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managerial economics_10

# managerial economics_10 - (b However in checking with...

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3. Hanna Corporation markets a compact microwave oven. In 2010 they sold 23,000 units at \$375 each. Per capita disposable income in 2010 was \$6,750. Hanna economists have determined that the arc price elasticity for this microwave oven is −1.2. (a) In 2011 Hanna is planning to lower the price of the microwave oven to \$325. Forecast sales volume for 2011. (Assume that all other things remain equal) Arc price elasticity = ΔQ/ [(Q1 + Q2)/2] ΔP/ [(P1 + P2)/2] -1.2 = (Q-23000)/[(23000+Q)/2] (325-375)/[(375+325)/2] => -1.2 x -1/7 = (Q-23000)/[(23000+Q)/2] => 1.2/7 x (11500 + Q/2) = Q - 23000 => 13800/7 + 23000 = Q – 0.6/7Q => 174800 = 6.4Q => Q = 27312.5
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Unformatted text preview: (b) However, in checking with government economists, Hanna finds that per capita disposable income is expected to rise to \$7,000 in 2011. In the past the company has observed an arc income elasticity of +2.5 for microwave ovens. Please forecast 2011 sales, given that the price is reduces to \$325 and that per capita disposable income increases to \$7,000. (Assume that the price and income effects are independent and additive) Q2 = Q1[1 + ED(% ΔP) + EY(% ΔY) + Ecross(% ΔPR)] => 23000 [ 1 + -1.2{(325-375)/ [(375 + 325)/2]} + 2.5{(7000-6750)/ [(6750 + 7000)/2]} = 23000 + 27600/7 + 46000/59 = 23000 + 3942.86 + 779.66 = 27722.52 => Q = 27722.52...
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