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ECON 201 SC 2011
ASSIGNMENT 1
Answer all questions. Questions are each worth 12 marks. Total = 36 marks.
Julia lives for food (F) and entertainment (E). Her preferences are described by the utility function u(F, H) = vF + 2vE.
Find Julia’s marginal rate of substitution between food and entertainment. Are Julia’s preferences homothetic or not? Explain briefly.
Julia has $120 a week to spend. Find her optimal weekly consumption of food and entertainment if a bag of food costs $15 and an evening’s entertainment costs $20. (Assume both commodities are infinitely divisible.) Illustrate this optimum in a diagram.
How will Julia’s optimal consumption bundle change if her weekly budget increases to $180? Illustrate this optimum in the diagram drawn for part (b).
Define an Engel curve. Find Julia’s Engel curve for food if the costs of food and entertainment are as given in (b).
Antony has dental problems and consumes only beer (B) and cheap wine (W). His preferences over beer and wine are given by the utility function u(B, W) = lnB + lnW. He has $16 a day to spend at his local supermarket.
The normal price of beer is $4 a litre and wine is $8 a litre. Find Antony’s optimal daily amounts of beer and wine. Illustrate this in a diagram.
The supermarket now advertises a half-price sale for one day on Antony’s brand of beer. Consumers are able to purchase up to two litres of beer at half-price but additional quantities cost the normal price. Find Antony’s optimal choice of beer and wine during the sale day. Illustrate this in a separate diagram.
How would Antony’s choices be altered if his preferences were given by the utility function u(B, W) = 3BW? Explain briefly.
Sara’s preferences over consumption this year and next (years 1 and 2) are given by her intertemporal utility function u(C1, C2) = min[3C1, 4C2], where C1 and C2 are her consumption levels of the composite commodity in the respective years. Sara’s income this year is $34,000 and she expects to…