Problem 4. Suppose that the production set of a firm is given by P := {2:1 = (31,12) ER?,05015 VE)}; where good 1 is the output and good 2 is the input. Each pair (11,12) in the set P specifies which pairs of output and input are feasible to the firm. That is, if (11,12) P, then the firm can produce ei units of output given 12 units of input. (i) Sketch the production set in a two-dimensional graph, with inputs denoted on the horizontal axis and outputs on the vertical. (5 marks] (ii) Determine whether the production set is closed. Precisely motivate your answer. [3 marks) (iii) Determine whether the production set is compact. Precisely motivate your answer. [2 marks] (iv) A production function assigns the highest possible output level to each level of input. What is the production function corresponding to the production set P? (3 marks) Suppose that the firm has lost its main supplier of inputs and can rely only on up to 100 units of input that can be provided by their secondary supplier. (v) Given the above information, what is the current production set of the firm? Sketch the graph of the productions set and determine if it is closed. Is it compact? Pre- cisely motivate your answer. [7 marks] Problem 4. Suppose that the production set of a firm is given by P := {2:1 = (31,12) ER?,05015 VE)}; where good 1 is the output and good 2 is the input. Each pair (11,12) in the set P specifies which pairs of output and input are feasible to the firm. That is, if (11,12) P, then the firm can produce ei units of output given 12 units of input. (i) Sketch the production set in a two-dimensional graph, with inputs denoted on the horizontal axis and outputs on the vertical. (5 marks] (ii) Determine whether the production set is closed. Precisely motivate your answer. [3 marks) (iii) Determine whether the production set is compact. Precisely motivate your answer. [2 marks] (iv) A production function assigns the highest possible output level to each level of input. What is the production function corresponding to the production set P? (3 marks) Suppose that the firm has lost its main supplier of inputs and can rely only on up to 100 units of input that can be provided by their secondary supplier. (v) Given the above information, what is the current production set of the firm? Sketch the graph of the productions set and determine if it is closed. Is it compact? Pre- cisely motivate your answer. [7 marks]