Question

Answer the following questions using the graph below. The figure below displays several of Emma's indifference curves. Although there are 168 hours in every week, Emma sleeps and bathes, attends classes, etc. for exactly 108 hours weekly, so she has 60 hours to divide between work and play. Emma receives $100 per week in interest on her savings, which is her only income from nonwork sources. The price of the consumption good is $1 per unit, and her wage is $10 per hour. Consumption T X 100 C 10 20 30 40 50 60 70 80 Leisure

Answer 1

Let us first superimpose the budget constraint as shown below.

Consumption 10 20 30 40 50 60 70 80 Leisure

Emma has 60 hours to choose between work and play. Additionally, Emma gets $100 per week as nonlabor income and hence the budget constraint is vertical at leisure = 60, which means that if she chooses a leisure of 60 hours, total income would be 100, i.e., the nonlabor income and labor income = 0. Suppose now if she chooses entire 60 hours to work, she can earn $600 at a wage rate of $10. Hence, when she chooses 60 hours of work, she has $600 labor income and $100 non-labor income, i.e., a total income of $700. Hence, the vertical intercept of the budget constraint would be 700. If we connect 700 on Y-axis, the (60,100) co-ordinates and (60,0) co-ordinates, we will get the entire budget constraint as shown by the red line on the graph.

Superimposing rge budget line, it can be observed that it is tanget to the indifference curve U3 at leisure = 20 hours, i.e., the optimal choce would be at point A, as shown in the diagram. Therefore, total work hour for Emma would be 60-20 = 40 hours. With 40 hours work, she will get $40x$10 = $400 of labor income and total income would be $400+$100 = $500.

Therefore, the answer to the given questions will be as follows:

At Emma's optimal choice, she works for 40 hours.

The wage income in dollars per week for Emma = $400

Please note that because of the position of indifference curve (slight angle is there while taking screenshot I believe), the answer might not be 100% correct. If you draw the budget constraint on the actual graph, it would be more clear. Also, if we have the functional form of indifference curve, that would help to calculate these numbers more accurately. Nevertheless, I believe that the above answer should be correct.