A consumer has preferences over two goods, heating oil and food. The consumer prefers more of each good to less, and has a diminishing marginal rate of substitution between the two goods. Both are normal goods. (a) [6 marks] Draw a diagram showing indifference curves and the budget constraint of the consumer (with heating oil on the horizontal axis and food on the vertical axis). Show how the consumer's optimal consumption choice is found in the diagram. (b) [6 marks] The price of heating oil rises. Draw a diagram showing the change in consumption of heating oil, and how it can be broken down into income and substitution effects. (c) [6 marks] When the price of heating oil rises, the government gives a cash transfer that makes the consumer exactly as well off as before the price of heating oil increased. Would the consumer continue to purchase the same amount of heating oil in this case? Explain. (d) [6 marks] Instead of the cash transfer in part (c), the government gives the consumer heating oil vouchers of the same monetary value. The vouchers can only be spent on heating oil and cannot be transferred to any other individual. Explain whether there are circumstances where the consumer would prefer to have the vouchers, or prefer to have the cash transfer. (e) [6 marks] Instead of giving the cash transfer or vouchers considered in parts (c) and (d) to every consumer of heating oil, the government uses the same amount of money to subsidize heating oil, with the subsidy reducing the price consumers would otherwise pay. Assuming all consumers are the same, would they be better off, worse off, or just as well off compared to receiving the cash transfer? (Hint: Think about whether the amount of money available for the subsidy would be sufficient to restore the original price of heating oil.).

1. A hat contains 50 names, of which 23 are female. Five names are drawn as a group from the hat.
a) Create a probability distribution for all the different possibilities. b) What is the probability
that at least three female's name is drawn? c) What is the expected number of female names
being drawn from five total names?