# 9/24/2008. Utility. Utility and Consumer Demand. Law of DMU. Measuring Utility. Income Effect. Scarcity is our lot

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1 Utility Utility and Consumer Demand Ch. 6 We ll come back to Ch. 5 later Something s usefulness Or, the amount of satisfaction you get from an item You can create a monetary value to describe satisfaction Some would say that everything has its price. Everything!? Law of DMU Total Utility Diminishing marginal utility The more consumption the smaller the increase in total utility IOW: The more I have the less useful it becomes, the less satisfied I am Measuring Utility Monetary units aren t constant Arbitrary # s work well Marginal Utility Examples in your book Water(free good), Pizza/Videos Scarcity is our lot B/C things cost money we have to choose, but we will want to maximize total utility! We can do this if where MU/\$ is equal for all items in want. MU/P=MU/P Income Effect All this relates to QD If price falls for an item I will have left over money, making me feel wealthier and thus allowing me to increase Total Utility by purchasing more of a product. Which product I buy depends on which one offers more MU. 1

2 Examples Pizza/Videos - \$8/\$4 same MU Graph demand from MU Combination of products that max. TU with a \$2 budget. Student Practice (1 st part of Assign. #4) Bsk. Of Wings/Bsk. of Fries MU for wings starts higher. \$5 for each - \$25 budget Consumer Surplus The amount of money b/w your max. price and actual price. Most products will give you a consumer a surplus This works for individuals and for entire markets. Price Elasticity of D Elasticity A measure of Responsiveness: How much of an effect is generated by the cause? This measures the responsiveness of consumers to a change in price (QD) When the P changes how will that effect how much I purchase? PEd=%change QD/%change P Test #1: The Formula Test Generalize the price elasticity formula If the price drops from p to p, other things constant, the quantity demanded increases from q to q The change in price can be represented as p and the change in quantity as q E D = q (q+ q ) / 2 p (p+ p ) / 2 Price Elasticity of Demand Because the average quantity and average price are used as a base for computing percent change, the same elasticity results whether going from the higher price to the lower price or the other way around Since the focus is on the percent change, we need not be concerned with how output or price is measured 2

3 Price Elasticity of Demand Elasticity expresses a relationship between two amounts The percent change in quantity demanded The percent change in price Because the law of demand states that price and quantity demanded are inversely related, the change in price and the change in quantity demanded have opposite signs the price elasticity of demand has a negative sign Price Elasticity of Demand Since constantly referring to elasticity as a negative number gets cumbersome, we will discuss the price elasticity of demand as an absolute value positive number For example, absolute value of the elasticity for tacos computed earlier will be referred to as.5 rather than.5 Example Milk increases from \$2 to \$2.2 QD falls from 1m to 95m What is Ed? -.5 PED is simply a measure of Consumer Response QD is affected by price. Elasticity is a measure of how much QD is affected by price. The more sensitive the change in QD, the more elastic it is. If a product is not very sensitive, then it is said to be inelastic. Shortcuts Test #2: The four tailed test If Ed is > 1, D is E If Ed is = 1, D is Unit Elastic If Ed is < 1, D is inelastic Question Large % of Budget? Time to delay purchase? Need or want? Are there many substitutes? Elastic YES YES WANT YES Inelastic NO NO NEED NO 3

