Every week I spend a total of £400 buying two goods, luxuries (L) and necessities (N). I obtain utility (U) from these goods according to the rule U(L, N) = 10 + L + 20N−2N2. Suppose that I pay £10 for each unit of L and £20 for each unit of N and that I am a utility-maximiser. MUL=1 and MUN=20-4N. Define the Marginal Rate of Substitution (MRS) as MRS ≡ MUL/MUN). Calculate its value at the bundle (L = 0 and N = 4) and at (L = 1 and N = 4). By referring to a graphic illustration of the above calculations or otherwise, argue that an increase in my budget will have no effect on my consumption of N if I am already consuming 2.5 units of N. Calculate my optimum choice of L and N if instead I have £40 to spend. Fully explain your answer.
Every week I spend a total of £400 buying two goods, luxuries (L) and necessities (N). I obtain utility (U) from these goods according to the rule U(L, N) = 10 + L + 20N−2N2. Suppose that I pay £10 for each unit of L and £20 for each unit of N and that I am a utility-maximiser. MUL=1 and MUN=20-4N. Define the Marginal Rate of Substitution (MRS) as MRS ≡ MUL/MUN). Calculate its value at the bundle (L = 0 and N = 4) and at (L = 1 and N = 4). By referring to a graphic illustration of the above calculations or otherwise, argue that an increase in my budget will have no effect on my consumption of N if I am already consuming 2.5 units of N. Calculate my optimum choice of L and N if instead I have £40 to spend. Fully explain your answer.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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- Every week I spend a total of £400 buying two goods, luxuries (L) and necessities (N). I obtain utility (U) from these goods according to the rule U(L, N) = 10 + L + 20N−2N2. Suppose that I pay £10 for each unit of L and £20 for each unit of N and that I am a utility-maximiser. MUL=1 and MUN=20-4N.
- Define the Marginal Rate of Substitution (MRS) as MRS ≡ MUL/MUN). Calculate its value at the bundle (L = 0 and N = 4) and at (L = 1 and N = 4).
- By referring to a graphic illustration of the above calculations or otherwise, argue that an increase in my budget will have no effect on my consumption of N if I am already consuming 2.5 units of N.
- Calculate my optimum choice of L and N if instead I have £40 to spend. Fully explain your answer.
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