In upstream layer of the industry, there is a single supplier, Supplier $1,$ whose marginal cost of

production is $1.$ The downstream industry is competitive and buys inputs from the upstream

supplier at the cost of k $.$ Downstream industry also hires workers at a competitive wage of $w=$$$2.$

The firms in downstream produce a final good using the production function $Q=K^{\frac{1}{2}}{W}^{\frac{1}{2}},$

where K and W are the amounts of inputs purchased from Supplier $1$ and labor market,

respectively. The inverse demand faced by downstream industry is $P=20-3Q.$