4 the demand for company xs product is given by y x x

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4. The demand for company X’s product is given by y x x P P Q 4 3 12 + - = . Suppose good X sells for $3.00 per unit and good Y sells for $1.50 per unit. a. Calculate the cross-price elasticity of demand between goods X and Y at the given prices. b. Are goods X and Y substitutes or complements? c. What is the own price elasticity of demand at these prices? d. How would your answers to parts a and c change if the price of X dropped to $2.50 per unit? 5. Suppose the demand for sunscreen (X) has been estimated to be y x x A S P Q ln 3 ln 3 ln 7 . 1 5 ln - + - = , where S denotes the average hours of sunshine per day and y A represents the level of advertising for good Y. a. What would be the impact on demand of a 5 percent increase in the daily amount of sunshine?
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b. What would be the impact of a 10 percent reduction in the amount of advertising toward good Y? c. What might be good Y in this example? 6. An econometrician has estimated the inverse demand relation e bQ a P + + = and found that 400 ˆ = a , 75 . 2 ˆ - = b , 8 ˆ = a σ , and 75 . 0 ˆ = b σ . Find the approximate 95 percent confidence interval for the true values of a and b . 7. A firm is considering raising its price by 9 percent and has hired an econometrician to estimate the elasticity of demand for its product. The econometrician estimates the parameters of a log-liner demand function and reports that the parameter estimate for the elasticity of demand is -1.5 and the standard error of the estimate is 0.3. a. If the firm raises its price by 9 percent, what is the expected change in quantity demanded? b. Approximate the upper and lower bounds on the 95 percent confidence interval for the change in quantity demanded. Multiple Choice Questions
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