Use this test determine whether the indicated products are...

Use this test determine whether the indicated products are competitive, complementary, or neither.
The daily demand equations for the sale of brand $A$ coffee and brand $B$ coffee in a supermarket are
$$
\begin{array}{l}
x=f(p, q)=200-5 p+4 q \\
y=g(p, q)=300+2 p-4 q
\end{array}
$$

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Key Concepts

Partial Derivatives in Demand Analysis

In the context of multivariable demand functions, partial derivatives help quantify the change in demand for a product with respect to a small change in one of its determinants, such as its own price or the price of another product, while holding other factors constant.

Substitutes and Complements

These are categories of goods based on how demand for one good responds to price changes in another. Substitutes are goods whose demand increases when the price of a related good rises, whereas complements are goods whose demand decreases when the price of the other good increases.

Demand Functions

A demand function describes the relationship between the quantity demanded of a product and various factors affecting it, such as its own price and the price of competing goods. It is fundamental in understanding how consumers adjust their purchases in response to price changes and other variables.

Cross-Price Elasticity

Cross-price elasticity of demand measures the sensitivity of the demand for one product to changes in the price of another product. A positive cross-price elasticity indicates that the products are substitutes (competitive goods), while a negative value suggests they are complements.

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