1. An individual has a utility function, U(q,42) = V91 42). (Mathematical assistance: x = x2). (a) Derive the individual's demand curve for q, and q, Hint: solve for the utility maximising values of q, and q2 for any set of prices (p, and p2) and income (!). (b) Suppose p, = £10 and p2 = £25 and total income is £100. Calculate the optimal consumption choices and the maximised utility value. (c) Compute the value for the Lagrange multiplier for the individual's budget constraint and explain its meaning.

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Chapter10: Consumer Choice Theory
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1.
An individual has a utility function, U(q,42) = /91 92).
%3D
(Mathematical assistance: Vx = x2
(a)
Derive the individual's demand curve for q, and q2
Hint: solve for the utility maximising values of q, and q2 for any set of
prices (p, and p,) and income (I).
Suppose p, = £10 and p, = £25 and total income is £100. Calculate the
optimal consumption choices and the maximised utility value.
(b)
(c)
Compute the value for the Lagrange multiplier for the individual's
budget constraintand explain its meaning.
Transcribed Image Text:1. An individual has a utility function, U(q,42) = /91 92). %3D (Mathematical assistance: Vx = x2 (a) Derive the individual's demand curve for q, and q2 Hint: solve for the utility maximising values of q, and q2 for any set of prices (p, and p,) and income (I). Suppose p, = £10 and p, = £25 and total income is £100. Calculate the optimal consumption choices and the maximised utility value. (b) (c) Compute the value for the Lagrange multiplier for the individual's budget constraintand explain its meaning.
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