Supply Chains A new product is produced in two stages. Output Q is the sum of input X1, which is produced in-house, and input X2, which is purchased from contractors on the market. The inverse demand function is P = 20 Q. The cost of processing is $2 per unit. The cost of production in-house is $3 per unit, and the cost per-unit of producing by contractors is $X2, which means that the marginal cost of production for contractors is increasing. Assume the firm-owner purchases the inputs from contractors at marginal cost (i.e. does not have monopsony power, and so just uses the marginal cost of purchasing input from the market to determine the optimal amount to purchase). 1. How much output will be produced under vertical integration (only using in-house production)? What will be the price of the output? 2. How much output will be produced under contract (only using production from contracting)? What will be the price of the output? 3. What is the optimal outcome from the perspective of the entrepreneur running the supply chain (i.e. how much in-house production do they choose versus production through contracting)? 1