Question

A consumer has the following utility function for good X and good Y 

𝑈 = 4𝑋 + 8𝑌 

The consumer’s income is KShs 12,000, the price of good X is KShs 300 and the price of good Y is KShs 500. 

Required: 

(i) What type of preferences do the two goods represent? Explain  (ii) Compute the marginal rate of substitution of the two goods  (iii) Calculate the corresponding consumer demand functions  

Answer 1

i). Straight line preference: The utility function is a linear equation implying that the two goods are perfect sabstitutes which are characterised by straight line prefernce.

ii). $Marginal Rate of Substitution (MRS)=\frac{MUX}{MUY}$

$MUX=4$

$MUY=8$

$MRS=\frac{4}{8}=0.5$

iii). Corresponding demand functions

$MRS=0.5$

$\frac{PX}{PY}=\frac{300}{500}=0.6$

$\frac{PX}{PY}>0.5$

Therefore the consumer will not consume Y and the resulting demand function will be

$Y=\frac{M}{PY}= \frac{12,000}{500}=24$

$Y=24$