Assume that the demand for beef can be expressed as Q_(beef)=127-0.23P_(beef)+ 0.15P_(pork)+0.27P_(chicken)+1.07I Also assume that the average per capita beef consumption is 75.73 Kgs. the average price of beef is Ksh190.88perKg the average price of pork is Ksh 145.52 per Kg. the average price of chicken is Ksh68.48 per Kg, and the average disposable income is Ksh7,715.49 Required i) Interpret this equation for substitutes and complements. (4 Marks) ii) Calculate the own cross-, and income -clasticities of demand and interpret your results. (6 Marks)

i) **Interpretation of the Equation for Substitutes and Complements:**<br /><br />In the demand equation \( Q_{beef} = 127 - 0.23P_{beef} + 0.15P_{pork} + 0.27P_{chicken} + 1.07I \):<br /><br />- The coefficient of \( P_{beef} \) is -0.23, indicating that beef has a negative relationship with its own price, as expected. This means that as the price of beef increases, the quantity demanded decreases, which is typical for most goods.<br /><br />- The coefficient of \( P_{pork} \) is 0.15, which is positive. This suggests that pork is a substitute for beef. As the price of pork increases, the demand for beef also increases because consumers may switch from pork to beef.<br /><br />- The coefficient of \( P_{chicken} \) is 0.27, which is also positive. This indicates that chicken is another substitute for beef. An increase in the price of chicken leads to an increase in the demand for beef.<br /><br />- The coefficient of \( I \) (income) is 1.07, which is positive. This implies that beef is a normal good, meaning that as disposable income increases, the demand for beef also increases.<br /><br />ii) **Calculate the Own, Cross-, and Income Elasticities of Demand:**<br /><br />To calculate elasticities, we use the formula:<br /><br />\[ E = \left( \frac{\partial Q}{\partial X} \right) \times \left( \frac{X}{Q} \right) \]<br /><br />where \( \frac{\partial Q}{\partial X} \) is the coefficient of the variable, \( X \) is the average value of the variable, and \( Q \) is the average quantity demanded.<br /><br />1. **Own Price Elasticity of Demand for Beef:**<br /><br /> \[ E_{beef} = (-0.23) \times \left( \frac{190.88}{75.73} \right) \approx -0.58 \]<br /><br /> Interpretation: The own price elasticity of demand for beef is approximately -0.58, indicating that beef is inelastic. A 1% increase in the price of beef results in a 0.58% decrease in the quantity demanded.<br /><br />2. **Cross Price Elasticity of Demand with Respect to Pork:**<br /><br /> \[ E_{pork} = (0.15) \times \left( \frac{145.52}{75.73} \right) \approx 0.29 \]<br /><br /> Interpretation: The cross-price elasticity of demand with respect to pork is approximately 0.29, suggesting that pork is a substitute for beef. A 1% increase in the price of pork results in a 0.29% increase in the demand for beef.<br /><br />3. **Cross Price Elasticity of Demand with Respect to Chicken:**<br /><br /> \[ E_{chicken} = (0.27) \times \left( \frac{68.48}{75.73} \right) \approx 0.24 \]<br /><br /> Interpretation: The cross-price elasticity of demand with respect to chicken is approximately 0.24, indicating that chicken is also a substitute for beef. A 1% increase in the price of chicken results in a 0.24% increase in the demand for beef.<br /><br />4. **Income Elasticity of Demand:**<br /><br /> \[ E_{income} = (1.07) \times \left( \frac{7715.49}{75.73} \right) \approx 109.08 \]<br /><br /> Interpretation: The income elasticity of demand is approximately 109.08, indicating that beef is a highly elastic normal good. A 1% increase in income results in a 109.08% increase in the demand for beef.