Question

Many people consume eggs and toast at breakfast. Assume the typical person spends $15 per week on eggs and toast. Currently the price of eggs is $0.75 per egg, and the price of toast is $0.50 per piece.

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

(b) Assume that some people have a utility function given by U = min[T, 2E] 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 ?? with a representative indifference curve.

iv. (5 points) If income were decrease by 1/2, to $7.50, how much toast and eggs would the typical person consume?

Answer 1

a) The budget constraint will be given by P_TT+P_EE=M where,

P_T= price of toast

T= quanitity of toast

P_E= price of egg

E= quantity of eggs

M= Weekly expenditure

According to the given figures, the budget constraint will be

0.5T+0.75E=15

The graph of this budget constraint is shown in the following graph by the line AB

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

i) Given the utility function we can analyse the relationship between toast and eggs by equating the two, therefore T=2E which gives us the ratio T:E=2:1. This explains that for single unit of egg consumes, the consumer would prefer to have 2 toasts, i.e. double the quantity of eggs. If the consumer increases the quantity of eggs but consumes the same amount of toasts, his utility will not change because he prefers to consume eggs and toasts proportionately in this ratio.

ii) In the given utility function, the opyimal allocation will be given by the points that satisfy the equation T=2E since in such a utility situation, the optimal bundles are the ones located at the kinks of the indifference curve.

Therefore considering this condition T=2E, we have the following budget constraint

0.5T+0.75E=15

0.5(2E)+0.75E=15

1.75E=15

E=8.571 and T=17.142

iii) Adding the consumption bundle to our budget constraint graph, we see that the indifference curve of this allocation intersects the given budget constraint AB at the optimal point where E=8.571 and T=17.142. The following is the graph.

iv) Given the new income M=7.50, the new budget constraint would be

0.5T+0.75E=7.5

Following the optimality condition we have,

0.5(2E)+0.75E=7.5

1.75E=7.5

E=4.285 and T=8.5714

therefore, we can notice that the consumption level of the optimal bundle has decreased proportionately to the income. This is because the consumer preferences are such that he consumes the 2 goods only proportionately and therefore any increase or increase in this income would also affect their quantities proportionately.