Test graduate students' ability to apply Bertrand and Cournot models to duopolies with binding capacity constraints: derive best-response functions, compute Nash equilibria in price-setting and quantity-setting frameworks for given demand and cost parameters, calculate equilibrium prices, outputs and profits, perform comparative statics for changes in capacities and demand, and compare welfare and strategic implications across the two models; include short analytical derivations, numerical equilibrium computations, and brief interpretation of results for firm strategy and policy.