ECON 306 Worksheet 3 Part 1 A student at UMD on financial aid consumes Books (q1) and Food (q2). Her preferences are represented by the utility function: 𝑼(𝒒𝟏, 𝒒𝟐) = 𝒒𝟐𝟏 q2 She has an initial budget of $300 and the price of books is $10, and the price of food is $5. 1. Find the student’s original consumption bundle. 2. Suppose the price of food rises to $10. How much additional income would she need to be able to afford her original consumption bundle with the new price of food? 3. Suppose that her budget is increased by the dollar amount you found in the question above. What bundle will she consume with the higher food price and with that larger budget (round to nearest 1/10th of a unit)? 4. Will she be better off, worse off, or equally well off at the new price and budget compared to with her original budget and prices? Part 2 Bonnie is obsessed with making perfect milkshakes. To her, the perfect milkshake must contain exactly 3 scoops of ice cream to 1 cup of milk. She refuses to make any milkshake with more or less than that ratio of ice cream to milk and will simply throw out any extra of an ingredient. She wants to make as many milkshakes as possible. She shops at Safeway where ice cream is sold at a price of $1.50 per scoop and milk sells for $0.50 per cup. She has $20 in income to spend. 5. What is the name given to Bonnie’s particular preferences? 6. Provide a utility function to represent these preferences. 7. On a graph, draw the indifference curve that passes through bundle (3,3). 8. What is Bonnie’s optimal bundle of ice cream and milk? Part 3 Dotty buys pencils. Two types of pencils are sold: Ticonderoga which are sold with 10 pencils per pack, and Learner which are sold with 12 pencils per pack. Dotty only cares about the total number of pencils she has. Let q1 be the number of packs of Ticonderoga pencils, and q2 as the number of packs of Learners. The prices of packs are p1=6 and p2=7. Dotty spends $84 on packs of pencils. 9. What is the name given to these kinds of preferences? 10. Provide a utility function representing these preferences. 11. What is Dotty’s utility maximizing bundle of packs of Ticonderoga and Learner pencils? Part 4 A worker has preferences given by the utility function 𝑼(𝑵, 𝒀) = 𝑵𝟐 𝒀 where N is the hours of leisure per day and Y is their spending on purchased goods. 12. If the consumer faces a wage rate of w=30, how much leisure and purchased goods do they consume? What is the quantity of labor supplied? 13. Suppose the wage increases to w=40. What is the quantity of labor supplied?