4 Substitutes and their effects on elasticity Demand tends to be elastic when there are many substitutes, and visa-versa. versa. (Trash) Trash Example Charlottesville, VA tries to slow trash production. Raises prices for collection. There are few substitutes for trash collection. Demand for that is inelastic However, found that it does increase recycling/illegal dumping Exhibit 5: Demand Becomes More Elastic over Time Initial price = \$1. D w = the demand curve one week after the price change D m = one month after D y, = one year after. Suppose the price now increases to \$1.25. The more time for consumers to respond to price increase, the greater the reduction in quantity demanded. \$ D w Test # 3: The Quick and Dirty There is a relationship b/w slope and elasticity. When measuring slope by %change, it is the Inverse of the elasticity. D w shows that one week after the price increase, the quantity demanded has not changed much in this case from 1 to 95 per day. Conversely, after one month, the quantity demanded has declined to 75, and after one year to 5 per day Quantity per period Note that among these demand curves and over the range starting from the point where the demand curves intersect, the flatter the demand curve, the more price elastic the demand. D w D m D Inelastic Elastic D Test #4: The Total Revenue (TR) Test These relationships can be tied together by looking at a linear demand curve A linear demand curve is simply a straight- line demand curve Exhibit 2 presents these ideas Unit Elastic Point is max. TR!!! Exhibit 2: Demand, Price Elasticity and Total Revenue Panel (a) shows the linear demand curve and panel (b) shows the total revenue generated by each pricequantity combination along the demand curve. Since the demand curve is linear, its slope is constant a given decrease in price always causes the same unit increase in quantity demanded. The price elasticity of demand is greater on the higher-price end of the demand curve than on the lower-price end. \$ \$25, Total revenue (a) Demand and Price Elasticity , Quality per period (b) Total Revenue Quantity per period 5 D TR = p x q Total revenue 1, 4

5 Exhibit 2: Demand, Price Elasticity and Total Revenue Consider a movement from point a to point b on the demand curve. The 1-unit increase in quantity demanded is a percent change of 1/15 =.67 while the \$1 drop in price is a percent change of 1/85 = 12% the price elasticity of demand here is 5.6 Between points d and e on the lower end, the 1-unit quantity increase is a percent change of 1/85 = 12% and the \$1 price decrease is a percent decline of 1/15 = 67% a price elasticity of.2 \$1 (a) Demand and Price Elasticity 9 a 8 7 b 6 5 c d 1 e D \$25, Total revenue , Quality per period (b) Total Revenue Quantity per period 5 TR = p x q Total revenue 1, Exhibit 2: Demand, Price Elasticity and Total Revenue Demand becomes less elastic as we move down the curve. Halfway down, the elasticity equals 1.. Since we have a linear demand curve, the slope is constant but the elasticity varies slope is not the same thing as elasticity. Where demand is elastic, a decrease in price will increase total revenue because the gain in revenue from selling more units exceeds the loss in revenue from selling at the lower price. Where demand is inelastic, a price decrease reduces total revenue because the gain in revenue from selling more units is less than the loss in revenue at the lower price. \$1 (a) Demand and Price Elasticity 9 a Elastic E D > b 6 Unit elastic E D = 1 5 c 4 Inelastic E 3 D < 1 2 d 1 e D \$25, Total revenue , Quality per period (b) Total Revenue Quantity per period 5 TR = p x q Total revenue 1, Exhibit 3: Constant Elasticity Demand Curves Exhibit 6: Selected Price Elasticities of Demand p (a) Perfectly elastic E D = D (b) Perfectly inelastic D' E D = Quantity Q Quantity 6 1 Quantity per period per period per period Demand curve in (a) indicates consumers will demand all that is offered at the given price, p. If the price rises above p, quantity demanded drops to zero perfectly elastic demand curve. \$1 Demand curve in (b) is vertical, quantity demanded does not vary when the price changes no matter how high the price, consumers will purchase the same quantity perfectly inelastic demand curve. 6 (c) Unit elastic E D = 1 a b D" (c) shows a unit-elastic demand curve where any percent change in price results in an identical offsetting percent change in quantity demanded. Product Short Run Long Run Cigarettes (among adults).4 Electricity (residential) Air travel Medical care and hospitalization.3.9 Gasoline Milk.4 Fish (cod).5 Wine Movies Natural gas (residential) Automobiles Chevrolets 4. Using Ed Predicting changes in QD Book examples: Ed= (% QD) (% P) EX. 1.:College tuition: \$4, - \$4,4 PED for college tuition is 1.4 EX. 2.: Ed of young drinkers 1.3 and then there is an %2 increase in beer prices due to tax Price Elasticity of Supply Prices are signals to both sides of the market about the relative scarcity of products High prices discourage consumption but encourage production The price elasticity of supply measures how responsive producers are to a price change 5

