Question

Demand Estimation Project

Fred’s Accounting & Tax services is new but a locally well-known accounting firm in San Angelo, TX that completes TAX returns for individuals. Every year firms like Fred’s decide how much to charge to complete an individual return.

The price determines how many tax returns firms complete each year. Suppose you are the NEW OFFICE manager at Fred’s who is tasked to determine what your office should charge next year for tax returns.

Since this is all new to you, over a period of time, you’ve tried or experimented with a number of prices when running few specials to try to attract customers. As such, you have the following Price and number of completed returns data.

Use this data to answer the following :

Number of returns completed (Q)	Return Price (P)
932	$70
932	70
910	75
920	75
876	80
852	80
811	85
857	80
847	80
865	80
785	90
802	90
789	95
731	95
663	100
709	100
771	90
792	90
831	85
834	80

1. Enter the data in an Excel spread sheet and graph the data using a SCATTER plot and insert a Trendline function (Place this graph below data and label both axes).
   
2. Using Excel’s Regression analysis, estimate the simple regression (demand for TAX returns) and report the estimated demand equation (you can round the estimated coefficients to 2 or 3 decimal points). Place the regression output in a separate sheet in the same excel file and label the sheet as Reg_Output.
   
3. What is the R² (report this as a percentage), and based on the reported R² do you think this regression can reasonably be used for analysis?
   
4. At the 5% level, how significant is the intercept and the return price variables (report the t-statistics for both)?
   
5. How many returns do you expect to be completed if your firm charge $85 per return (round your answer since returns are completed in whole units)?
   
6. All else constant, what is the impact on the number of returns demanded if the price of a return increases by $7 (round your answer)?
   
7. What is the point price elasticity of demand at the charged price of $85?
   
8. At this price (i.e., $85 per return) are you on the elastic, inelastic or unit-elastic portion of your demand function?
   
1. Do you recommend an increase, a decrease, or a no change in price (i.e., from the $85 per return) ? How do you justify your recommendation?

Answer 1

A).

The following fig shows the scatter plot, where we have measured “Number of returns Completed” on the horizontal axis and “Return Price” on the vertical axis.

The Trend line is given by, => P = 182.8 - 0.1191*Q.

B).

The following table shows the regression result, where “Q” is the dependent variable and “P” is the explanatory variable.

C).

Here the “R^2” is given by “0.94”, => 94% variation in “Q=number of returns completed” is being explained by the regression equation, => the regression model is very good fitted model.

D).

From the regression result we can see that the “t value” of “return price” is “(-16.09)” and the “p value” is less than “0.05”, => at the 5% level of significance the “return price” is significant variable.

E).

The estimated regression equation is, => Q = 1488.89 – 7.85*P. For, “P = $85” the estimated value of “Q=number of returns completed” is “Q = 1488.89 – 7.85*85 = 821.64 = 822”. So, the estimated number of returns completed is “822”.