Question

The coconut oil demand function (Bushena and Perloff, 1991) is Q = 1,200-95p + 162pₚ + 0.2Y, where Q is the quantity of coconut oil demanded in thousands of metric tons per year, p is the price of coconut oil in cents per pound, pp is the price of palm oil in cents per pound, and Y is the income of consumers. Assume that p is initially 55 cents per pound, Pₚ is 31 cents per pound, and Q is 1,325 thousand metric tons per year.

Calculate the price elasticity of demand for coconut oil and the cross-price elasticity of demand (with respect to the price of palm oil)

Answer 1

The calculations for the price elasticity and cross-price elasticity of demand for coconut oil involve inserting the given values into the respective formulas based on the provided demand function and simplifying.

Step-by-step explanation:

The student's question is about calculating two types of elasticities of demand: the price elasticity of demand for coconut oil, which measures the responsiveness of the quantity demanded to changes in the good's own price, and the cross-price elasticity of demand, which measures the responsiveness of the quantity demanded to changes in the price of a related good, in this case, palm oil. To calculate these elasticities, we apply the formulas derived from calculus where the elasticity of demand is the percentage change in quantity demanded divided by the percentage change in price. Since the function provided is Q = 1,200 - 95p + 162pṗ + 0.2Y, with given values for p, pṗ, and Q, we can insert these values to find the respective elasticities.

For price elasticity of demand, we use the formula (dQ/dp)(p/Q). Assuming the given demand function and values, the calculation would be (-95)(55)/1,325. For cross-price elasticity of demand, the formula is (dQ/dpṗ)(pṗ/Q), which would be (162)(31)/1,325 when we substitute the given values into the formula. These calculations give us the respective elasticities at the specified point on the demand curve.