Question

The weekly demand for sandwiches at a local sandwich shop is given by:

Qd = 2,000 – 5P + 2Pj – 0.01INCOME,

            where Qd is the number of sandwiches demanded per week, P is the per-sandwich price, Pj is the price of a related product, and INCOME is the average monthly income of consumers. 

Suppose that P = $10, Pj = $50, and INCOME = $5,000. What is the value of the cross-price elasticity of demand? Is the related product a substitute good or a complement?

Suppose that P = $10, Pj = $50, and INCOME = $5,000. What is the value of the income elasticity of demand? Are sandwiches a normal or an inferior good?

Answer 1

$Q= 2000- 5(10)+2(50)-0.01(5000)= 2000$

$IE=\frac{ \Delta Q}{\Delta P}\times \frac{I}{Q}$

$-0.01\times \frac{5000}{2000}= -0.025$

This an inferior good

Cross Elasticity$=$ $\frac{ \Delta Q}{\Delta P}\times \frac{P}{Q}$

$2\times \frac{50}{2000}= 0.05$

This is a compliment good