An MBA student has proposed the following demand equation for good Y. Q d Y = a

Question

An MBA student has proposed the following demand equation for good Y.

                                                QdY = a + b PY + c M

where:    QdY = quantity demanded of good Y in millions of tons per year

               PY = Price of good Y in dollars per ton

               M = Average consumer income in thousands of dollars

What sign should this student expect a, b, and c to have? Explain.

The regression output from the computer is as follows:

Dependent Variable: QdY         R-Square        F-ratio           p-value on F

Observations:             90                 .6              12.84              0.015                      

Variable         Parameter Estimate Standard Error      T-ratio        P-Value

Intercept                      60.00               5468.32                 3.12           0.0082

PY                                     -2.00                     0.65                 -2.86           0.0145            

M                                0.01                       3.29                  4.12         0.0831

This economist is confortable using parameter estimates that are statistically significant at the 10 percent level or better.

Does PY have a statistically significant effect on the quantity demanded of good Y? Explain, using the appropriate p-value.

Does M have a statistically significant effect on the quantity demanded of good Y? Explain, using the appropriate p-value.

What fraction of the total variation in the quantity demanded of good Y remains unexplained?   What can the student do to increase the explanatory power of his demand equation? What other variables might he add to his demand equation?

What is the expected quantity demanded of good y when PY = 50 and M = 20,000?

Explanation / Answer

Ideally sign of a should be +ve , b to be -ve and c to be +ve

explanation : as price of product rises , qty demand by consumer falls, hence a -ve relation ship

.As Income of consumer rises, he usually demand more , hence c is +ve

At 0 income and 0 price , qty demand is +ve.

Regression Output::

Py have a statistical effect on qty demanded as p value is less than 0.05

M does not have a statistical effect on qty demanded as p value is not less than 0.05

fraction remain unexplained is 1 - 0.6(R square vlaue) =0.4

To increase the explanatory value : add more data points and new variables

New variable can be Price of substitute goods , interest rate

Expected Qty demand = 60.00 -2*50 +0.01*20000 = 60 - 100 + 200 = 160 answer   

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