Question

5. You own goods A and B. You are considering increasing price of good A by 10%. Here is the information you have

Pa = 20

Qa = 1000

For each $1 increase in Pa, Qa will decrease by 100.

Pb = 12

Qb = 750

For each $1 increase in Pa, Qb will increase by 100.

(The point of this exercise is to have you do everything the long way then use the delta r formula so you can see the difference)

h. What is the own price elasticity for good A?

i. What is the cross price elasticity of A and B?

j. Calculate the change of revenue using the formula provided in class.

k. Explain why the two methods have different answers.

l. To calculate the change in total revenue from the price change, which method do you prefer? Doing parts a-g or doing part h-j? Briefly explain.

Answer 1

The following statements are given for good a and good b----

Pa. Qa. Pb. Qb

20. 1000. 12. 750

21. 900. 13. 850

#h) Own price Ed for good a------

Price Ed= - ∆q/∆p×(p/q)

∆q=100. (1000-900)

∆p=1 (21-20)

p=20

q=1000

Ed=(-) 100/1(20/100)= 2

Price Ed of good a= 2 ( elastic)

#i) Cross price elasticity of demand-------

Ed( cross)= percentage change in Quantity demanded of good 1/ percentage change in price of good 2

We will find cross elasticity of demand for both goods.

*Good a------

100/1000×100 ÷ ( 1/12)(100)= 1•2

*Good b------

(100/750)100 ÷ (1/20)100. = 2•67

So, cross elasticity of demand for good a= 1•2

Cross elasticity of demand for good b= 2√67

#J) change in Revenue for good a & b-----+

*Good a------

Change in revenue = initial Revenue - new Revenue

Initial Revenue = p×q = 20×1000=$20000

New Revenue= 21×900=$ 18900

Change in Revenue=20000-18900=$1100( decrease)

* Good b------

Initial Revenue = 12×750=$ 9000

New Revenue = 13×850=$11050

Change in Revenue = 11050-9000=$2050( increase)

So, Decrease in Revenue of good a=$ 1100

Increase in revenue for good b=$2050

Thank you...

P.S --- Answer to parts k & l not possible as no sufficient information is available for these parts.