Question

4. Blythe currently spends all of her income on B = bottles of beer and R=Red Wing games. Beer costs $15 per bottle, and the price of hockey games is $14 per game. Assume that Blythe is not allowed to drink her beer at the Red Wing games. Blythe's marginal utility for beer is 300, and her marginal utility for Red Wing games is 294. (Assume all goods are perfectly divisible.). Determine whether Blythe is at her optimal consumption. If Blythe can make herself better off, how should she rearrange her spending between beer and Red Wing games? Carefully explain how you arrived at your answer.

Answer 1

Given

Marginal utility for beer=MUB=300

Marginal utility for Red Wing Games=MUG=294

Price of beer=Pb=$15 per bottle

Price of Red Wing games=Pg=$14 per game

Marginal Utility for beer per dollar spent=MUB/Pb=300/15=20 utils per dollar

Marginal Utility for Red Wing game per dollar spent=MUG/Pg=294/12=21 utils per dollar

Condition for utility maximization requires that Marginal utility per dollar spent should be same for both goods. We find that Marginal utility for beer per dollar spent is less than Marginal utility for Red Wing game per dollar spent. So, we can say that Blythe is not at optimal consumption combination.

Since marginal utility for beer per dollar spent is lower, Blythe should reduce consumption of beer and increase the number of Red Wing games as long as marginal utility per dollar spend is same for both cases

So, we can say that Blythe should allocate the lower fraction of spending on beer and higher fraction of spending on Red Wing games.