you invent a new product, Product X. The demand for product X is given by X(P)=1
ID: 1245194 • Letter: Y
Question
you invent a new product, Product X. The demand for product X is given by X(P)=100-P, and the the cost function is given by C(X)=X^2, and the marginal cost is MC=2X. It is then discovered that there is a positive eXternality associated with good X. Each unit you produce actually offers $4 of benefit to society. What is the deadweight loss of not taking this externality into consideration?Explanation / Answer
the quantity demanded of lettuce will increase by 51%. [ Cross price elasticity = (% change in quantity demanded of lettuce / % change in the price of spinach) means in this case, 3.4 = X / 15, or, X= 3.4 * 15 = 51 ] Notes: 1. cross price elasticity of demand measures the responsiveness of the quantity demand of a good to a change in the price of another good. It is measured as the percentage change in quantity demanded for the first good that occurs in response to a percentage change in price of the second good. For example, if, in response to a 10% increase in the price of fuel, the quantity of new cars that are fuel inefficient demanded decreased by 20%, the cross elasticity of demand would be -20%/10% = -2. Two goods that complement each other show a negative cross elasticity of demand.In the example above, the two goods, fuel and cars(consists of fuel consumption), are complements - that is, one is used with the other. In these cases the cross elasticity of demand will be negative. In the case of perfect complements, the cross elasticity of demand is infinitely negative. Where the two goods are substitutes the cross elasticity of demand will be positive, so that as the price of one goes up the quantity demanded of the other will increase. For example, in response to an increase in the price of carbonated soft drinks, the demand for non-carbonated soft drinks will rise. In the case of perfect substitutes, the cross elasticity of demand is equal to infinity. Where the two goods are complements the cross elasticity of demand will be negative, so that as the price of one goes up the quantity demanded of the other will decrease. For example, in response to an increase in the price of fuel, the demand for new cars will decrease. Where the two goods are independent, the cross elasticity demand will be zero: as the price of one good changes, there will be no change in quantity demanded of the other good. When goods are substitutable, the diversion ratio - which quantifies how much of the displaced demand for product j switches to product i - is measured by the ratio of the cross-elasticity to the own-elasticity multiplied by the ratio of product i's demand to product j's demand. In the discrete case, the diversion ratio is naturally interpreted as the fraction of product j demand which treats product i as a second choice,[1] measuring how much of the demand diverting from product j because of a price increase is diverted to product i can be written as the product of the ratio of the cross-elasticity to the own-elasticity and the ratio of the demand for product i to the demand for product j. In some cases, it has a natural interpretation as the proportion of people buying product j who would consider product i their `second choice.' 2. The Cross-Price Elasticity of Demand measures the rate of response of quantity demanded of one good, due to a price change of another good. If two goods are substitutes, we should expect to see consumers purchase more of one good when the price of its substitute increases. Similarly if the two goods are complements, we should see a price rise in one good cause the demand for both goods to fall. Your course may use the more complicated Arc Cross-Price Elasticity of Demand formula. If so you'll need to see the article on Arc Elasticity. The common formula for the Cross-Price Elasticity of Demand (CPEoD) is given by: CPEoD = (% Change in Quantity Demand for Good X)/(% Change in Price for Good Y) Calculating the Cross-Price Elasticity of Demand You're given the question: "With the following data, calculate the cross-price elasticity of demand for good X when the price of good Y changes from $9.00 to $10.00." Using the chart on the bottom of the page, we'll answer this question. We know that the original price of Y is $9 and the new price of Y is $10, so we have Price(OLD)=$9 and Price(NEW)=$10. From the chart we see that the quantity demanded of X when the price of Y is $9 is 150 and when the price is $10 is 190. Since we're going from $9 to $10, we have QDemand(OLD)=150 and QDemand(NEW)=190. You should have these four figures written down: Price(OLD)=9 Price(NEW)=10 QDemand(OLD)=150 QDemand(NEW)=190 To calculate the cross-price elasticity, we need to calculate the percentage change in quantity demanded and the percentage change in price. We'll calculate these one at a time. Calculating the Percentage Change in Quantity Demanded of Good X The formula used to calculate the percentage change in quantity demanded is: [QDemand(NEW) - QDemand(OLD)] / QDemand(OLD) By filling in the values we wrote down, we get: [190 - 150] / 150 = (40/150) = 0.2667 So we note that % Change in Quantity Demanded = 0.2667 (This in decimal terms. In percentage terms this would be 26.67%). Calculating the Percentage Change in Price of Good Y The formula used to calculate the percentage change in price is: [Price(NEW) - Price(OLD)] / Price(OLD) We fill in the values and get: [10 - 9] / 9 = (1/9) = 0.1111 We have our percentage changes, so we can complete the final step of calculating the cross-price elasticity of demand. Final Step of Calculating the Cross-Price Elasticity of Demand We go back to our formula of: CPEoD = (% Change in Quantity Demanded of Good X)/(% Change in Price of Good Y) We can now get this value by using the figures we calculated earlier. CPEoD = (0.2667)/(0.1111) = 2.4005 We conclude that the cross-price elasticity of demand for X when the price of Y increases from $9 to $10 is 2.4005. How Do We Interpret the Cross-Price Elasticity of Demand? The cross-price elasticity of demand is used to see how sensitive the demand for a good is to a price change of another good. A high positive cross-price elasticity tells us that if the price of one good goes up, the demand for the other good goes up as well. A negative tells us just the opposite, that an increase in the price of one good causes a drop in the demand for the other good. A small value (either negative or positive) tells us that there is little relation between the two goods. Often an assignment or a test will ask you a follow up question such as "Are the two goods complements or substitutes?". To answer that question, you use the following rule of thumb: If CPEoD > 0 then the two goods are substitutes If CPEoD =0 then the two goods are independent (no relationship between the two goods If CPEoD < 0 then the two goods are complements In the case of our good, we calculated the cross-price elasticity of demand to be 2.4005, so our two goods are substitutes when the price of good Y is between $9 and $10.Related Questions
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