Derive and interpret the mathematical equation
Managerial Economics
Question 1. The price of a GD (PC ) is $10 and the price of a DVD (PD) is $20. Philip has his income (M) of $100 to spend on the two goods. Consider three consumption bundles: (G, D) = (£, 3); (4, 3); (6, 3), where G is the amount of GDs and D is the amount of DVDs.
(a) Derive and interpret the mathematical equation of his budget line.
(b) Graph the budget line on a two-dimensional plane (with D on the vertical axis and G on the horixontal axis).
(c) Represent the three bundles on the graph in (a).
(d) Suppose he wants to spend his entire income on GDs and DVDs to obtain utility. Examine if i) if there is any bundle that he cannot afford and ii) if there is any bundle that cannot fully satisfy his consumption desire.
Question 2. Continue considering the budget line obtain in question 1.
(a) Suppose that Philip‘s income rises to $200.
1. Derive and interpret the mathematical equation of his budget line.
2. Graph the budget line on a two-dimensional plane (with D on the vertical axis and G on the horixontal axis).
3. Compare the new budget line with the old one. How does the income increase change his budget line?
(b) Suppose that the price of a DVD falls to $10.
1. Derive and interpret the mathematical equation of his budget line.
2. Graph the budget line on a two-dimensional plane (with D on the vertical axis and G on the horixontal axis).
3. Compare the new budget line with the old one. How does the price increase change his budget line?
Question 3. Julia receives utility from days spent traveling on vacation dometically (D) and days spent traveling on vacation in a foreign country (F), as given by the utility function
U = √(DF)
In addition, the price of a day spent traveling domestically (PD) is $100, the price of a day spent traveling in a foreign country (PT ) is $400, and Julia‘s annual income (M) allocated for travel is 84,000. Suppose she spends her entire budget and there are four consumption bundles for her: bundle A is (D, F) = (12, 7); bundle B is (D, F) = (20, 5); bundle G is (D, F) = (24, 6); and bundle D is (D, F) = (28, 3)
(a) Derive and interpret the mathematical equation of her budget line.
(b) Graph the budget line on a two-dimensional plane (with F on the vertical axis and D on the horixontal axis).
(c) Indicate bundle A, B, G and D on the graph in part b, and examine if all the bundles are on her budget constraint.
(d) Galculate the level of utility that she obtains from each possible bundle, and determine the optimal bundle that maximixes her utility.
(e) If her budget line is tangent to an indifference curve at the optimal bundle, obtain the marginal rate of substitution of F for D (MRSDF ) at the optimal bundle.
