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Sagot :
हामीले प्रश्नलाई सुल्झाउनको लागि केही महत्वपूर्ण चरणहरूको पालना गर्नुपर्नेछ।
### (i) If the price of good [tex]$Y$[/tex] increases from Rs. 2 per kg to Rs. 4 per kg, then find the cross elasticity of demand between goods [tex]$X$[/tex] and [tex]$Y$[/tex]. Also, interpret the result thus obtained.
#### Step 1: Calculate the percentage change in demand for good X.
[tex]\[ \text{Initial demand for good X} = 10 \text{ Kg} \][/tex]
[tex]\[ \text{Final demand for good X} = 8 \text{ Kg} \][/tex]
[tex]\[ \text{Percentage change in demand for good X} = \left(\frac{\text{Final demand} - \text{Initial demand}}{\text{Initial demand}}\right) \times 100 \][/tex]
[tex]\[ \text{Percentage change in demand for good X} = \left(\frac{8 - 10}{10}\right) \times 100 = -20\% \][/tex]
#### Step 2: Calculate the percentage change in price for good Y.
[tex]\[ \text{Initial price of good Y} = Rs. 2 \text{ per Kg} \][/tex]
[tex]\[ \text{Final price of good Y} = Rs. 4 \text{ per Kg} \][/tex]
[tex]\[ \text{Percentage change in price for good Y} = \left(\frac{\text{Final price} - \text{Initial price}}{\text{Initial price}}\right) \times 100 \][/tex]
[tex]\[ \text{Percentage change in price for good Y} = \left(\frac{4 - 2}{2}\right) \times 100 = 100\% \][/tex]
#### Step 3: Calculate the cross elasticity of demand.
[tex]\[ \text{Cross elasticity of demand} = \frac{\text{Percentage change in demand for good X}}{\text{Percentage change in price for good Y}} \][/tex]
[tex]\[ \text{Cross elasticity of demand} = \frac{-20\%}{100\%} = -0.2 \][/tex]
#### Step 4: Interpret the result.
A negative cross elasticity of demand (-0.2) indicates that goods [tex]$X$[/tex] and [tex]$Y$[/tex] are complementary goods. This means that an increase in the price of good [tex]$Y$[/tex] has led to a decrease in the demand for good [tex]$X$[/tex].
### (ii) Based on the cross elasticity of demand, identify the type of [tex]$X$[/tex] and [tex]$Y$[/tex] goods.
Since the cross elasticity of demand is negative, we can infer that:
- Goods [tex]$X$[/tex] and [tex]$Y$[/tex] are complementary goods.
Complementary goods are those goods that are usually consumed together. An increase in the price of one good leads to a decrease in the demand for the other good.
Hence, the cross elasticity of demand calculation and the interpretation of the value indicate that goods [tex]$X$[/tex] and [tex]$Y$[/tex] are complementary.
### (i) If the price of good [tex]$Y$[/tex] increases from Rs. 2 per kg to Rs. 4 per kg, then find the cross elasticity of demand between goods [tex]$X$[/tex] and [tex]$Y$[/tex]. Also, interpret the result thus obtained.
#### Step 1: Calculate the percentage change in demand for good X.
[tex]\[ \text{Initial demand for good X} = 10 \text{ Kg} \][/tex]
[tex]\[ \text{Final demand for good X} = 8 \text{ Kg} \][/tex]
[tex]\[ \text{Percentage change in demand for good X} = \left(\frac{\text{Final demand} - \text{Initial demand}}{\text{Initial demand}}\right) \times 100 \][/tex]
[tex]\[ \text{Percentage change in demand for good X} = \left(\frac{8 - 10}{10}\right) \times 100 = -20\% \][/tex]
#### Step 2: Calculate the percentage change in price for good Y.
[tex]\[ \text{Initial price of good Y} = Rs. 2 \text{ per Kg} \][/tex]
[tex]\[ \text{Final price of good Y} = Rs. 4 \text{ per Kg} \][/tex]
[tex]\[ \text{Percentage change in price for good Y} = \left(\frac{\text{Final price} - \text{Initial price}}{\text{Initial price}}\right) \times 100 \][/tex]
[tex]\[ \text{Percentage change in price for good Y} = \left(\frac{4 - 2}{2}\right) \times 100 = 100\% \][/tex]
#### Step 3: Calculate the cross elasticity of demand.
[tex]\[ \text{Cross elasticity of demand} = \frac{\text{Percentage change in demand for good X}}{\text{Percentage change in price for good Y}} \][/tex]
[tex]\[ \text{Cross elasticity of demand} = \frac{-20\%}{100\%} = -0.2 \][/tex]
#### Step 4: Interpret the result.
A negative cross elasticity of demand (-0.2) indicates that goods [tex]$X$[/tex] and [tex]$Y$[/tex] are complementary goods. This means that an increase in the price of good [tex]$Y$[/tex] has led to a decrease in the demand for good [tex]$X$[/tex].
### (ii) Based on the cross elasticity of demand, identify the type of [tex]$X$[/tex] and [tex]$Y$[/tex] goods.
Since the cross elasticity of demand is negative, we can infer that:
- Goods [tex]$X$[/tex] and [tex]$Y$[/tex] are complementary goods.
Complementary goods are those goods that are usually consumed together. An increase in the price of one good leads to a decrease in the demand for the other good.
Hence, the cross elasticity of demand calculation and the interpretation of the value indicate that goods [tex]$X$[/tex] and [tex]$Y$[/tex] are complementary.
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