Question

A supply function of good X is given as

Qsx = 8 + 0.6Px – 0.4Py + 0.3Pz – 0.4C

where Qsx is quantity supplied of good X, Px is price of the good in question, and 

are 

prices of related goods, and C is cost of production. Y is good Y and Z is good Z.

i. What type of good is Y? Explain your answer. 

ii. What type of good is Z? Explain your answer.

iii. Interpret the coefficients of Px, Py, and Pz, and C. 

Answer 1

$$Solution$$

i) Good $y$ , is a complimentary good since it has a negative cross-price elasticity of supply

ii) Good $z$ is a substitute good because it has a positive price elasticity

iii) The sign of the coefficient of good Z($Pz)$ is negative and good x($Px)$ are intuitive, reflecting respectively an inverse and a positive relationship between the two variables, quantity and the goods being consumed.

The positive sign on an average price of good $x$ and $z$ may indicate that if good $x$ and $z$ decreases in price respectively, more of it will be supplied hence more of good $z$ and $x$ will be consumed.

$c$ reflects the opportunity cost in producing the two products.

This coefficients can also be interpreted as;

$+0.6 \implies$ price elasticity of supply of good $x$ . The supply of good x increases by 0.6 units as a result of change prices of 1 unit good $y$ and good $z$ at that point.

-0.4P → implies price elasticity of supply of good $y$ . The supply of good $y$ decreases by 0.4 units as a result of change prices of 1 unit good $x$ and good $z$ at that point.

+0.3 → implies price elasticity of supply of good $z$ . The supply of good $z$ increases by 0.3 units as a result of change prices of 1 unit good $x$ and good $y$ at that point.

0.4 → implies the units of raw materials used to produce 1 unit of good $x$ during production.