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Problem Set # 1

Econ 281

Due Date: 11:59 pm, Oct. 2, 2023

For problems 2-4, show your work and express your answer in a short sentence. Unless otherwise stated, assume that fractional units of goods can be produced and sold (meaning answers do not necessarily need to be whole numbers). Round your final answers to three decimal places when necessary.

Problem 1 (20 Marks)

For each example, draw three indifference curves that represent the given preferences. You are free to provide me with any set of indifference curves that would fit the description. Please also show the direction of increasing utility.

(a) Melissa considers tennis to be kind of meh – she doesn’t get any satisfaction from playing it, but it also isn’t as though she actively dislikes it either. On the other hand, she loves playing pickleball!

(b) Carlos loves to binge watch shows on Amazon Prime. His two favourites right now are “Rings of Power” and “Wheel of Time.” He never stops enjoying watching either show. But with each individual show, each additional episode he watches gives him less enjoyment than the episode before.

(c) Andrea’s two favourite movies right now are “Barbie” and “Oppenheimer.” She watches them over and over again – they never get old! However, she thinks the only way worth watching them is back-to-back – watching one without the other seems pointless to her.

(d) Ben is a huge fan of Taylor Swift’s “1989” album – every minute spent listen ing to it is more enjoyable than the last! He also feels the exact same way about the “Hamilton” soundtrack.

Problem 2 (22 Marks)

(a) Suppose that the market for weighted blankets is in equilibrium when the price of a weighted blanket is $80. At that price, 1000 weighted blankets are sold, the price elasticity of supply is 4, and the price elasticity of demand is −8. Find and graph the supply and demand curves (Note: assume both are linear).

(b) Suppose now that a major advance in blanket weighting technology is made, which greatly eases the weighted blanket production process. As a result, at every price level producers now supply 1000 more weighted blankets than they did previously. Find the new equilibrium price and quantity, as well as the price elasticities of both supply and demand.

Problem 3 (36 Marks)

Sam only consumes two goods: cookies (c), and concert tickets (t). His utility function and associated marginal utilities are as follows:

U = 1200c 0.1 t 0.4

MUc = 120c −0.9 t 0.4

MUt = 480c 0.1 t −0.6

Each cookie costs $2.50 and each concert ticket costs $20.

(a) How much money would Sam need to achieve utility = 10,000?

(b) From now on, assume Sam has $1000 to spend. How many cookies and concert tickets will Sam consume?

(c) Suppose cookies cost $4 each instead of $2.50. How many cookies and concert tickets will Sam consume?

(d) Find the substitution and income effects for the change from part (b) to (c).

(e) Find the Compensating and Equivalent Variations for the change from part (b) to (c).

(f) Suppose Sam’s utility function was actually the following:

U = 1200c 0.5 + 160t

MUc = 600c −0.5

MUt = 160

Assuming again that each cookie costs $2.50 and each concert ticket costs $20, and Sam has $1000 to spend, how many cookies and concert tickets will Sam consume?

Problem 4 (22 Marks)

Gary and Maja are the only people in town who drink cashew milk (c). The other good they both consume is avocado (a). Gary’s utility function is UGary = 3ca, so his marginal utility functions are MUc = 3a and MUa = 3c. Maja’s utility function is UMaja = 3c + 24√ a, so her marginal utility functions are MUc = 3 and MUa = √ 12 a . They each have $200 to spend.

(a) On separate graphs, plot Maja and Gary’s demand curves for cashew milk, assuming the price of avocados is constant at $2.

(b) Find the equation for the aggregate demand curve for cashew milk and plot it, keeping the price of avocados constant at $2.