Question

2. Many people consume eggs and toast at breakfast. Assume the typical person spends $20 per week on eggs and toast. Currently the price of eggs is $1 per egg, and the price of toast is $0.25 per piece.

(a) (10 points) Graph the budget constraint budget constraint.

(b) Assume that some people have a utility function given by U = min[2T, E] where T is the quantity of toast measured in slices, and E is the quantity of eggs.

i. (5 points) Explain the relationship between toast and eggs. Be specific.

ii. (15 points) What is the utility maximizing consumption bundle?

iii. (10 points) Add this bundle to your graph in part a with a representative indifference curve.

iv. (5 points) If income were to double, how much toast and eggs would the typical person consume?

Answer 1

A)

Given M = 20, where M = total spending per week

P_E=1, where P_E = price of egg

P_T=0.25, where P_T =Price of toast

Therefore, the standard budget constraint can be given by E(P_E)+T(P_T)=M where E = quantity of eggs and T = quantity of toasts.

Substituting the given values in the equation we get,

E+0.25T=20

Therefore, the budget constraint will be given by the line AB in the following graph.

B)

i) Given the utility function U = min(2T,E)

We can analyse the relation between toast and eggs as 2T=E, therefore, we have T:E=1:2. This ratio tells us that to derive 1 unit of utility the consumer prefers to have 1 egg with 1/2 toast, therefore for all given levels of utility the consumer prefers eggs in double quantity to the toast.

Assuming that T=3 and E=2 therefore the utility would be U=min(2*3,2) which means that his utility=2, therefore no amount of increase in his consumption of toast will increase his utility until he consumes eggs in double proportion to toasts.

ii) Given U = min(2T,E), the consumer will achieve his optimal consumption at points of kinks on his indifference curve, in other words, the optimal allocation must satisfy 2T=E.

Therefore substituting this consition in the given budget constraint we get,

E+0.25T=20

2T+0.25T=20

2.25T=20

T=8.88 and E=17.77

iii)

The following graph shows the optimal bundle (T,E)=(8.88,17.77) at the point of intersection of the indifference curve IC₁ and the budget constraint AB.

iv)

If income were to double M=40, therefore the corresponding budget constraint would be

E+0.25T=40

given the utility relationship 2T=E, we get

2T+0.25T=40

2.25T=40

T=17.77 and E=35.55

Therefore we can observe that the quanitites of T and E would double with a double in the income, this is because the consumer consumes both the goods proportionately.