Price elasticity of demand

You are a manager at Sievert Devices, Inc., a manufacturer of scientific instruments. You are attending an executive meeting when Rolf, another manager at your company, announces:

(a) (4 marks) “Our marketing department has estimated the own-price elasticity of demand for our Geiger counter at its current price of $10. We are confident that the coefficient of elasticity is 0. This means that if we slightly increase our price above $10, the quantity demanded would not change and this would increase our revenue and our profits.” Evaluate Rolf’s claim. Is he correct? If not, explain which parts of his statement are incorrect.
(b) (4 marks) “This is nothing!” Rolf adds, “Why should we limit ourselves to small price changes? Clearly, if the coefficient of price elasticity of demand is zero, then increasing the price above $10 by any amount is going to increase revenue and profits without changing the quantity demanded.” Evaluate Rolf’s claim as in part (a).
(c) (4 marks) “But this is not all, ladies and gentlemen!” Rolf continues, “As you are all well aware, Sievert Devices Inc. is also the proud manufacturer of the world-famous Curie radiometer. We have also estimated the cross-price elasticity of demand for our Geiger counters with respect to the price of the Curie radiometer, and we have found that it equals 3. Naturally, this means that the two goods are complements and that if we increase the Curie radiometer’s price by 1%, the quantity demanded for our Geiger counter will go up by 3%.” Evaluate Rolf’s claim as in part (a).
(d) (4 marks) “Of course, this gives me another idea about how to increase profits,” concludes Rolf, “If we increase the price of the Curie radiometers, we will see an increase in demand for our Geiger counters and higher profits from the sale of Curie radiometers. Overall, this would guarantee an increase in the profits of the firm as a whole.” Evaluate Rolf’s claim as in part (a).
(e) (4 marks) Consider a good with demand represented by the inverse demand function P = 10−0.5Qd. Using the point elasticity method, find the price elasticity of demand for this good when price equals $3 and again when price equals $8. In each of these cases, state whether demand is elastic or inelastic.
(f) (5 marks) Consider a good with demand represented by the demand function Qd = A/P for some positive parameter A > 0. Using the arc elasticity method, find the price elasticity of demand for this good when price increases from $1 to $4. Then, using the same method, find the price elasticity of demand for this good when price drops from $10 to $5. Discuss the results you observe. What kind of demand does this good have?

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