Exam sample 1

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GAMS Exam-Like Sample Problems Problem 1 You are the production manager of a firm that produces a single good 𝑄, from a set of 4 production inputs, 𝑓𝐴, 𝑓𝐵, 𝑓𝐶, 𝑓𝐷. The production function of the firm has the following shape: 𝑄(𝒇) = ∏ 𝑓𝑖 𝛼𝑖 𝑖 Where 𝒇 is the vector of production inputs. The list of inputs, together with unitary prices and exponents 𝛼𝑖 can be found in the table below: Production Input A B C D Unitary Price 1 2 4 3 Alpha 0.50 0.15 0.15 0.20 Your marketing manager tells you that for the following month you need to produce 𝑄 = 75 Your objective is to produce the needed quantity spending the least amount of money possible Respond to these questions: 1. Comment on the production function (name, its main general features, do you have economies of scale?) 2. Write a GAMS programme that allows you to solve this problem 3. How do you compute the cost of an additional unit of output? 4. The alphas of all production inputs but B are increased by 0.05. Modify the code developed in 1. to address this. 5. To perform a sensitivity analysis, you want to see how your solution changes with a -10%, -5%, +5%, +10% increase in the price of input A and D. What would you add to the code to model this? (Using a for is a very good idea…)