1. Jim sees commuting by bus and T as perfect substitutes (U = T + B), that is, he would exchange one commute by bus for one commute by T. The price of a bus ticket is $1.50 and the price of a T ticket is $2.00. Jim has $6.00 to spend on commuting. (a) Graph the budget constraint. (b) Find the best affordable bundle and add it to the graph with the relevant indifference curve.
2. Kim has $200 per week to spend on gas and food. The price of gas is $4/gallon and the price of food is $2/unit. (a) Sketch Kim’s budget constraint with gas on the y-axis. (b) What is the opportunity cost of an additional unit of food in terms of gallons of gas? (c) Suppose that gas prices spike to $5/gallon but the price of food remains constant. Sketch the new budget constraint with gas on the y-axis. (d) Now what is the opportunity cost of an additional unit of food in terms of gallons of gas? (e) Explain the relationship between the slope of the budget constraint and the opportunity cost of food in terms of gas.
3. Sometimes stores have sales that limit the quantity you can purchase at the sale price. If you buy more than the limit, you pay the full price. Assume that your local grocery store is having a sale on yogurt where the first 4 are on sale for $1.00 per container, after which they cost $2.00. 1 (a) Graph your budget constraint if you have $20 to spend on yogurt. Label your x and y axis clearly and accurately to receive credit. (b) Add a budget constraint to the graph that represents a decrease in income.
4. Shannon loves fashion and her hats and scarf must always match. However, Shannon loses her hats all the time so she buys two hats for each scarf she buys. In other words, she views scarves and hats as complements in a 1:2 ratio U = min{2S, H}. Shannon has $120 to spend on hats and scarves. Hats are $10 and scarves are $20. (a) Graph Shannon’s indifference curves for scarves and hats. (b) Find Shannon’s best affordable bundle assuming U = min{2S, H}.
5. Use the table below to answer the following questions. The table contains the marginal rates of substitution at different quantities of two goods (X and Y) for different levels of utility – this is a table of the indifference curves in the graph below. The table uses the utility function U = (XY ) 1 2 which yields indifference curves of the form Y = U2 X . U=2 U=3 U=4 U=6 X Y MRS X Y MRS X Y MRS X Y MRS 1 4 4 1 9 9 1 16 16 1 36 36 2 2 1 2 4.5 2.25 2 8 4 2 18 9 3 1.33 0.44 3 3 1 3 5.33 1.78 3 12 4 4 1 0.25 4 2.25 0.56 4 4 1 4 9 2.25 5 0.8 0.16 5 1.8 0.36 5 3.2 0.64 5 7.2 1.44 6 0.67 0.11 6 1.5 0.25 6 2.67 0.44 6 6 1 7 0.57 0.08 7 1.29 0.18 7 2.29 0.33 7 5.14 0.73 8 0.5 0.06 8 1.13 0.14 8 2 0.25 8 4.5 0.56 (a) Write and graph the equation for the budget constraint if M=48 and Px=8 and Py=8. (b) What is the utility maximizing bundle of x and y given this budget constraint? What is the consumers level of utility. Add a representative indifference curve for convex preferences that includes this bundle to your graph.