Based on 11 annual observations, the following regressions were obtained: Model
ID: 1228338 • Letter: B
Question
Based on 11 annual observations, the following regressions were obtained:
Model A:Yt = 2.6911 - 0.4795Xt
se = (0.1216) (0.1140) r2 = 0.6628
Model B: ln Yt= 0.7774 - 0.2530 ln Xt
se = (0.0152) (0.0494) r2 = 0.7448
where Y = the cups of coffee consumed per person per day and X = the price of coffee in dollars per pound.
a. Interpret the slope coefficients in the two models.
b. You are told that Y = 2.43 and X = 1.11. At these mean values, estimate
the price elasticity for Model A.
c. What is the price elasticity for Model B?
d. From the estimated elasticities, can you say that the demand for coffee is price inelastic?
e. How would you interpret the intercept in Model B? (Hint: Take the antilog.)
f. Since the r2 of Model B is larger than that of Model A, Model B is preferable
to Model A. Comment on this statement.
Explanation / Answer
Answer a:
Slope coefficient of model A :
As the price of coffee increases by one dollar per pound , the quantity consumed of coffee will decrease by 0.4795 units, other things remaining constant.
Model B:
In Log Log regression model, the regression coefficient or the slope coefficient represents the elasticity of demand for coffee. A 10 per cent increase in the price of the good will lead to decline in the quantity demanded of coffee by 2.5 per cent.
Answer b:
Price elasticity of demand for Model A = Slope coefficient * (Mean value of X / Mean Value of Y)
= 0.4795 * 1.11 / 2.43 = 0.22 approximately
Answer c:
Slope coefficient represents the elasticity of demand of coffee. Thus, elasticity of coffee is 0.25.
Answer d:
Since the elasticity of the product in both the models A and B is less than 1, so the demand for coffee is price inelastic.
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