A consumer chooses non-negative quantities of two goods, denoted by x and z, in order to...

  

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A consumer chooses non-negative quantities of two goods, denoted by x and z, in order to maximise the utility function : R2 → R+, defined by u(x,z) := ln(x + 1) + z. Assume that the price of one unit of good z is equal to 1 (so z can be viewed as left- over money). Denote the unit-price of good x by p, and the consumer's income by m. Assume also that m > 0. (In(t) denotes the natural logarithm of a real number t, which is defined for all t > 0. Recall that In is strictly increasing and concave, that In (1) = 0, and that dIn(t) dt }.) 1 x+1 Mu,=- Mu, 1 MRS(x, 2) = 1 x+1 Evaluate the marginal rate of substitution of u at points where x = 0 or z = 0. (The answer for z=0 is: ) For z=0, x=-1, MRS=-e- How to do the evaluation at x = 0 and z = 0 step by step? A consumer chooses non-negative quantities of two goods, denoted by x and z, in order to maximise the utility function : R2 → R+, defined by u(x,z) := ln(x + 1) + z. Assume that the price of one unit of good z is equal to 1 (so z can be viewed as left- over money). Denote the unit-price of good x by p, and the consumer's income by m. Assume also that m > 0. (In(t) denotes the natural logarithm of a real number t, which is defined for all t > 0. Recall that In is strictly increasing and concave, that In (1) = 0, and that dIn(t) dt }.) 1 x+1 Mu,=- Mu, 1 MRS(x, 2) = 1 x+1 Evaluate the marginal rate of substitution of u at points where x = 0 or z = 0. (The answer for z=0 is: ) For z=0, x=-1, MRS=-e- How to do the evaluation at x = 0 and z = 0 step by step?