Question

Logan also wants to make hamburgers for his party. To do this, he will need meat and bread. He has $100 to spend on food and the price of a meat patty is $5 and the price of one bread is $2. Each hamburger requires one meat patty and two breads such that his utility function is: U(M, B) = min{2M, B} Write out Logan’s maximization problem. What is the best feasible bundle of meat and bread?

I know someone else answered this but the steps werent clear to me. Please explain each step so I know how the answer was found.

Answer 1

We have the following utility function

U(M,B) = min{2M, B}

In the above M is meat and B is bread. The utility function shows perfect complementary goods. Perfect complementary goods are those that are always consumed together in fixed proportion. The utility function shows that 2 units of bread are consumed with 1 unit of meat patty.

The price of meat (P_M) = $5, and price of bread (P_B) = $2. Total money income with Logan (I) = $100

So, the budget constraint is given by the following

I = P_MM + P_BB

100 = 5M + 2B

Now, we know that the consumer is consuming the two goods together in a fixed proportion. So, the optimal choice is given as following

2M = B or M = B/2

So,

I = P_MM + P_BB

I = P_MM + P_B2M

100 = 5M + (2 × 2M)

100 = 5M + 4M

9M = 100

M = 100/9

B = 2M

B = 200/9

So optimal consumption of meat patty and bread is

Meat patty =100/9

Bread = 200/9