Dr. Seiji Steimetz ECON 101 Department of Economics California State University, Long BeachPage 1 of 12 ANSWERS FOR PROBLEM SET 4 LEARNINGOBJECTIVE LEARNING OBJECTIVE 6.1 Define the price elasticity of demand and understand how to measure it. Review Questions 1.1Price elasticity of demand = (percentage change in quantity demanded)/(percentage change in price). It isn’t measured by the slope of the demand curve because the slope depends arbitrarily on what units you are using. Slope will change by a factor of 100 if you use cents instead of dollars, for example. Or, to take another example, consider the case of six-packs of soda versus cans of soda: If the price drops by $1.00 per six-pack and this causes quantity demanded to increase by two six-packs, that is the same thing as demand going up by 12 cans. So, you could either calculate the slope as −1/2 six-packs, or you could calculate it as −1/12 cans. In addition, using percentage changes in the elasticity formula allow for meaningful comparisons of demand responsiveness between very different kinds of goods: for example, breakfast cereal versus health care. Because the slope uses physical units of quantities, such comparisons become impossible. 1.2The price elasticity = (percentage change in quantity demanded)/(percentage change in price) = –25%/10% = –2.5. This is elastic. 1.3In calculating the percentage change in price and quantity, the midpoint formula divides by the average of the starting and ending values. Midpoint Formula:(Q2−Q1)Q1+Q22⎛⎝⎜⎞⎠⎟÷(P2−P1)P1+P22⎛⎝⎜⎞⎠⎟Percentage changes can also be calculated by using the starting or ending value without averaging, but this gives different results depending on whether the starting or ending value is used.
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Dr. Seiji Steimetz ECON 101 Department of Economics California State University, Long BeachPage 2 of 12 1.4A perfectly inelastic demand curve is shown by a vertical line, as shown at the bottom of Table 6-1. Such a good will have no substitutes; for example, a life-saving drug. Problems and Applications 1.5a. 000,000,400.3$00.2$000,000,8000,000,12−=−−b. 400.3$00.2$812−=−−. This is a much smaller value than in a. c. We can calculate the price elasticity using the midpoint formula as follows: Percentage change in quantity demanded = %40100000,000,10000,000,8000,000,12=×−Percentage change in price = %4010050.2$00.3$00.2$−=×−So, the price elasticity of demand = 1%40%40−=−Notice that this value is significantly different than the ones calculated in a. and b.