John Kelso, a magazine reporter from New York, is visiting Savannah, GA. Each Monday, John visits to the Savannah Cafe and spends $6 on Danishes and muffins. At the cafe, the price of a Danish is $1.20. The price of a muffin depends on the number of muffin a customer buys. For each muffin, customers have to pay a number of dimes equal to the number of muffins that buy. If they buy one muffin, they pay one dime. If they buy two muffins, they pay two dimes per muffin. If they buy three muffins, they pay three dimes per muffin, and so forth. John has no preference for Danishes or muffins and his preferences are represented by the utility function U(b, m) = d + m where d is the number of Danishes and m the number of muffins he buys.
1. Find the equation of John's budget constraint.
2. Suppose you measure muffins along the horizontal axis. Along John's budget constraint, is it true that the slope of the budget constraint is Pm/PD? Discuss.
3. Write John's Lagrangian function.
4. Write the first order conditions for John's Lagrangian function.
5. Solving the first order conditions from part d) find how many muffins and Danishes John purchases.