Question

Question: If Coke and Pepsi are perfect substitutes for Lynn. She is always willing to substitute 1.1 Pepsis for 1 Coke. That is, her utility function is: U(Cokes, Pepsis)= 1.1*Cokes + Pepsis

If she has an income of $100 and the price of Cokes is $1.20 and Pepsis is $1, then what is the optimal bundle that Lynn should consume?

Answer 1

Coke and Pepsi are perfect substitutes in this case as shown by the utility function of Lynn.

U(Coke, Pepsi) = 1.1Coke + Pepsi

Income = 100

Price of coke = 1.2

Price of Pepsi = 1

Now we look at the marginal rate of substitution between two goods and the price ratio of two goods and see which one is greater in order to determine the optimal bundle.

Marginal rate of substitution = marginal utility of coke / marginal utility of pepsi

= 1.1 / 1

So, marginal rate of substitution = 1.1

Price ratio = price of coke / price of pepsi

= 1.2 / 1

So, price ratio = 1.2

Since in this case marginal rate of substitution is less than the price ratio that is 1.1 < 1.2, the consumer will consume only good pepsi and the quantity of pepsi that the consumer will consume = Income / price of pepsi that is,

Quantity of pepsi = 100 / 1 = 100

So, the optimal bundle of the consumer is o units of coke and 100 units of pepsi.