Consider the classic consumer's choice problem of an individual who is allocating Y dollars of wealth amongst two goods. Let c1 denote the amount of good 1 that the individual would like to consume at a price of P1 per unit and (:2 denote the amount of good 2 that the individual would like to consume at a price of P2 per unit. The individual's utility is dened over the consumption of these two goods (only). Suppose we allow the individual's happiness to be measured by a utility function U(C1,Cg) which is increasing and strictly concave in both goods while also satisfying the Inada condition, llmclmo W = limcl_,0 #252) = 00. The Inada conditions simply say that the s10pe of the utility function becomes vertical in the direction of the good that has its consumption level go to zero. By assuming increasing and strictly concave utility in both directions, we are assuming that the shape of the utility function is such that, holding constant the amount of one good, as the individual consumes more of the other good, they are happier but each additional unit of consumption yields less extra happiness than the previous unit (diminishing marginal utility of consumption). These assumptions imply that the rst-order partial derivative of the utility function with reSpect to good one, u1(cl,c2) = W, and good two, u2(cl, (:2) = W, exist and are positive. Moreover, holding (:2 constant, if cl increases, u1(cl, Cg) remains positive but gets smaller. Similarly, holding Ci constant, if c2 increases, Uz(61,02) remains positive but gets smaller. 1. Let the budget constraint faced by the individual be Plcl + P202 = Y. In words, interpret the meaning of the mathematical budget constraint. 2. The individual's problem is to choose the consumption bundle (01,02) optimally. Specically, max {11,(01, 02)} (31,02 subject to (01,02) satisfying the budget constraint, P101 + P202 = Y. Using the Method of Lagrange, let A be the Lagrange multiplier on the budget constraint. The the Lagrangean function can be written as (Cl, 62, A) = 15(01, 02) 'l' A (Y P101 P202) . Take the rst orderderivative of the Lagrangean function with respect to cl, 02 and A. Set each of them equal to zero in order provide the equations that can be used to identify the Lagrangean function's \"critical points\". 3. Take the rst-order conditions for c1 and 62 as a system of two equations. Use one of these equations to nd an expression for A. Then use that expression to eliminate A from the other equation. This will give you a trade-off between purchasing more cl at the expense of (:2 or vice versa. 4. In words, interpret the economic trade-off between good one and good two that you obtained in the previous step