Qz = 4500- 1/8 Pz + 1/5 Pa – 1/9 Pb + 2Y
Solution:
i.). The law of demand is valid in this demand equation since it shows an inverse relationship between the price of good z with its quantity demanded. That is, the quantity demanded varies inversely with the price. Therefore, at higher prices consumers will demand a lower quantity of good z, thus the law of demand.
ii.). The two main reasons why the law of demand is always valid are as follows:
· Law of diminishing marginal utility – This states that as we consume more units of a good, the utility derived from each successive unit goes on diminishing. Therefore, the demand of a good depends on its utility. If the consumers get more satisfaction from a particular good, they will pay more.
· Substitution effect – A consumer will always substitute one product in place of another when it becomes relatively cheaper. If one product becomes expensive, a consumer will purchase a substitute product whose price is cheaper.
iii.). Good z is a normal good since it has a direct positive relationship with a consumer’s income. It also has a positive income elasticity of demand. That is, the demand for normal goods increases with an increase in the consumer’s income and vice versa.
iv.). Yes, good a and good b are related to good z.
Good a has a positive coefficient which suggests that an increase in the price of good a will lead to an increase in the quantity demanded for good z, which indicates that the two goods are substitutes.
On the other hand, good b has a negative coefficient which suggests that an increase in the price of good b will lead to a decrease in the quantity demanded for good z, which indicates that the two goods are complements.
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