6 Price Elasticity of Supply The price elasticity of supply equals the percent change in quantity supplied divided by the percent change in price Since the higher price usually results in an increased quantity supplied, the percent change in price and the percent change in quantity supplied move in the same direction the price elasticity of supply is usually a positive number If the price increases from p to p', the quantity supplied increases from q to q' Exhibit 7: Price Elasticity of Supply The price elasticity of E s, is p' p S Exhibit 7 depicts a typical upward-sloping supply curve Where q is the change in quantity supplied and p is the change in price. q q' Quantity per period Determinants The elasticity of supply indicates how responsive producers are to a change in price Their responsiveness depends on how easy it is to alter output when price changes If the cost of supplying additional units rises sharply as output expands, then a higher price will elicit little increase in quantity supplied But if the marginal cost rises slowly as output expands, the lure of a higher price will prompt a large increase in output Length of Time Just as demand becomes more elastic over time as consumers adjust to price changes, supply also becomes more elastic over time as producers adjust to price changes The longer the time period under consideration, the more able producers are to adjust to changes in relative prices Exhibit 9 illustrates this Price-Change Formula You can predict price change when you have a D or a S and you know both the Es and the Ed % P = D or S (Es + Ed) Income Elasticity of Demand The income elasticity of demand measures how responsive demand is to a change in income Measures the percent change in demand divided by the percent change in income Categories Goods with income elasticities less than zero are called inferior goods demand demand declines when income increases 6

7 Income Elasticity of Demand Normal goods have income elasticities greater than zero demand increases when income increases Normal goods with income elasticities greater than zero but less than 1 are called income inelastic goods demand increases but not as much as does income Goods with income elasticity greater than 1 are called income elastic demand not only increases when income increases but increases by more than does income Exhibit 1 presents some income elasticity estimates for various goods and services Exhibit 1: Selected Income Elasticities of Demand Income Income Product Elasticity Product Elasticity Private education 2.46 Physicians services.75 Automobiles 2.45 Coca-Cola.68 Wine 2.45 Beef.62 Owner-occupied housing 1.49 Food.51 Furniture 1.48 Coffee.51 Dental service 1.42 Cigarettes.5 Restaurant meals 1.4 Gasoline and oil.48 Shoes 1.1 Rental housing.43 Chicken 1.6 Beer.27 Spirits ( hard liquor) 1.2 Pork.18 Clothing.92 Flour.36 Cross Price Elasticity BOOK Definition -By Kiefer O Connor, Vince Blake and Leah Chapman How a change in the price (P) of one product will affect the demand (D) for another. Ex: Price of coke with lemon changes demand of original coke The percentage change in the demand of one good divided by the percentage change in the price of another good. Another cool video EQUATION % D / % P The numerical value can either be positive, negative, or zero. Positive= substitutes Negative= compliments Zero= unrelated Substitute Increase in the price of Coke leads to an increase in the demand of Pepsi. Coke prices goes from \$3 to \$5 Demand of Pepsi goes from 2 twelve packs to 5 twelve packs A cartoon version of Mr. Frank, with less hair and a weird nose 7

8 Compliment Increase in the price of gas leads to a decrease in the demand of tires. Less people driving= less need to buy tires. UNRELATED Most of the goods to be compared selected at random are unrelated, so they have no cross-price elasticity of demand. Oh look, there he is again Don t pay attention to the sweet rims just the tires Unrelated picture Quiz 1. Change in Price of a product affects the change in for another. A. Elasticity B. Price C. Demand D. Quality 2. When the numerical value is positive, the products are. A. Unrelated B. Compliment C. Substitutes 3. To find Cross- Price Elasticity of Demand, you Divide % D by. A. % QD B. % Q C. % P D. % KO 4. If the Cross- Price Elasticity of Demand is Unrelated, the value is. A. Positive B. Negative C. Zero D. False END 5. In order to find the Cross-Price Elasticity of Demand you must have price and. A. True B. False C. Answer Not Here 8

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