Sally is a frequent flyer whose fares are reduced through coupon offerings. She receives a 20% reduction on fares after she flies 20,000 miles, and 40% reduction after she flies 40,000 miles.
a) Illustrate her budget constraint.
b) Illustrate how her level of utility will change given these frequent-flyer coupons.
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I am very confused by this question. Here we are asked to find the budget constraint, but I am not even sure what the two goods are...what are the goods that should be plotted on the vertical and horizontal axes? Will the budget line be a straight line? How would the coupons change the budget line?
Can someone please help me?
Thank you very much!
Ok, Put air-line travel miles on the x-axis, "all other goods" on the y-axis. On the x-axis, mark a point for 20000 miles, and another at 40000.
Begin high up on the on the y-axis and start drawing a standard budget constraint line. However, when the line hits the 20000 level, the price of travel suddenly drops. This is represented as a kink on the budget line; Sally can get more airline miles than a straight-line budget constraint would show. Continue the new budget constraint line from the kink point until you hit 40000, in which you get another kink point. Continue from here until you eventually hit the x-axis.
Pat yourself on the back.
b) Utility maximization will still occur when the highest indifference curve is tangent to the 3-part budget constraint line. It will be theoretically possible that a single indifference curve could be tangent at 2 or even all 3 parts of the constraint.
a) Let p1 be the original price to travel 1 mile.
Between 20k and 40k miles, slope (in absolute value) of budget line is p1/1=p1
Between 20k and 40k miles, slope (in absolute value) of budget line is 0.8p1/1=0.8p1.
More than 40k miles, slope (in absolute value) of budget line is ??? Is it just 0.6p1?
b) For this part, the question asks how her level of utility will CHANGE given these frequent-flyer coupons. I don't quite understand it.
How it will CHANGE relative to what? My best guess is that it is asking us to compare the budget line in part a with the straight budget line that has a slope of p1 everywhere (i.e. for the case in which there is no flyer coupons).
I think it is trying to ask whether her utility will be better off, worse off, or the same. But we aren't even told what her utility maximizing points are, how can we answer this question?
Thank you very much!
No problem, I can help you understand this question!
In order to illustrate Sally's budget constraint, we need to first determine the goods that should be plotted on the vertical and horizontal axes. In this scenario, the goods we are referring to are the quantity of airline tickets Sally buys and the amount of money she spends on them, respectively.
Let's assume the quantity of airline tickets is plotted on the horizontal axis (x-axis) and the amount of money spent is plotted on the vertical axis (y-axis).
To determine Sally's budget constraint, we need to consider the reduction in fares she receives based on her miles flown. The budget constraint will show the different combinations of airline tickets and money spent that Sally can afford given the fare reductions.
Let's say Sally's initial fares are denoted by the straight line AB, representing the full price of the tickets. Now, when Sally reaches 20,000 miles flown, she receives a 20% reduction on fares. This means that for every dollar she spends on tickets, she only has to pay 80 cents. This fare reduction will shift the budget constraint line inward, making it steeper. The new budget constraint line after reaching 20,000 miles flown will be line CD.
Similarly, when Sally reaches 40,000 miles flown, she receives a 40% reduction on fares. This means that for every dollar she spends on tickets, she only has to pay 60 cents. This fare reduction will shift the budget constraint line inward again, making it steeper. The new budget constraint line after reaching 40,000 miles flown will be line EF.
In summary:
a) Initially, the budget constraint line is AB. After reaching 20,000 miles, it becomes CD. After reaching 40,000 miles, it becomes EF.
b) The level of utility represents how satisfied Sally is with the set of goods she can afford. With the frequent-flyer coupons and corresponding fare reductions, Sally will be able to afford more airline tickets for the same amount of money spent. This means that her level of utility will increase since she can now consume more of the desired good (airline tickets) given her budget constraint.
I hope this explanation helps! Let me know if you have any further questions.