Answer to Question #222169 in Microeconomics for Ankita

Question

Suppose the prices of the commodities A and B are p₁ and p₂ respectively. The consumer purchases X₁ unit of A and X₂ units of B. Suppose, the consumer has an income denoted by M and the consumer would spend the entire amount of M on these two commodities. How are p₁, p₂, X₁, X_2, and M related?

Answer 1

Given prices, p1 and p2, find the quantities x1 and x2 which maximise consumer purchases

Necessary condition: 

$MRS=\frac{M\times U1}{M\times U2}=\frac{p1}{p2}\\MU1=1\\MU2=\frac{1}{x2}\\$

so

$MRS=x2$

Therefore the optimum occurs when

$x2=\frac{p1}{p2}$

Money left to buy x1 for:  

$m-p2\times x2=m-p2\times \frac{p1}{p2}=m-p1\\x1=\frac{m-p1}{p1}=\frac{m}{p1}-1$

if m>p1

b) Yes, if m>p1 he won’t buy any more beer when m increases.