Question

As the owner of Barney’s Broilers—a fast-food chain—you see an increase in the demand for broiled chicken as consumers become more health conscious and reduce their consumption of beef and fried foods. As a result, you believe it is necessary to purchase another oven to meet the increased demand. To finance the oven, you go to the bank seeking a loan. The loan officer tells you that your revenues of$\mathit{\backslash (}\mathbf{750}\mathbf{,}\mathbf{000}$ are insufficient to support additional debt. To qualify for the loan, Barney’s Broilers’s revenue would need to be$\mathit{\backslash )}\mathbf{50}\mathbf{,}\mathbf{000}$ higher. In developing a strategy to generate the additional revenue, you collect data on the price (in cents) per pound you charge customers and the related quantity of chicken consumed per year in pounds. This information is contained in the file called Q18.xls available online at www.mhhe.com/baye8e. Use these data and a log-linear demand specification to obtain least squares estimates of the demand for broiled chicken. Write an equation that summarizes the demand for broiled chicken, and then determine the percentage price increase or decrease that is needed in order to boost revenues by$\mathit{\$}\mathbf{50}\mathbf{,}\mathbf{000}$ .

Short answer

With adecrease in price by $1 the quantity will increase by 1 unit. Hence, the price charged should be decreasedby 78%.

Step-by-step solution

Create a data table 

In(Quantity)	In(Price)
0.85	2.38
0.95	2.36
1.04	2.34
1.08	2.33
1.15	2.28
1.18	2.3
1.2	2.23
1.23	2.2
1.3	2.18
1.32	2.12
1.34	2.11
1.36	2.11
1.4	2.09
1.38	2.04
1.45	2.05
1.48	2.08
1.48	2.04
1.49	2.04
1.52	2.04
1.56	2
1.56	1.99
1.57	2
1.56	2.11
1.56	2.04
1.56	2.05
1.58	2
1.59	1.95
1.62	1.96
1.66	1.95
1.65	1.93
1.67	1.88
1.68	1.85
1.69	1.83
1.72	1.85
1.77	1.78
1.75	1.83
1.77	1.78
1.79	1.81
1.82	1.82
1.84	1.78

Find the Regression statistics 

Below is shown the table of summary of input and output from a Multiple Regression based on the given data.

Multiple R	0.97046385
R Square	0.942800084
Adjusted R Square	0.940307779
Standard error	0.04156382
Observations	41

Also,

	df	SS	MS	F	Significance F
Regression	1	1.090264531	1.090234531	631.1040656	1.07641E-25
Residual	39	0.067374493	0.001727551
Total	40	1.157639024

	Coefficients	Standard Error	T stats	P- value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	3.033970128	0.040142901	75.57924397	6.53832E- 44	2.952773446	3.11516681	2.952773446	3.11516681
In(Quantity)	-0.674091777	0.026832957	-25.12178468	1.07641E-25	-0.728366556	-0.619816998	-0.728366556	-0.619816998

Therefore, the regression equation that summarizes the demand for broiled chicken is:

$\mathrm{In}\left(P\right)=3.0339-0.6740\mathrm{In}\left(Q\right)$

Or 1 unit (in whole)

Thus, with a decrease in price by $1 the quantity will increase by munits.

Hence, to generate revenue the price should be increased by 785.

$\begin{array}{l}=1.78-1\\ =0.78\times 100\\ =78\end{array}$