Please help me to answer this question. 2. Suppose that an econometric study fin
ID: 3060163 • Letter: P
Question
Please help me to answer this question.
2. Suppose that an econometric study finds that in Ghana average annual per capita grain consumption follows the relationship In(grain) 1.7 +0.81n(annual per capita income) _ 0.51n(price of grain) where grain is measured in klograms per person, annual per capita income in Ghanaian Cedi, and the price of grain in cedi per kilogram (a) What is per capita grain consumption when per capita income equals 1,000 Ghanaian Cedi and the price of grain is 10 Ghanaian Cedi per pound? (b) If income rises from 1,000 to 1,010 Ghanaian Cedi , compute what happens to grain consumption. How does this computation compare with the prediction from elasticity that 1% rise in income will bring an 0.8% rise in consumption? (c) If income rises from 1000 to 1,500 Ghanaian Cedi, compute what happens to grain consumptino. How does this computation compare with the prediction from elasticity that a 50% rise in income will bring a 40% rise in consumption? (d) What do you conclude from (b) and (c) together?Explanation / Answer
(a)
10 Ghanaian Cedi per pound means 10/0.453 Ghanaian Cedi per kilogram, i.e 22 Ghanaian Cedi per kilogram
We substitute the given value in above equation,
ln(grain) = 1.7 + 0.8ln(1000) -0.5ln(22) = 5.68068299651
thus, per capita grain consumtion = e^5.68068299651 = 293.14 kilogram
(b) if it increases to 1010
ln(grain) = 1.7 + 0.8ln(1010) -0.5ln(22) = 5.68864326119
thus, per capita grain consumtion = 295.49
Percentage increase = (295.49-293.14)/293.14 = 0.0080 = 0.8%
Thus, It almost equals with the prediction of 0.8% rise in consumtion
(c) if it increases to 1500
ln(grain) = 1.7 + 0.8ln(1500) -0.5ln(22) = 6.00505508299
Per capita grain consumption = 405.47
Percentage increase = 0.383 = 38.3%
Thus it is almost equal to 40% but not exactly equal.
(d) Per capita grain consumtion at very high increase in incomes not matches up with the predicted elasticity demand. This, in economy means that people are not spending in grain consumption as expected when their incomes become too high. Either they start saving or find other means of spending.
Their marginal propensity to consume decreases after certain limit.