John likes coffee and cookies. The price for one cup of coffee is $1; the price for one cookie is $1. His marginal utility for coffee is 10 - x, where x is the amount of coffee. His marginal utility for cookies is 21 - 2y, where y is the number of cookies. How many cups of coffee and units of cookies will John buy if he has only $10?

 

Answer:

If John only has $10,he will be able to afford 3 cups of coffee and 7 units of cookies.

In order to maximize utility,the marginal utility of coffee divided by the price of coffee must equal the marginal utility of cookies divided by the price of cookies.

Therefore:

MU_c/P_c=MU_ck/P_ck

(10-x)/1=(21-2y)/1

10-10x=21-2y

x=2y-11

John's budget is $10. This means that the price of coffee multiplied by the quantity of coffee when added to the price of cookie multiplied by the quantity of cookie should equal to $10.

Therefore:

(P_c*X)+(P_ck*Y)=10

X+Y=10

But X=2Y-11

Therefore:

2Y-11+Y=10

2Y+Y=10+11

3Y=21

Y=31/3=7

X+Y=10

But Y=7

X+7=10

X=10-7

X=3

With $10 dollars,John can afford 3 cups of coffee and 7 units of cookies.