $1.10 (because the government takes a dime). Chapter 4: Elasticity

Supply shift for a sales tax • An ad valorem sales tax causes a rotational (not parallel) shift in supply. • A specific sales tax causes a parallel shift in supply. • The following graph will show a specific tax. Chapter 4: Elasticity

Supply shift with specific tax Consumers pay $1.07 but producers only receive $.97. S+tax S $1.10 add $.10 tax $1.07 $1.00 100 Chapter 4: Elasticity

After the tax • If Supply slopes up and Demand slopes down (neither curve perfectly elastic or inelastic), then following an imposition of the sales tax, price will rise, but it will not rise the full amount of the tax. • The percentage of the tax paid by consumers and producers depends on relative elasticity of the two curves. • Consumers pay more in terms of higher market price. • Producers receive less because the price they receive is lower than before (they have to subtract the tax). Chapter 4: Elasticity

Rules for “Tax Shifting” • If Ed>Es, then producers pay more of the tax than consumers. • If Ed<Es, then consumers pay more of the tax than producers. • The group with highest elasticity gets hurt the least (memory aid: the more inflexible you are in life, the more you get hurt). Chapter 4: Elasticity

Some examples • If Ed=5 and Es=0.4, producers pay more of the tax. • If Ed=0.9 and Es=1.8, consumers pay more of the tax. • If Ed=7 and Es=2, producers pay more of the tax. • If Ed=0.1 and Es=0.9, consumers pay more of the tax. Chapter 4: Elasticity

Extra Material for Chapter 4