Suppose that a consumer with an income of $1,000 finds that basket A maximizes utility subject to his budget constraint and realizes a level of utility U1. Why will this basket also minimize the consumer’s expenditures necessary to realize a level of utility U1?
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Suppose that a consumer with an income of $1,000 finds that basket A maximizes utility subject to his budget constraint and realizes a level of utility U1. Why will this basket also minimize the consumer’s expenditures necessary to realize a level of util
Explain why utility maximization subject to the budget constraint implies that the consumer purchases that basket of commodities for which 1. all income is used up. 2. the marginal rate of substitution equals the price ratio. 3. the marginal utilities per dollar of the two goods are equal. If you use a diagram in your answer, make the diagram large and label all curves, axes, and points.
Solve Problem 2
1. A consumer maximizes his utility function, 122, subject to the budget constraint, 75x1 +150x2-525· (M-$75, P2-$150, M-$525). Set up the Lagrangian function and use the first-order and second-order conditions to find the values of x1 and x2 that solve the consumer's problem 2. This problem is an extension of Problem 1. Now, the consumer faces an additional constraint. Specifically, good 1 is rationed, and the consumer can buy no more than three units of that good....
Suppose a person has a utility function U(x1,x2)= xa1+xa2, which
she maximizes subject to her budget constraint, px1 + qx2 = m,
where p, q, m are all positive. Use the Lagrangian method to solve
the maximization problem, and find the demand functions for the
consumer. Show that the demand functions are homogeneous of degree
zero in prices (p, q) and income (m)
(2.5 marks) Suppose a person has a utility function U(x1, x2) = xq +xm, which she maximizes...
1. (24 total points) Suppose a consumer’s utility function is given by U(X,Y) = X1/2*Y1/2. Also, the consumer has $72 to spend, and the price of Good X, PX = $4. Let Good Y be a composite good whose price is PY = $1. So on the Y-axis, we are graphing the amount of money that the consumer has available to spend on all other goods for any given value of X. a) (2 points) How much X and Y...
1. Consumer’s utility function is: U (X,Y) = 10X + Y. Consumer’s income M is 40 euros, the price per unit of good X (i.e. Px ) is 5 euros and the price per unit of good Y (i.e. Py) is 1 euro. a) What is the marginal utility of good X (MUx) for the consumer? ( Answer: MUx = 10) b) What is the marginal utility of good Y (MUy) for the consumer? ( Answer: MUy = 1) c)...