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1. A student has a budget of $200 for their meals outside of the home per week. One possibility is purchasing a meal at a restaurant, which we will call x1, and which costs $20, and a second possibility is purchasing a meal at the school cafeteria, x2, which costs $10.
a) Draw a graph depicting the budget set for this choice. Label the axes, the two intercepts of the budget line, and the slope of the budget line.
b) The student’s utility is represented by the equation:
U(x1,x2)=5x1x2
How many meals of each type will she eat?
Give expressions for the marginal utility of x1 and x2 for each of the following utility functions.
a) U(x1,x2)=x1^5x2^5
b) U(x1,x2)=ln(x1)+5x2
c) U(x1,x2)=2x1x^32