Question

In: Economics

Sarah’s utilities from consumption of two goods, hummus and falafel, are shown in the table below....

Sarah’s utilities from consumption of two goods, hummus and falafel, are shown in the table below.

Sarah’s daily income is $23 and she spends her entire income on these two goods. Assume the price of hummus (PH) is $2 and the price of falafel (PF) is $5.

Ounces of Hummus	Total Utility from Hummus	MUH	MUH/PH	Pieces of falafel	Total Utility from falafel	MUF	MUF/PF
1	10			1	20
2	18			2	35
3	24			3	45
4	28			4	50
5	30			5	52

Fill in the columns.

What is Sarah’s equilibrium consumption of hummus and falafel? What is her marginal utility per dollar spent on each good?
If Sarah’s income increases to $30, what will be her new equilibrium consumption of hummus and falafel be? What will the marginal utility per dollar spent on each good be?
For Sarah, is hummus a normal or inferior good? How about falafel – is it a normal or inferior good? Explain.

Expert Solution

It is given that price of hummus (PH) is $2 and price of falafel (PF) is $5. Sarah's daily income is $23.

Ounces of Hummus	TU from hummus	MU_H	(MU_H/P_H)	Pices of Falafel	TU from falafel	(MU_F)	MU_F/P_F
1	10	10	10/2 = 5	1	20	20	20/5 = 4
2	18	8	8/2 = 4	2	35	15	15/5 = 3
3	24	6	6/2 = 3	3	45	10	10/5 = 2
4	28	4	4/2 = 2	4	50	5	5/5 = 1
5	30	2	2/2 = 1	5	52	2	2/5 = 0.4

✓ Sarah's equilibrium consumption is determined by (MU_H/P_H) =( MU_F/P_F) such that total income is spend on each good. It means ratio MU and price of two goods will be same and PH*QH + PF*QF = $23.

In the above table this condition is matched when 4 Ounces of Hummus is consumed and 3 Pices of Falafel is consumed. At this level MUH/PH = 2 and MUF/PF = 2 . The total income of Sarah is also spend. Because the cost of 4 Ounces of Hummus is and 3 Pices of Falafel is 4*$2 + 3*$5 = $(8 + 15) = $23.

So, when Sarah's daily income is $23, then equilibrium consumption of Sarah is 4 ounces of Hummus and 3 Pices of Falafel.

Marginal utility of per dollar spend on Hummus is 2.

Marginal utility of per dollar spend on Falafel is 2.

✓ If Sarah's income increases to $30. Then for equilibrium (MUH/PH) = (MUF/PF) such that PH*QH + PF*QF = $30.

This condition satisfied when 5 Ounces of Hummus is consumed and 4 Pices of Falafel is consumed.

At 5 Ounces of Hummus consumed MUH/PH = 1 and 4 Pices of Falafel consumed MUF/PF = 1.

If Sarah's income increases to $30, then equilibrium consumption of Sarah is 5 Ounces of Hummus and 4 Pices of Falafel.

The MU per dollar spend on Hummus is 1.

The MU per dollar spend on Falafel is 1.

✓ For Sarah Hummus is normal good. Because when income increases from $23 to $30 , the consumption of hummus increases from 4 Ounces to 5 Ounces. As consumption increases from 4 Ounces to 5 Ounces due to increase in income we can call it normal good. Because in case of normal good consumption increases with increase in income.

Falafel is also normal good because consumption of Falafel increases from 3 Pices to 4 Pieces due to increase in income from $23 to $30. As consumption of Falafel increases with increase in income we can call Falafel is normal good.

Rahul Sunny answered 1 year ago

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