Text ch 4 Prob 17 adapted. The demand curve for product “a” is given as Q = 2000

Question

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.

A. How many units will be sold at $70? At $80?

B. What is the price elasticity between $70 and $80? Use the “arc elasticity” method found on page 70 and shown here:

C. 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?

D. What will be the total revenue at a price of $70? What will be the total revenue at a price of $80?

E. 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

A)

P = $70 , Q = 2000 - 20 x 70 = 600

P = $80, Q = 2000 - 20 x 80 = 400

B)

PE = -(400-600)/(80 - 70) x (80+70)/(400 + 600) = -3

C) Since abs (PE) > 1, demand is price elastic. When the price is increased, there would be more than proportional reduction in the quantity demanded. As a result, total revenue would reduce.

D)

TR = P x Q

P = 70 , TR = 70 x 600 = $42000

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

E) As can be seen above, total revenue decreases when the price increases if the demand is price elastic.

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