Question

Problem # 4 Rail Tours, Inc., sells packaged tours on rail lines, including gourmet meals and a reserved bed. The most popular tours are in the autumn, when foliage colors are at their peak. The overnight package for Saturday and Sunday morning are especially heavily booked. A market survey firm has just completed a study in which they conclude that if the package cost is $200 per couple, then Rail Tours can expect to sell 400 spaces on a typical Saturday. If the price is raised to $225, then unit sales will drop to 390. If the price is raised further to $250, unit sales drop to 380.

a) From the data given, write down the demand equation and determine its intercepts. Are there any precautions needed when operating at the extreme ends of the demand curve?

b) The survey firm also reports that if per capita income changes, Rail Tours can expect a large change in bookings. In particular, if per capita income falls by 1%, then bookings will tend to fall by about 2%. Are tour packages a normal good? Explain.

c) If you were responsible for making a forecast for bookings, would you accept this forecast as is? Or would you want additional information about demand? Explain.

Answer 1

A) Let 'P' be price & 'Q' be the quantity or unit sold.

Let the equation of demand curve be: P=a+bQ .... (1)

We need to find a & B.

Given at P=200 , Q=400

So, 200=a+b(400) .... (2)

At P =225, Q= 390

So, 225=a+b(390) .... (3)

Subtracting equation 3 from 2

-25=10b -> b= -2.5

Substituting the value of b in equation 2

200=a + 400 (-2.5)

200+1000=a

1200= a

So, equation of demand curve is : P=1200-2.5Q

Y intercept: P = 1200 -2.5Q=1200-2.5(0) =1200

X intercept: P = 1200 -2.5Q

0=1200-2.5Q -> Q=480.

At the upper end of the demand curves the demands is elastic, so increase in price will lead to fall in revenue .

At the lower ends of the demand curve the demands in inelastic hence fall in price reduces revenue.

B) when income per capita falls the demand also falls. Graphically it means the leftward shift of demand curve.

The demand of normal goods fall as income falls & demand increases when income increases.

So, tour packages are normal goods.