Question

In any given week, Anne receives satisfaction only from the consumption of goods and from the consumption of leisure LL, which is measured in hours. Obviously, Anne consumes many different types of goods, but for simplicity we aggregate the dollar value of all the goods that she consumes during the week and call it CC. Assume that if Anne chooses to work, the hourly wage rate is w=5 and she has to sleep 8 hours per day. Potentially, if she wants, she can work up to 7 days a week.

1) If Anne chooses to devote 0 hours to leisure during the week, how much can she consume? C= ?

2) If Anne chooses to devote all available hours (except those she has to sleep) to leisure during the week, how much can she consume? C =?

3) If Anne chooses to devote 30 hours to leisure during the week, how much can she consume? C

4) Suppose w=5w=5 and the government gives Anne a subsidy of $250. She receives this money unconditionally, regardless of how many hours she works. We define Anne's budget set over bundles of C and L, i.e. (C,L). Placing C on the horizontal axis and L on the vertical axis, depict Anne's budget set. The outer boundary of Anne's budget set has a kink at (C,L)=(250,____) (fill in the blank)

5) Suppose w=5w=5 and the government gives Anne a subsidy such that her consumption is at least $250. That is, if she does not work at all, the government gives her $250. If she works enough to earn some d<250d<250 dollars towards consumption, the government gives her $250−d$250−d. If she works enough to earn d≥250d≥250, the government does not give her anything. We define Anne's budget set over bundles of C and L, i.e. (C,L). Placing C on the horizontal axis and L on the vertical axis, depict Anne's budget set. The outer boundary of Anne's budget set has two kinks. One kink - the one with the higher LL of the two - is at (C,L)=(250,____) (fill in the blank)

6) ... while the other kink - the one with the lower LL of the two - is at is at (C,L)=(250,____) (fill in the blank)

Answer 1

wage rate that Anne receives when she works =5

If she has to sleep 8 hours per day, time in a day left = 16 hours

1. If she devotes 0 hours to leisure, she will devote the entire 16 hours to work. Hours that Anne works in a week = 16*7 = 112 hours

If she earns $5 per hours, then for working 112 hours, she would earn $560.

If Anne chooses to devote 0 hours to leisure during the week, she can consume $560.

2. If Anne chooses to devote all available hours (112 hours) to leisure during the week, then she will not earn anything (because she spends 0 hours working). If she does not earn anything, Anne can consume $0.

3. Amount of hours devoted to leisure in the week = 30 hours

Amount of hours that she works = available hours - leisure hours = 112 - 30 = 82 hours

If she earns $5 per hours, then for working 82 hours, she would earn $410.

Therefore, she can consume $410.

figure 1

4. The government gives Anne a subsidy of $250, no matter how many hours she works. Figure 1 denotes Anne's budget set.

Even if she has 112 hours (all available hours) of leisure, she still would be able to consume $250.

However, if she work for entire 112 hours at $5 per hour, she can earn 112*5 = 560. . Apart from this, she also gets $250 from the government. Therefore, she can consume a total of $810.

The outer boundary of Anne's budget set has a kink at (C,L)=(250,112)

5.

figure 2

Government gives Anne a subsidy such that her consumption is at least $250.

a.) If she does not work at all, she gets $250. Her budget line is depicted by AB in this portion (figure 2). She can consume $250 if she does not work and enjoys 112 hours of leisure.

b.) if she earns < $250, the government gives her $250-d. This portion of budget line is depicted by BC in figure 2

Number of hours that Anne needs to work in order for her to earn $250 = 250/5 = 50 hours

If Anne works for 50 hours with a wage of $5, then she gets $250. If she works for 50 hours, she enjoys 112-50 = 62 hours of leisure.

If she works for x hours, income she gets = d = 5x

Grant received by the government = 250-5x

total income of Anne = 5x + 250-5x = 250

Therefore, if she works for up to 50 hours she gets 250.

c.) if she earns > $250, the government gives her nothing. This portion of budget line is depicted by CD in figure 2

Number of hours that Anne needs to work in order for her to earn $250 = 250/5 = 50 hours

If Anne works for 50 hours with a wage of $5, then she gets $250. If she works for more than 50 hours, she earns more than $250. This means when her leisure is < 62 (112-50), she does not get anything and her entire income is her wage income.

If she works for y hours, income she gets = d = 5y

Grant received by the government = 0

total income of Anne = 5y

Therefore, if she works for more than 50 hours she gets more than 250.

One kink - the one with the higher LL of the two - is at (C,L)=(250,112)

6. .. while the other kink - the one with the lower LL of the two - is at is at (C,L)=(250, 62)

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