Consider a monopolist (call them the manufacturer) who produces SOMA

Consider a monopolist (call them the manufacturer) who produces SOMA. SOMA is bought by another monopolist (call them the retailer) who turns SOMA into AMOS for sale to customers. 1 unit of SOMA can be turned into 1 unit of AMOS at no cost. If the retailer charges a price p for AMOS, the demand for AMOS will be 100 - p. The elasticity of demand at price p, in this case, is p/(100 - p).

1. Let c be the price per unit that the manufacturer charges the retailer for SOMA. Use the markup formula to determine what price (as a function of c) the retailer should charge her customers so as to maximize profit.

2. The manufacturer produces SOMA at a constant marginal cost of $1 a unit. What should he set c at so as to maximize his profit? What will his maximum profit be?

3. Now suppose that the manufacturer was to integrate with the retailer, .i.e., the manufacturer sells AMOS directly to the customer. What will the maximum profit of the integrated enterprise be? Compare the profit from integrated enterprise to the total profit ( i.e. the sum of profit from manufacturer and retailer ) of the selling structure in part (1) and (2). What do you find?