Question

Assume that the demand for beef can be expresses as Qbeef= 127 - 0.23Pbeef+ 0.15Ppork+ 0.27Pchicken + 1.071. Also assume that the average per capita beef consumption is 75.73 pounds, the average price of beef is 190.88 cents per pound, the average price of pork is 145.52 cents per pound, the average price of chicken is 68.48 cents per pound , and the average disposable income is $7,715.49. (1) Interpret this equation for substitutes and complements, as well as whether beef is a normal or inferior good; (2) calculate the own-, cross-, and income-elasticities of demand, and interpret your results.

Answer 1

The given demand equation represents beef as a complement to pork and chicken and a normal good. The elasticities of demand can be calculated by taking the partial derivatives of the demand equation and substituting the given values.

Step-by-step explanation:

(1) The given demand equation includes the prices of pork and chicken as well as an intercept term. Beef is a complement to pork and chicken because as the prices of pork and chicken increase, the demand for beef decreases. This means that as the prices of pork and chicken rise, people substitute away from beef and consume less of it. Moreover, since the coefficient of the beef price term is negative, we can conclude that beef is a normal good. As income increases, the quantity demanded of beef decreases.

(2) The own-elasticity of demand measures the percentage change in the quantity demanded of a good in response to a percentage change in its price. The cross-elasticity of demand measures the percentage change in the quantity demanded of a good in response to a percentage change in the price of another good. The income-elasticity of demand measures the percentage change in the quantity demanded of a good in response to a percentage change in income. To calculate these elasticities, we need the partial derivatives of the demand equation with respect to the prices and income. Once we have those, we can substitute the given values to obtain the numerical results.