Elasticity Scenario: Suppose in the beer market the price is originally $3 per 6-pack (on Wednesday). When the price rises to $6 (on Friday), the quantity demanded for beer falls from 200 6-packs to 60 6-packs. When the price of beer rises to $6, the quantity demanded of pretzels also changes. Originally, pretzel quantity demanded was 400 bags (on Wednesday), but now the quantity demanded is 350 bags (on Friday). In addition, the beer price change caused the quantity demanded of red wine to rise from 200 bottles (on Wednesday) to 220 bottles (on Friday). On Sunday, several beer drinkers won 400 total dollars on lottery scratch-off tickets, increasing consumer income from 1600 dollars (on Friday) to 2000 dollars (on Sunday). The quantity demanded of beer changed from the 60 6-packs (on Friday) to 65 6-packs (on Sunday) Marginal cost (MC) per six-pack for beer producers is currently $3 or $4. They can’t quite calculate it exactly at this moment in time, but they know it is "somewhere in that range
a. Calculate the arc price elasticity of demand for six packs of beer. Classify the number you find, i.e. is beer elastic, inelastic, or unit elastic?
b. Calculate the arc cross-price elasticity of demand between six packs of beer and bags of pretzels. Classify the number you find, i.e. are these goods complements, substitutes, or not related?
c. Calculate the arc cross-price elasticity of demand between six packs of beer and bottles of red wine. Classify the number you find, i.e. are these goods complements, substitutes, or not related?
d. Calculate the arc income elasticity of demand for beer. Classify the number you find, i.e. is beer inferior, cyclically normal, or non-cyclically normal?
e. Calculate the range of optimal prices for beer producers (per 6-pack). [Assume for this question that we calculated the point elasticity instead of the arc elasticity in part a]