Question

Percy consumes cakes and ale. His demand function for cakes is qc = m − 30pc + 20pa, where pa is the price of ale, and pc is the price of cakes, and qc is his consumption of cakes. Percy’s income is $100, and the price of ale is $1 per unit.(a) Is ale a substitute for cakes or a complement?(b) Write an equation for Percy's demand function for cakes where income and the price of ale are held fixed at $100 and $1 respectively.(c) Write an equation for Percy's inverse demand function for cakes where income is $100 and the price of ale remains at $1.

Answer 1

Answer:

The answers to the problem are given below

Explanation:

(a) Is ale a substitute for cakes or a complement?

Ale is a substitute since a increase in the price of ale increases the demand for cakes.

(b) Write an equation for Percy's demand function for cakes where income and the price of ale are held fixed at $100 and $1 respectively.

qc = 120−30pc.

(c) Write an equation for Percy's inverse demand function for cakes where income is $100 and the price of ale remains at $1.

pc = 4−(qc/30).

Answer 2

Answer + Explanation:

(a) The demand function for cakes states that there is a positive relationship between the quantity of cakes consume and the price of ale. This means that as the price of ale increases then as a result the demand for cakes also increases. Hence, ale and cakes are substitute goods.

(b) Income and price of ale held fixed at $100 and $1 per unit, respectively. Therefore, the equation for demand function is shown as follows:

Qc = M – 30Pc + 20Pa

Qc = 100 – 30Pc + 20(1)

Qc = 120 – 30Pc

(c) The equation for Percy's inverse demand function for cakes is as follows:

Qc = 120 – 30Pc

30Pc = 120 – Qc

Pc = 4 – (1/30)Qc