a) Suppose there are two goods a consumer can choose between, and that the prices are equal. First, construct a diagram, with quantities on the X- and Y-axes, where you show a utility maximizing choice for the consumer.
b) Then, show what happens if you vary the price of good 1. Construct one budget line corresponding to the case when the price is cut by half, and another one when it is doubled. Will the consumer maximize her utility in the same point as before? Show how to derive the price-consumption curve using this technique.
c) Use the price-consumption curve to derive the consumer's demand curve for good 1.
d) Suppose that you also have another consumer's demand curve. Show in a new diagram how you can derive the market's demand curve, assuming the market only consists of these two consumers. You may assume that the consumers' demand curves are straight lines.