3. Zach’s utility preferences are given by U(x1,x2)= 3x1 + 6x2 a) What is Zach’s

Question

3. Zach’s utility preferences are given by U(x1,x2)= 3x1 + 6x2

a) What is Zach’s Marginal Rate of Substitution?

b) If income is $100, and p1 = 2, and p2 =4 determine if Zach has a corner or interior solution for his optimized bundle.

c) If income is $100, and p1 = 3, and p2 =4 determine if Zach has a corner or interior solution for his optimized bundle.

d) If income is $100, and p1 = 2, and p2 =5 determine if Zach has a corner or interior solution for his optimized bundle.

e) Draw a graph for each part of this question (b,c, and d) showing the budget line and where Zach’s optimized preference bundle would lie. Try to determine, if possible, what is the optimal bundle of (x1,x2). f) Find an equation for the indifference curves for Zach’s preferences and sketch a graph of an indifference curve set at a level of your choosing.

Explanation / Answer

a) Zach's Marginal rate of Substitution will be =- (du/dx1)/(du/dx2) = -1/2.

b) Here P1 = 2 and P2 = 4 so, the slope of the budget line, in this case, will be -1/2 and this will coincide with the slope of IC, so the entire budget line will be the solution in this case.

c) Here P1 = 3 and P2 = 4 so, the slope of the budget line, in this case, will be -3/4 which is greater than the slope of the IC. In this case, the consumer will only consume good X1, which is 100/3. [Corner Solution].

d) Here P1 = 2 and P2 = 5 so. the slope of the budget line is -2/5, which smaller than the slope of IC. So, the consumer will only consume good X2, which is 20.

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.