5. Text ch 4 Prob 17 adapted. The demand curve for product “a” is given as Q = 2

Question

5. Text ch 4 Prob 17 adapted. The demand curve for product “a” is given as Q = 2000 -20P and the price is currently P = $70. How many units will be sold at $70? At $80? What is the price elasticity between $70 and $80? Use the “arc elasticity” method found on page 70 and shown here: Arc Elasticity = (Q2 - Q1)/((Q1 + Q2)/2)÷(P2 - P1)/((P2 + P1)/2) Based on this measure, is demand price elastic? Based on this measure, do you expect total revenue to increase or to decrease if the price is raised to $80? What will be the total revenue at a price of $70? What will be the total revenue at a price of $80? Be sure that your answer to part “d” is consistent with your answer to part “c.” (If it is not, go back and check for errors.)

Explanation / Answer

P1 = 70 :

Q1 = 2000 - 20 x 70 = 600

P2 = 80

Q2 = 2000 - 20 x 80 = 400

PE = (P1 + P2)/(Q1 + Q2) x (Q2 - Q1)/(P2 - P1)

PE = 150/1000 x -200/10 = -3

Demand is price elastic as abs (PE) > 1

Total revenue would decrease if price is raised to $80, this is because a given change in price level (increase) would lead to more than proportional decrease in the quantity demanded. As a result, total revenue would decrease.

TR = P x Q

P = 70: TR = $42000

P = 80: TR = 80 x 400 = $32000

Answer is consistent, total revenue decreases when price is increased to $80

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