Question

For lunch, Maria eats only salads or vegetarian burgers. Her weekly food budget is $36. Each salad costs $6 and each vegetarian burger costs $3. When deciding how much of each good to buy, Maria knows that 2 salads and 4 vegetarian burgers will give her a utility of 8. Maria’s utility-maximizing point is:

Answer 1

3 salads, 6 vegetarian burgers

Step-by-step explanation:

Data provided in the question:

Weekly food budget = $36

Cost of salad, Cs = $6

Cost of vegetable burger, Cv = $3

Now,

Let the number of salads be 'S'

and, the number of vegetable burgers be 'V'

thus,

S × Cs + V × Cv = $36

or

S × $6 + V × $3 = $36 ............(1)

also,

2 salads and 4 vegetarian burgers will give her a utility of 8

i.e U(2, 4 ) = 8

or

U( S, V ) = SV

Now,

From optimal marginal utility condition

Marginal rate of substitution =
`(MU_S)/(MU_V)=(Cs)/(Cv)`

or

`(V)/(S)=(6)/(3)`

or

V = 2S ..........(2)

substituting the above value in 1

S × $6 + 2S × $3 = $36

or

6S + 6S = 36

or

12S = 36

or

S = 3

substituting S in (2)

V = 2(3)

or

V = 6

Hence,

3 salads, 6 vegetarian burgers