Question

Please explain the solutions well. I have a test on this and i don’t understand it.

7. Anne has a job that requires her to travel three out of every four weeks. She has an annual travel budget and can travel either by train or by plane. The airline on which she typically flies has a frequent-traveler program that reduces the cost of her tickets according to the number of miles she has flown in a given year. When she reaches 25,000 miles, the airline will reduce the price of her tickets by 25 percent for the remainder of the year. When she reaches 50,000 miles, the airline will reduce the price by 50 percent for the remainder of the year. Graph Anne's budget line, with train miles on the vertical axis and plane miles on the horizontal axis.

Answer 1

First of all :-

Usually the budget constraint does not have a changing prices of any commodity as it is a simple negatively slopes straight line. But with changing prices of any one commodity as here the prices of airlines fare we will have a kink in the demand curve. Since the price changes twice here so we will have 2 kinks.

Slope of Budget line = - Price of commodity in vertical axis / Price of commodity in horizontal axis

Let the initial fare of train be = P_{​​​​​T}

& Initial fare of travel by plane = P_{​​​​​​F}

Flight on vertical axis and train on horizontal axis

​​​​​Budget Equation under the 3 cases :-

• Before travelling 25000 miles

(P_{​​​​​​T} * T) + (P_{​​​​​​F} * F) = I

So the slope is = - P_{​​​​​​F}​​​​​ / P_{​​​​​​T}

• After traveling 25000 miles

Train fare remains same i.e. P_{​​​​​​T}

But flight fare reduces by 25%

So Flight fare is 0.75P_F

_​​​​(P_{​​​​​​T} * T) + (0.75P_F * F) = I

So the slope is = - 0.75P_F / P_{​​​​​​T}

• After traveling 50000 miles

Train fare again remains same P_{​​​​​​T}

Flight fare reduces by 50%

So flight fare is 0.5 P_{​​​​​​F}

(P_{​​​​​​T} * T) + (0.5P_F * F) = I

So the slope is = - 0.5P_F / P_{​​​​​​T}

So we get three slopes of budget line

1. Slope 1 = - P_{​​​​​​F}​​​​​ / P_{​​​​​​T}
2. Slope 2 = - 0.75P_F / P_{​​​​​​T}
3. Slope 3 = - 0.50P_F / P_{​​​​​​T}

The negative slope of budget line is due to the downward slope hence for slope we can consider the absolute value of slope (i.e. the modulus of slope)

We can see as the distance of travel increases in plane the slopes are continuously falling i.e.

|Slope 1| > |Slope 2| > |Slope 3|

Using these slopes we can draw the budget line as follows :-

Thain miles - 0.15 Sufe s05k/4 5రణు కరoD Clame ouiles

Where, P_{​​​​​​F} is the fare of travel by plane.

P_{​​​​​​T} ​​​​​​​is the fare of travel by train.