Problems
1. You have decided to sell some goods at a local music festival. You have hired a sales stand for $500. Your cost per item is $3 and you will sell each item for $5. When you did your initial calculations, you expect to sell 300 items and have purchased 500 just to be sure. You can return any un-sold items to the supplier and get your $3 back.
(a) What benefits do you expect?
(b) What costs did you expect?
(c) Suppose that due to rain the prospects look bad and you now only expect to sell 200 items. At this point you have already paid the $500 for the stand, but you can decide not to sell if you want. Would you prefer to not sell now?
(d) What other costs might you have that have not been expressed here? Would they perhaps change your answer to (c)?
2. You can buy any quantity of cooking oil at $5 per litre and any quantity of flour at $2 per kilo. You have allocated $20 to spend on cooking oil and flour.
(a) If you choose to buy 2 litres of cooking oil, what is the maximum amount of flour you can buy with your $20 budget?
(b) If you choose to buy no cooking oil, then how much flour can you afford with your $20 budget?
(c) Draw your budget constraint for cooking oil and flour.
(d) If you get hungry on the way to the shop and spend $5 of your $20 budget on a snack, then how does this affect your budget constraint for flour and oil? Show how the constraint changes in the diagram.
(e) This part is a bit more demanding, but you may find it fun. If you did not spend the $5 on a snack, so you have still $20 in your budget, then are there any prices for cooking oil and flour that would leave you with the same budget constraint as in part (d)? If you think the answer is no, you haven't thought enough. Hint: Both of the budget constraints are straight lines. Think about what must be true about the prices for a straight line with a $20 budget to be the same as the straight line in (d)?
3. You can buy as many drinks as you want at $1 each. You can also buy as many chocolate bars as you want at $2 each. You have $5 to spend. You must buy whole bars and drinks, that is, you cannot buy 1/2 a drink or 1/2 a chocolate.
(a) List the combinations of drinks and bars that exhaust your $5 in a table.
(b) Suppose that you must spend all your $5 on the drinks and bars. You would like to have as close to an equal number of drinks and bars if possible. How many bars and drinks will you consume?
(c) Suppose now that you do not have to spend all your $5, that is, you may have some change left over. You want to consume drinks and chocolate bars only in equal amounts, i.e., 1 bar and 1 drink, or two bars and two drinks, etc., but you will consume as much as your budget allows. Given these wants, how much chocolate and drinks will you consume? How much money do you have left over?
4. You are allocating money between pizza and Chinese food over a month. You like a variety.
(a) Letting C denote the quantity of Chinese meals you consume in a month and P denote the quantity of pizza, construct a diagram and draw some indifference curves that might represent your preferences.
(b) Suppose that you have $100 to spend per month on the two and pizzas cost $5 each and Chinese meals cost $10. Draw your budget line and an indifference curve with a consumption level that you regard as being optimal.
(c) If the price of pizza falls, show how your optimal consumption might change? Could you perhaps consume more Chinese food after the change?
5. Your welfare depends on how much time you travel T and how much time you play P and is the product of the two, i.e., .
(a) The total amount of time you have is 10 hours, i.e., T+P=10.
(b) If you spend 2 hours traveling and 8 hours playing, how much is your welfare?
(c) If you spend 8 hours traveling and 2 hour playing, how much is your welfare?
(d) Consider the simple average of the outcomes in (b) and (c). Is that possible given your time constraint? How high is your welfare in this case? What does it suggest about your feeling for averages versus extremes?
6. You will gain welfare from consuming bread and chocolate. Your welfare is described numerically by , where B denotes the quantity of bread you choose to consume, and C denotes the quantity of chocolate, and W denotes your welfare level.
(a) You have $20 to spend on bread and chocolate. The price of chocolate is $2 per unit, and the price of bread is $1 per unit. Draw your budget constraint, and an indifference curve depicting your welfare level when you optimise. How much chocolate will you buy?
(b) If the price of chocolate increases to $4, does this affect how much chocolate you buy? Does it affect your budget line?
(c) Given that bread costs $1, how low must the price of chocolate be before you start buying any chocolate?
7. Jim buys only milk and biscuits.
(a) In 2004, Jim earns $100, milk costs $2, biscuits cost $4 per dozen. Draw Jim’s budget constraint
(b) Now suppose that all prices increase by 10% in the year 2005 and that Jim’s salary increases by 10% as well. Draw Jim’s new budget constraint. How would Jim’s optimum combination of milk and biscuits in 2005 compare with his optimum combination in 2004.
(c) Would your answer to part (b) change if Jim’s salary didn’t change? Why?
8.You have $21 to spend on prawns and potatoes. Prawns cost $20 per kilo and potatoes cost $2 per kilo.
(a) Supposing you can buy as much or as little as you want of prawns and potatoes and you will spend the entire $21, then prepare down your budget constraint. You may simply prepare out the equation or draw the budget line. You don't need to do both.
(b) If you buy 2.5 kilos of potatoes, how many kilos of prawns can you afford?
(c) If your wants are to have twice as many (kilos) of prawns as (kilos) of potatoes, show that you would buy 0.5 kilo of potatoes and exactly 1 kilo of prawn. How much money will you spend on each? Remember you must spend exactly $21.
(d) If the price of potatoes rises to $3 per kilo and the price of prawns falls to $18 per kilo, then can you still purchase the quantity of prawns and potatoes you chose in (c)?
Based on your answer, argue that your welfare is likely to be greater in this new situation where the price of potatoes is higher, but the price of prawns is lower.
9. You have $20 to spend on high quality pens and low quality pens. High quality pens cost $5 each and low quality pens cost $2 each.
(a) Suppose that you will spend your entire $20. prepare down your budget constraint. You may simply prepare out the equation or draw the budget line. You don't need to do both.
(b) If you buy 5 low quality pens, how many high quality pens can you afford?
(c) If you are given 25% increase in your budget, prepare down your budget constraint. You may simply prepare out the equation or draw the budget line. You don't need to do both.
(d) If you were not given a 25% increase in your budget, are there any prices for high quality pens and low quality pens that would leave you with the same budget constraint as part (c)? If yes, what are they?