Math  /  Data & Statistics

Question7. Based on the following table which indicates expenditure of the household on a commodity, answer the questions that follow (The price of the good is Br .10 ) \begin{tabular}{|c|c|} \hline \begin{tabular}{c} Income \\ (Br. / month) \end{tabular} & \begin{tabular}{c} Quantity Demanded \\ (units / month ) \end{tabular} \\ \hline 10,000 & 50 \\ \hline 20,000 & 60 \\ \hline 30,000 & 70 \\ \hline 40,000 & 80 \\ \hline 50,000 & 90 \\ \hline \end{tabular} A) Calculate income elasticity of demand, if income increases from Br.10,000\mathrm{Br} .10,000 to Br . 20,000 and if income increases from Br.40,000\mathrm{Br} .40,000 to Br.50,000\mathrm{Br} .50,000. B) Is this a normal or an inferior or a luxury good? Justify. C) Does the proportion of household income spent on this good increase or decrease as income increases? .Why?
8. When price of tea in local café rises from Br. 10 to 15 per cup, demand for coffee rises from 3000 cups to 5000 cups a day despite no change in coffee prices. A) Determine cross price elasticity. B) Based on the result, what kind of relation exists between the two goods?

Studdy Solution
Determine the relationship between tea and coffee based on the cross-price elasticity.
Since the cross-price elasticity is positive (EC=1.25E_{C} = 1.25), tea and coffee are substitute goods.
**Solution**: A) Income elasticity of demand: - From Br. 10,000 to Br. 20,000: EI0.273E_I \approx 0.273 - From Br. 40,000 to Br. 50,000: EI0.529E_I \approx 0.529
B) The good is a normal good, as the income elasticity is positive and less than 1.
C) The proportion of household income spent on this good decreases as income increases, indicating that the good takes up a smaller fraction of the budget at higher income levels.
D) Cross-price elasticity between tea and coffee is EC=1.25E_{C} = 1.25.
E) Tea and coffee are substitute goods.

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