Question

Question: Ahmed has an income of 37 Rial Omani (R.O) and the price of goods X, Y and Z, are R.O 5, R.O 1 and R.O 4 respectively, The amount of total utility he would derive from consuming X, Y and Z is shown in the Table below: Quantity Product Product Product Z Total Utility MUP Total Utility MUy/Py Total Utility MUP (TU) (TU) (TU) Given the above Table, answer the following questions: 1. Fill in the blank (in the above table) 2. Write down the two conditions for consumer's equilibrium in the above case 3. Find the consumer's equilibrium and show how many units of the three products will Ahmed purchase?

Answer 1

income of consumer, m = 37 price of good 1, P1 = 5 price of good y, Py = 1 price of good 2, P. = 4

Part a)

quantity	total utility from good x	marginal utility from good x, $MU_{x}$	$\frac{MU_{x}}{P_{x}}$	total utility from good y	marginal utility from good y,$MU_{y}$	$\frac{MU_{y}}{P_{y}}$	total utility from good z	marginal utility from good z, $MU_{z}$	$\frac{MU_{z}}{P_{z}}$
1	21	21	4.2	7	7	7	16	16	4
2	41	20	4	13	6	6	30	14	3.5
3	59	18	3.6	18	5	5	42	12	3
4	74	15	3	22	4	4	50	8	2
5	85	11	2.2	25	3	3	55	5	1.25
6	91	6	1.2	27	2	2	58	3	0.75
7	91	0	0	28	1	1	60	2	0.5

Part b)

Assuming Ahmad spends his income on these 3 goods only

$consumer's\ utility\ is\ maximized\ at\ point\\ \frac{MU_{x}}{P_{x}}=\frac{MU_{y}}{P_{y}}=\frac{MU_{z}}{P_{z}}\\ \&\\ xP_{x}+yP_{y}+zP_{z}=m$

Part c)

first condition of equality of marginal utility price ratio for all 3 goods is met in 2 cases

$When,\frac{MU_{x}}{P_{x}}=\frac{MU_{y}}{P_{y}}=\frac{MU_{z}}{P_{z}}=4\\$

Ahmad consumes 2 units of good x, 4 units of good y and 1 unit of good z

$When,\frac{MU_{x}}{P_{x}}=\frac{MU_{y}}{P_{y}}=\frac{MU_{z}}{P_{z}}=3\\$

Ahmad consumes 4 units of good x, 5 units of good y and 3 units of good z

Ahamd's utility is maximized at point when he consumes 4 units of good x, 5 units of good y and 3 units of good z