Question

A soft-drink bottler collected the following monthly data on its sales (measured in             thousand units) of 12-ounce cans at different prices.

						Month
	1	2	3	4	5	6	7	8	9	10	11	12
Price	$0.45	0.50	0.45	0.40	0.35	0.35	0.50	0.55	0.45	0.50	0.40	0.40
Quantity	98	80	95	123	163	168	82	68	96	77	130	125

            (a) Using Excel run a linear regression with Quantity the dependent variable and price    the independent variable. Provide detailed regression output. Explain if the intercept             and the price coefficients are significant. Write the estimated demand equation.             Determine by how much the sales volume will increase if price is cut by 10 cent.

            (Use the Excel Regression tool as described in the text.)

            (b) Use a log-linear (or log-log) regression to estimate a demand curve of the form

            . Provide detailed regression output. Write the estimated demand equation.

            Does this regression fit the data better than the linear regression in (a). Determine the       price elasticity of demand.

            (Hint: The log-linear (or log-log) regression requires you to run a regression of ln Q on ln    p, instead of a regression of Q on p. You need to calculate the natural log (or ln) of Q        and the natural log of p and run a regression with these natural log data where lnQ is the       dependent variable and lnp is the independent variable.

Answer 1

Answera

a)

As we can see from above table that p value is 0.00 which is less than 0.05 for both Intercept and Price, hence we reject null hypothesis of no significant impact.

So, Both have significant effect on quantity.

Estimated demand equation

Demand = 332.5 - 506.6Price

Hence If we decrease price by 10 cents demand will increase

506.6/10 units = 50.66 units

b)

Estimated output equation

Q = 2.97P^-2.02

Yes this model fits data better as we can see fromabove tables that, R² of log log model is greater than linear model

coefficient of Ln(P) represents elasticity of demand hence elasticity of demand = -2.02