Dennis is only interested in two things, eating food and playing the online mult

Question

Dennis is only interested in two things, eating food and playing the online multiplayer game Globe of Gratuitous Violence (GoGV) – a close competitor to world of warcraft. Dennis’s utility is given by the function U(qf,qg) = 0.25ln(qf) + 0.75ln(qg) where qf is the quantity of food and qg is the hours of GoGV play. The price of a meal of food is $10, the hourly fee for GoGV is $2.50, and Dennis’s income is $1,000/month.


a.) Write the general expression for Dennis’s marginal utility with respect to food and GoGV play.

b.) What is the Marginal Rate of Substitution (MRS) between food and GoGV play? (e.g. the rate at which Dennis willing to exchange a meal for another hour of GoGV play, qF/qG?)

c.) Assume Dennis has a budget of $1,000/month. Draw Dennis’s monthly budget line, with food on the vertical (y axis) and GoGV on the horizontal axis.

Now consider the GoGV promotion that gives reduces the hourly price to $2.00/hr for more than 100 hours of play per month for players that achieve the status of Gore Wizard level V or higher. Dennis is well above this status level and qualifies for the promotion. In other words, his price is $2.50/hr for quantities less than 100 hours and $2.00/hr for quantities greater than 100 hours. Draw his new budget line.

Explanation / Answer

a.) Write the general expression for Dennis’s marginal utility with respect to food and GoGV play. b.) What is the Marginal Rate of Substitution (MRS) between food and GoGV play? (e.g. the rate at which Dennis willing to exchange a meal for another hour of GoGV play, ?qF/?qG?) c.) Assume Dennis has a budget of $1,000/month. Draw Dennis’s monthly budget line, with food on the vertical (y axis) and GoGV on the horizontal axis. Now consider the GoGV promotion that gives reduces the hourly price to $2.00/hr for more than 100 hours of play per month for players that achieve the status of Gore Wizard level V or higher. Dennis is well above this status level and qualifies for the promotion. In other words, his price is $2.50/hr for quantities less than 100 hours and $2.00/hr for quantities greater than 100 hours. Draw his new budget line.

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