Question

Suppose you are collecting data from a country like Japan where the government sets the price of health care. Each prefecture in Japan has a different set of prices (for example, Tokyo has higher prices than rural Hokkaido). Data for 2015 is displayed in Table 1. What is the arc price elasticity of demand for health care consumers in Japan (using only this data)? Suppose that incomes are generally much higher in Tokyo than Hokkaido. Is your answer to the last question an overestimate or underestimate of price elasticity? Justify your answer. Using your estimated elasticity. What would the demand for health care be if the price in Tokyo were raised to 30 Yen. What would the demand for health care be if the price in Hokkaido were lowered to 5 Yen per visit. You continue your observations of the Japanese market into the year 2016. That year Japan changed the price in both Tokyo and Hokkaido. Data for 2016 is displayed in Table 2. What is the arc price elasticity of demand for health care consumers in Japan (using only data for the year 2016)? Use data for both years to compute the arc price elasticity of demand for health care for Tokyo and Hokkaido, separately. Using your estimated elasticities. What would the demand for health care be if the price were raised to 45 Yen in both cities.

Answer 1

a) Are elasticity of demand - Midpoint of elasticity E_d = (-) Delta Q/1/2 (Q_1 + 2) divided Delta P/1/2 (P_1 + P) = -Delta Q/1/2(Q_1 + Q) times 1/2 (P_1 + P)/Delta p = -0.25/1/25 (1.5 + 1.25) times 1/2 (20 + 10)/10 = -0.25/1.375 times 15/10 = -0.1818 times 1.5 = -0.27 b) It is an as the demand is elastic Vertical-bar p Vertical-bar lessthanorequalto 1 c) Elasticity of element of Tokyo Ed = % Delta Q/% Delta P % Delta p = 30 - 20/20 = 10/20 = 0.5% Ed = % Delta Q times p = - 0.27 = % Delta Q/0.5 % % Delta Q = -0.135 % Therefore The quantity demanded decrease - 10 - 5 % Delta P = 5 - 10/5 = -5/9 = 1 % - 0.27 = % Delta Q/1 % % Delta Q = -0.27 % decrease in demand Table 2: d) E_d = (-) 0.2/1/2 (12 + 1.0) times 1/2 (30 + 15)/15t = 0.2/1.1 times 22.5/15 = 0 + 8 times 1.5 = -0.27 e) Tokyo = Ed = (-) (- 0.25)/1/2(1.0 + 1.25) times 1/2 (30 + 20)/10 =