a) A consumer\'s utility function for rice and coffee is given by the following

Question

a) A consumer's utility function for rice and coffee is given by the following function: U = F(x, y) = 5x6 y4 where.r is the amount of rice in kg and y is quantity of tea in packets. The price of rice is 115, while a packet oftea costs RM8, and his income is RM405. If the consumer maximizes utility subje i. The linear budget line. i. The optimum quantities of rice and tea consumed. ii. The maximum utility (10 points) he supply equatie Say+ 4 where p is the price in RM/kg. Find the consumers' surplus andt The demand function for cooking oil, in kg, is D(x)- p 49 -x and t

Explanation / Answer

i) The linear budget line is

15x+8y=405

ii) -Marginal utility of x/Marginal utility of y= -price of /Price of y

30x5y4/ 20x6y3= 15/8

3y/2x= 15/8

4y=5x

Now we know  15x+8y=405

Putting this value in budget line we get

15(4y/5)+8y=405

20y=405

y=20.25

or 20 approx

x= 16

the optimal bundle is 16 kg of rice and 20 packets of tea

iii) the maximum utility

= 5* 166 *204

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