a) When the prices of coke decreases from $7.98 to 6.98 per case of 24, the quantity Pepsi demanded went from 1000 to 700 cases of 24. Calculate the cross elasticity of demand. What types of products are present here?
b)does this make sense? Explain.
Hello chinky.
a) Do you know the formula for cross-price elasticity of demand? It is (Proportional ch. in demand for good A) divided by (Proportional ch. in price of good B)
In this case, good A is Pepsi and good B is Coke.
The proportional change in demand for Pepsi is $\displaystyle \frac{700-1000}{1000} = -0.3 $
The proportional change in price for Coke is $\displaystyle \frac{6.98-7.98}{7.98} = -0.125 $ to 3 decimal places
Thus the cross elasticity of demand is roughly (+)2.4. Since the value is positive $\displaystyle \Rightarrow $ the products are substitutes.
(b) Yes. Try to think about this intuitively. The price of Coke falling would probably lead to some people switching from Pepsi to Coke, since the opportunity cost of Coke has fallen.
Furthermore, you could also say since its value of the cross elasticity of demand is greater than 1 $\displaystyle \Rightarrow $ the goods are strong substitutes.
I don't know how advanced your answer must be, but you can also link in the marginal rate of substitution and budget constraint / indifference curve analysis. If you need assistance in doing so, I'll be more than happy to help.
What is the formula that I stated above?
I divided the proportional change in demand for pepsi (-0.3) by the proportional change in price for coke, which is (-0.125) to 3.d.p.
$\displaystyle \frac{-0.3}{-0.125} = 2.4 $
Do you understand it now?
It's really just about using the formula. I suggest you practice a few similar questions so you get the feel for these types of problems.
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