nations to Tea Party candidates D His 5. Charles Koch has utility Ucharles- 10/

Question

nations to Tea Party candidates D His 5. Charles Koch has utility Ucharles- 10/ + 15D over private jets J and do brother David has utility UDavid - 2J + 3D. Which of these is true? a. Charles will consume more jets and make more donations than David. b. At any bundle, Charles' MRS is exactly the same as David's. c. Given the same income, Charles and David will tend to make identical consumption choices. d. Both (b) and (c). e. If Charles' income is 5 times David's then they will tend to choose the same bundle.

Explanation / Answer

Statement d. Both (b) and (c) are true

The explanation for this answer is as follows:-

Utility function for Charles is UCharles = 10 J +15 D

Marginal Utility of Jets (J) for Charles (MUJ) = 10

Marginal Utility of Donations to Tea Party Candidates (D) for Charles (MUD) = 15

Thus, Marginal Rate of Substitution between J and D i.e. MRSJD = MUJ/ MUD = 10/15 =2/3

Utility function for David is UCharles = 2 J +3 D

Marginal Utility of Jets (J) for David (MUJ) = 2

Marginal Utility of Donations to Tea Party Candidates (D) for David (MUD) = 3

Thus, Marginal Rate of Substitution between J and D for David i.e. MRSJD = MUJ/ MUD = 2/3

Hence, Marginal Rate of Substitution (MRS) for Charles and David is the same at any bundle.

Thus, statement b. in the question is true

Now, assume that income levels of both Charles and David are the same at $ 200. Also, assume that price of Jet is $ 10 whereas Donation to Tea Party Candidate is assumed to be priced at $5.

Hence, the budget line for both Charles and David is 10 J + 5D =200

For both Charles and David, when, J =0, D =40. Similarly, when D=0. J=20

Utility for Charles when J =0 and D =40 is 600

Utility for David when J =0 and D = 40 is 1200

Similarly, Utility for Charles when D =0 and J =20 is 200

Utility for David when D =0 and J= 20 is 400

Thus, Utility for both Charles and David when J =0 and D =40 is higher compared to the Utility when D =0 and J= 20

Hence, when income levels for Charles and David are the same, they both will tend to choose the same optimal consumption bundle.

Thus, Statement c. in the question is true

Hence, as both statements at b. and c. are true, the correct answer is d. Both (b) and (c)

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