Question

Jak’s utility function for Caramilk and Snickers bars is U(C, S) = 10C +5S . If...

Jak’s utility function for Caramilk and Snickers bars is U(C, S) = 10C +5S . If Caramilk cost $3 and Snickers cost $2 and Jak’s weekly budget for sweets is $18. How much Caramilk (C) and Snickers bars (S) should he buy to maximize his utility?

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Answer #1

The utility maximizing condition for Jak is

MUc/MUs = Pc/Ps

MUc = marginal utility of caramilk

MUs = marginal utility of sinckers bars

Pc = price of caramilk

Ps = price of snickers.

The given utility function is

U = 10C+5S

MUc =

MUc= 10

MUs =

MUs = 5

MUc /MUs = 10/5 =2

Pc = 3

Ps =2

Income = 18

Jak's budget constraint is

18 = 3*C+2*S

Where C and S are the quantity of caramilk and snickers bars repectively.

MUc/MUs =2

Pc/Ps= 3/2

Here,

MUc/MUs > Pc/Ps

As a result the agents consume only caramilk.

Therefore the optimum bundle consists 18/3 =6 units of caramilk and 0 units of snickers bars

Optimum bundle include

Caramilk = 6

Snickers bars = 0

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