2. A consumer has and income of 40 to spend in two commodities. Commodity 1 costs 10 per unit, and commodity 2 costs 5 per unit.

(i) What is the consumer's budget equation? If the consumer spends on his/her money on commodity 1, how much could he/she buy? Suppose the consumer was initially consuming 2 units of commodity 1 and 4 units of commodity 2. If the price of commodity 1 increases to 20 and the price of commodity 2 remains 5, by how much would the consumer's income have to rise so that he can still afford the initial bundle? (10 marks)

(ii) Now suppose this consumer is a rational consumer and would like to maximize his/her utility. Explain how an increase in income will affect the consumer's optimal consumption bundle? (10 marks)