A consumer’s utility function is u(x1, x2) = 5×1 + 2×2, where xi is the quantity of good i = 1,2. Her income is $100. The supplier of good 1 cannot provide good 1 at a constant price. Precisely, if the consumer consumes x1 units of good 1, each unit costs p1(x1) = 5ln(x1) dollars. The price of good 2 is $4 (a unit). What is her optimal consumption bundle?
Please show all steps of how this is solved and take if taking Langrangean use first order conditions and set to zero (not gradients please).
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