Question

1. Your uncle Eugenius generously gives you an allowance of $300 each semester to spend on ski lift tickets and meals out with friends. Every time you go out to eat you spend pM = $20 per meal. Ski lift tickets cost pS = $60 each. The quantities of meals out and ski days you consume are denoted qM and qS, respectively.

(a) Write down the equation for your budget constraint. Calculate the intercepts and slope (or, equivalently, the Marginal Rate of Transformation) of your budget line and graph the budget line. Label the budget line “B1” in your graph. Indicate on the graph where all the bundles of goods that you can afford are located (your opportunity set). (Note that ski lift tickets are on the x-axis and meals out are on the y-axis.) (4 points)

Answer 1

Total spending (I) = $300

pM = $20 per meal

pS= $60 per ticket.

qM and qS are the quantities of meals and ski lift tickets respectively.

Budget constraint :

pM qM + pS qS = I

(20)(qM) + (60) qS = 300

When the person spends all his spending on qS , then qM= 0 and qS = 300/60 = 5.

When the person spends all his spending on qM , then qS = 0 and qM = 300/20 = 15.

Slope of the budget constraint =Price of good on x-axis/ prce of good on y-axis= pS/ pM = 60/20 = 3

Now, from this we can plot the budget constraint: