(LO1) The demand function of a good is given by Q=100-3P+2P_(A)+0.1Y where Q. P. P_(A) and Y denote quantity demanded, price of the good, price of an alternative good and income, respectively. Find the cross-price elasticity of demand when P=20,P_(A)=15 and Y=300. 0.1 b) 0.2 c) 0.3 d) 0.4 e) 0.5

To find the cross-price elasticity of demand, we need to calculate the percentage change in quantity demanded with respect to the percentage change in the price of the alternative good ($P_A$).<br /><br />The formula for cross-price elasticity of demand is:<br /><br />Cross-price elasticity of demand = (Percentage change in quantity demanded) / (Percentage change in price of the alternative good)<br /><br />First, let's calculate the quantity demanded ($Q$) when $P=20$, $P_A=15$, and $Y=300$.<br /><br />Substituting the given values into the demand function:<br /><br />$Q = 100 - 3(20) + 2(15) + 0.1(300)$<br /><br />$Q = 100 - 60 + 30 + 30$<br /><br />$Q = 100$<br /><br />Now, let's calculate the percentage change in quantity demanded with respect to the percentage change in the price of the alternative good ($P_A$).<br /><br />Percentage change in quantity demanded = (Change in quantity demanded) / (Original quantity demanded) * 100<br /><br />Change in quantity demanded = $2 * 15 = 30$<br /><br />Percentage change in quantity demanded = (30 / 100) * 100 = 30%<br /><br />Percentage change in price of the alternative good = (15 / 15) * 100 = 100%<br /><br />Now, we can calculate the cross-price elasticity of demand:<br /><br />Cross-price elasticity of demand = (30%) / (100%) = 0.3<br /><br />Therefore, the correct answer is c) 0.3.