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Homework answers / question archive / Suppose the original quantity demanded for good R is 20 units and the new quantity demanded for R is 10 units

Suppose the original quantity demanded for good R is 20 units and the new quantity demanded for R is 10 units

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Suppose the original quantity demanded for good R is 20 units and the new quantity demanded for R is 10 units. For good T, the original price is $8 and the new price is $6. What is the cross-price elasticity of demand between R and T (using the arc or midpoint formula)?

A. 1/2

B. 2.33

C. 2/3

D. 0.43

E. 5

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  • The right answer choice is: B. 2.33.

Using the mid-point formula, we will calculate the cross-price elasticity of demand between good R and TR and T as:

ER,T=ΔQRΔPTׯPT¯QRER,T=ΔQRΔPT×P¯TQ¯R

where:

  • ¯PTP¯T is the average change in the price of good TT and,
  • ¯QRQ¯R is the average change in the price of good RR.

From the information in our question, we can deduce the following table.

 

PT QR
$8 20
$6 10

Therefore:

ΔQR=10−20=−10ΔPT=6−8=−$2¯PT=8+62=$7¯QR=10+202=15ΔQR=10−20=−10ΔPT=6−8=−$2PT¯=8+62=$7QR¯=10+202=15

Thus, the cross-price elasticity of demand is:

ER,T=−10−2×715ER,T≈2.333