Question

2.Mustafa has a fixed budget of 20 $.He spends his budget on two goods,X and Y. The price of good X is 4 $ and the price of good Y is 2 $.

The following table is given :

Quantity of X	TU from X	Quantity of Y	TU from Y
0	0	0	0
1	16	1	10
2	28	2	18
3	36	3	24
4	40	4	28
5	41	5	30

a.Mustafa is currently consuming 4 units of X and 2 units of Y. Use marginal analysis to explain why this combination is NOT optimal for Mustafa.Explain

b.What is Mustafa’s optimal combination of Good X and Good Y? Show your calculations.

c.Indicate whether each of the following will cause the optimal quantity of Good X to

increase,decrease or stay the same

i.The price of X doubles

ii.Mustafa’s income falls to 10 $ with no changes in prices.

Answer 1

2a. Total utility will be maximized if Marginal unit per dollar of consumption is maximized so , for X -

1st unit MU/$=16/4=4, 2nd unit=(28-16)/4=3,3rd unit=(36-28)/4=2,4th unit=(40-36)/4=1,5th unit=(41-40)/4=0.25

For Y, 1st unit=10/2=5,2nd unit=(18-10)/2=4,3rd unit=(24-18)/2=3,4th unit(28-24)/2=2,5th unit=(30-28)/2=1

Since we are consuming 4 unit of X and 2 of Y we are not maximizing MU/$

b. For Maximizing the utility from 2a. We can maximize by consuming 3 unit of X with MU/$ of 4,3,2 respectively and 4 unit of X with MU/$ of 5,4,3,2 Total cost =4*3(units of x)+2*4(units of Y)=$20=total budget and Total utility=36+28=64

c.i) if price of X doubles MU/$ will half hence, optimal Quantity of good X decreases.

ii) If income falls to 10 then also optimal Quantity of good X decreases since lower budget will not allow 3 unit of x Consumption as this itself overshoot the budget (4*3=12) of $10