Question

Juanita enjoys consuming both soda and coffee. Each can of soda costs Ps - $1, and each cup of coffee costs Po-$2. Suppose that Juanita buys 30 cans of soda and 20 cups of coffee per week. The following graphs show her marginal utility curves for soda and coffee. At her current consumption level, Santa's marginal utility from consuming the last can of soda she bought is MUs - 12 utils per can, and her marginal utility from consuming the last cup of coffee she bought is MUE-12 utils per cup. MU OF SOUS MUOF COFFEE fuis per ap) SODA Cans per week) COFFEE (Cups per week)

Answer 1

Solution:

At current consumption, MUc/Pc = 12/2 = 6 and MUs/Ps = 12/1 = 12

Since, MUc/Pc < MUs/Ps (6 < 12), this means that marginal utility per cost of coffee is lower than marginal utility per cost of soda, thus less of coffee (so that higher marginal utility from coffee is achieved) and more of soda (so that marginal utility from soda is lowered) should be consumed such that the two ratios equalize.

This, correct option is (B).

Using the given graph, and price values, we can fill in the table as follows:

	Coffee	Coffee	Soda	Soda
Combination	Quantity	MUc/Pc	Quantity	MUs/Ps
A	20	16/2 = 8	30	10/1 = 10
B	40	8/2 = 4	20	12/1 = 12
C	30	12/2 = 6	30	10/1 = 10
D	50	4/2 = 2	40	4/1 = 4

With budget of $165 per week, her budget line becomes:

Pc*C + Ps*S = 165

2*C + 1*S = 165

Clearly, from the above graphs, there exists a linear relation between marginal utility and quantity of a good. We have equation for straight line: dependent variable = dependent variable intercept + slope*independent variable.

With dependent variable as marginal utility (MU), and independent variable as quantity, we have:

For coffee: for every 10 cups increase in coffee, MU decreases by 4, so slope = -4/10 = -0.40

Also, MU intercept for coffee = 24, so required equation of marginal utility for coffee is: MUc = 24 - 0.4*C

Similarly, for soda: for every 10 cans increase in soda, its MU decreases by 2, so slope = -2/10 = -0.20. Also, MU intercept for soda = 16.

So, required equation is: MUs = 16 - 0.20*S

Now, at optimum, we require that MUc/Pc = MUs/Ps

So, it must be: (24 - 0.4*C)/2 = (16 - 0.20*S)/1

12 - 0.20*C = 16 - 0.20*S

C = (0.20*S - 4)/0.20 = S - 20 (at optimal level)

Thus, substituting this in the budget line, we get:

2*(S - 20) + 1*S = 165

2S - 40 + S = 165

So, S* = (165 + 40)/3 = 68.33 cans approx

C* = 68.33 - 20 = 48.33 cups approx

Thus, to maximize her utility, Juanita will purchase 68 cans of soda and 48 cups of coffee per week.