You have been assigned the task of helping the Midland Milk Producers Marketing Co-operative Association (MMPMCA), the sole marketing agency for milk produced in the Island State of Midland. In the past, the producers have been marketing their milk as a homogeneous commodity to all processors of milk. However, you have stud- ied the market extensively and realize that the market can actually be segmented into two separate units: (1) the market for fluid milk (milk for drinking) and (2) the mar- ket for processing milk (for manufacturing of cheese, etc.). In fact, you have done some preliminary analysis and generated demand curves for the two separate markets for the MMPMCA's milk output.
Fluid milk market:
Inverse demand curve: pfluid = 10 - 2qfluid. Marginal revenue curve: MRfluid = 10 - 4qfluid.
Processing milk:
Inverse demand curve: pprocessing = 5 - 0.5qprocessing. Marginal revenue curve: MRprocessing = 5 - 1qprocessing.
Cost of production:
Assume that individual firms have the same cost function as follows:
TC = 10 + 3q, where
q = qfluid + qprocessing.
a. Determine the marginal cost of milk production.
b. What is the desired allocation of milk production between the two markets, and what is the price they should charge for fluid and processing milk in the respec- tive markets, assuming that the MMPMCA wishes to maximize profits for the farmers they represent? In other words, given that they can practice price dis- crimination in the market, how much should they sell into each of the fluid milk and processing milk markets, and at what price?
c. Given that the price of milk without price discrimination is $4.50, how have prices changed for fluid milk and processing milk buyers?
d. How have total revenues changed if the actual total production of milk remains unchanged?
e. Calculate the own-price elasticities of demand for fluid and processing milk at the equilibrium values for p and q.