Question

Suppose that you are the consultant to an agricultural cooperative that is deciding whether members should cut their production of cotton in half next year. The cooperative wants your advice as to whether this action will increase members’ revenues. Knowing that cotton (C) and soybeans (S) both compete for agricultural land in the South, you estimate the demand for cotton to be C = 3.5 - 1.0PC + 0.25PS + 0.50I, where PC is the price of cotton, PS the price of soybeans, and income. Should you support or oppose the plan? Is there any additional information that would help you to provide a definitive answer?

Short answer

The decision to oppose or support depends on the elasticity of demand for which additional information about the initial price and quantity is needed.

Step-by-step solution

Explanation of the answer

Given the equation, C = 3.5 - 1.0PC + 0.25PS + 0.50I, you can see the demand curve for cotton is downward sloping.Hence, if the production of cotton is cut to half, the shortage in supply will raise the price. Higher price reduces the demand for cotton. The overall effect on the revenue is based on the elasticity of demand. If the demand is inelastic (fall in demand is lesser than the rise in price), then revenue will increase, and if the demand is elastic (fall in demand is greater than the rise in the price), then revenue will decrease.

Therefore, to decide whether to support the decision or not, a lot of information is needed, such as the initial price and quantity of cotton. Hence, a decision cannot be made.