ECON205 - Homework08 - S09

# ECON205 - Homework08 - S09 - c,~~ 1 Relationship between...

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Unformatted text preview: c,~~ 1. Relationship between total and marginal revenue ~suppose the,e's an appliancesto'e that sells ai, conditione,", It could set its p'ice high and sell ve", few ai, conditioners, or it could set its price low and sell lots of air conditioners. The following table shows some possible choices this store could make for its annual production. Price Quantity Total Revenue Choice A \$400 \$0 B 300 200 60,000 C 200 400 80,000 D 100 600 60,000 E 800 The graph below plots the firm's "total revenue" curve: that is, the relationship between quantity and total revenue given by the two right columns of the table above. The five choices are also labeled. Finally, two black lines are shown; these lines are tangent to the green curve at points Band D. DOLLARS (Thousands of dollars per year] 100 D ) ( c 30 20 10 40 90 80 70 60 50 o 100 200 300 400 500 600 700 OUTPUT lAir conditioners sold per year) The slope of the total revenue curve is the firm's marginal revenue 't/. Explanation: Close A The slope of a curve measures how much its vertical component changes for each unit increase in its horizontal component. In this case, the vertical component of the curve measures total revenue, and the horizontal component of the curve measures air conditioners sold. Therefore, the slope of the line represents the change in total revenue resulting from a one-unit increase in the number of air conditioners sold; this is the definition of marginal revenue. The diagram below plots this firm's demand curve. Using the total revenue graph above, calculate the slope of the lines tangent to the total revenue curve at points Band D. Based on this information, use the black line (X symbols) to plot the firm's marginal revenue curve on the graph below. DOLLARS[Dollars per air conditioner! Answer DOLLARS [Dollars per air conditioner! 500 400 300 200 100 o-100-200-300-400 Marginal Revenue " 500 400 300 200 100 o-100-200-300-400-500-500 o 100 200 300 400 SOD bOD 700 BOD 100 200 300 400 SOD bOD 700 BOD OUTPUT [Air conditioners per year! I Clear All I~ OUTPUT (Air conditioners per year! Explanation: Close A At point B, the total revenue curve is tangent to the black line that passes through the points (150 air conditioners per year, \$50,000 per year) and (250 air conditioners per year, \$70,000 per year). Therefore, the slope of that line is: Slope at Point B Rise Run \$70,000 per year - \$50,000 per year 250 air conditioners per year - 150 air conditioners per year \$20,000 per year 100 air conditioners per year \$200 per air conditioner (Note that there is a "per year" in the numerator and in the denominator, so these cancel.) Similarly, at point D, the total revenue curve is tangent to the black line that passes through the points (550 air conditioners per year, \$70,000 per year) and (650 air conditioners per year, \$50,000 per year). Therefore, the slope of that line is: Slope at Point D Rise Run \$50,000 per year - \$70,000 per year 650 air conditioners per year - 550 air conditioners per year...
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ECON205 - Homework08 - S09 - c,~~ 1 Relationship between...

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