Imagine a firm that has the following production function: y = x1x2 Note that this implies the following marginal products (Note very carefully the sub- scripts. They are not a mistake). M P1 = x2 M P2 = x1

Note that this question can be tricky if you try to do it too quickly. If you are having trouble, try at least showing what is happening graphically and explain the intuition. This will get you some good part marks. (please give points for the graph and show how to plot it)/if you cant draw it.

a) (5 marks) Suppose the price of input 1 was equal to $5, and the price of input 2 was equal to $10. What would be the optimal inputs for this firm if it wished to produce 450 units of output? Hint use the optimality ratio from having the slope of the isocost equal the slope of the isoquant. Combine this with the production function and you should get your answers. The numbers will be nice whole numbers. b) (5 marks) Suppose the price of input 1 increased to $20. What would be the optimal inputs for this firm if it still wished to produce 450 units of output? You can use the same approach as the last question. c) (5 marks) Explain how the firm responded to this increase in price, and how its total costs changed as a result.