# Calculating quantity demanded and elasticity measures

The research department of CFC Railboard estimated the following regression for the demand for its transportation services.

Qx=1-2Px+1.5I+0.8Py-3Pz+1Adv

Where

Qx=quantity of CFC transport in millions of ton-miles per year.

Px=the price of CFC transport in dollars per ton-mile.

Py=the price of Union Atlantic rail transport in dollars per ton-mile.

Pz=the price of Joe the trucker's transport in dollars per ton-mile.

I=total profits of shippers in the market served by CFC in billions of dollars/year

Adv=Advertising expenditures by CFC in millions of dollars per year

This year, the values for explanatory variables are:

Px=$2

Py=$2.50

Pz=$1

I=$4

Adv=$2

1. Estimate the quantity demanded for CFC transport this year.

2. Plot a demand curve for the year, and show the calculations for determining the points used to derive the curve.

3. Estimate the elasticity of demand with respect to each of the explanatory variables.

4. Estimate the quantity demanded next year if CFC reduces its price, and the other explanatory variables change as follows:

Px=$1.8

Py=$2.25

Pz=$1

I=$4.2

Adv=$2.4

5. Plot a demand curve for next year on the same graph as in question 2 above, again showing all calculations.

6. Is Joe the trucker a competitor for CFC Railboard? Explain.

https://brainmass.com/economics/elasticity/calculating-quantity-demanded-and-elasticity-measures-456189

#### Solution Preview

Please refer attached file for the graphs.

1. Estimate the quantity demanded for CFC transport this year.

Qx=1-2Px+1.5I+0.8Py-3Pz+1Adv

Put the value of various parameters

Qx=1-2*2+1.5*4+0.8*2.5-3*1+1*2=4

Quantity demanded=4 million of tons-miles

2. Plot a demand curve for the year, and show the calculations for determining the points used to derive the curve.

Qx=1-2Px+1.5I+0.8Py-3Pz+1Adv

Put the value of various parameters keeping Px variable, we get

Qx=1-2Px+1.5*4+0.8*2.5-3*1+1*2=8-2Px

Qx=8-2Px

For Px=0, Qx=8-2*0=8 (keeping the other parameters constant)

For Px=1, Qx=8-2*1=6 (keeping the other parameters constant)

For Px=2, Qx=8-2*2=4 (keeping the other parameters constant)

For Px=3, Qx=8-2*3=2 (keeping the other parameters constant)

For Px=4, Qx=8-2*4=0 (keeping the other parameters ...

#### Solution Summary

Solution calculates quantity demanded and various elasticity measures in the given case.

Point price, income and cross elasticities

The McNight Company is a major producer of steel. Management estimates that the demand for its steel is given by the equation: Qd = 500 - 1000P + 0.1Y + 300Pa, where Q = steel demand in thousands of tons per year, P = price of steel in dollars per pound, Y is income per capita, and Pa is the price of aluminum in dollars per pound. Initially the price of steel is $1 per pound, income per capita is $20,000, and the price of aluminum is $0.80 per pound.

A. How much steel will be demanded at the initial prices and income level?

B. Based on the equation, what is the relationship between steel and aluminum? Explain briefly how you know.

C. What are the point price, income, and cross elasticities at the present values? Interpret your answers, saying how much a 1% change in each variable impacts demand.

D. If the objective is to increase total revenue, should the price be increased or decreased? What if the objective is to increase total profit? Explain.