Problem 3: Income Effects [8 Points] Suppose that there is a household with $1,000 to spend, and they can choose between two goods: (i) bicycles and (ii) steaks. The price of a bicycle is $100 and the price of a steak is $40. Suppose that with the current prices, the rational, utility-maximizing household has chosen to purchase 10 steaks and 6 bicycles. Assume that their indifference curves are curved as in lecture. 11. Draw the budget constraint with bicycles on the x-axis and steaks on the y-axis. Label the x-intercept and y-intercept. Also draw on the above figure, the utility-maximizing consumption bundle and the indifference curve that is lies on. [HINT: you do not know much about this indifference curve, but you do know its shape, and where it must lie in relation to the budget constraint if the consumer is optimizing] [1 point] Now suppose that the household's income increases from $1,000 to $1,400. 12. Show how this budget constraint moves with this income increase. Again, do so with bicycles on the x-axis and steaks on the y-axis and label both the x-intercept and y- intercept. [1 point] Now suppose that both steaks and bicycles are normal goods. 13. What is the range of consumption bundles on the new budget constraint that this rational, utility-maximizing household may now choose to consumer? [3 points] [Hint: you have drawn your own indifference curve, and I have not given you enough information to know exactly at what point the new choice will be. But, with the information about what type of goods they are, you can rule some choices out.] Now suppose instead that steaks are a normal good and bicycles are an inferior good. 14. Again, what is the range of consumption bundles on the new budget constraint that this rational, utility-maximizing household may now choose to consume with bicycles now being an inferior good? [3 points] [Hint: same as above!]