Question 4: Consider a general utility function U(x₁, x2). Let's now solve for the optimal bundle generally using the Lagrangian Method. 1. Write down the objective function and constraint in math. 2. Set up the Lagrangian Equation. 3. Fnd the first derivatives. 4. Find the first order conditions. What's the interpretation for λ? 5. Rearrange them to get the tangency condition.
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- First household m=$2,500 per month, spends $125 dollars per month on electricity. Second household m=$10,000 per month and spends $200 per month on electricity. p1=0.1 and p2=1 x1=consumption of electricity and x2=everything else The preferences over electricity and other goods is described by a Cobb- Douglas utility function. What are the parameters of the utility function for each of the two households?Suppose a consumer is indifferent between the bundles (x1, x2) = (19, 10) and (15, 16), and suppose that the same consumer prefers the bundle (15, 14) to both. What can you say about his/her preferences when evaluated against standard assumptions of consumer preferences?Suppose a consumer is indifferent between the bundles (x1, x2) = (20, 10) and (15, 16), and suppose that the same consumer prefers the bundle (19, 9) to both. Is there anything wrong about her preferences when evaluated against the standard assumptions of consumer preferences?
- Assume that Rossi consumes only bananas and avocado. Fortunately, she likes both goods. The consumption bundle where Rossi consumes x1 units of bananas per week and x2 units of avocado per week is written as (x1, x2). In fact, Rossi’s preferences can be represented by the utility function u (x1,x2 )=4√(x1 )+ x2 . The price for bananas is $1 per unit and the price for avocado is $2 per unit. Rossi has $24 to spend on the two goods. Write down Rossi’s budget constraint and solve for her optimal consumption bundle.Assume that Rossi consumes only bananas and avocado. Fortunately, she likes both goods. The consumption bundle where Rossi consumes x1 units of bananas per week and x2 units of avocado per week is written as (x1, x2). A. In fact, Rossi’s preferences can be represented by the utility function u (x1,x2 )=4√(x1)+ x2 . The price for bananas is $1 per unit and the price for avocado is $2 per unit. Rossi has $24 to spend on the two goods. Write down Rossi’s budget constraint and solve for her optimal consumption bundle. B. Now Rossi has $10 more to spend on the two goods ($34 in total), and what is her optimal consumption bundle now? Compare your solution with the previous one. Can you say anything interesting?1. Consider a consumer who chooses bundles consisting of two commodities, x and y. Suppose that, regardless of the prices px and py (which are always positive), the consumer chooses to consume x and y in a ratio of 2:1. This behavior is consistent with: a. A consumer having Cobb-Douglas utility function. b. The consumer’s utility function exhibiting perfect complements. c. The consumer’s utility function exhibiting perfect substitutes. d. Any of the above could be correct.
- A consumer has the following utility function: U (x, y) = (x + a) (y + b) Prices of the two goods x and y respectively are px and py and the consumer has income m. We assume that all prices and income are strictly positive. Furthermore, throughout this question we assume that m is high enough so that both x and y are strictly positive in equilibrium. (a) Solve the consumer’s optimization problem and express the demand for the two goods in terms of prices and income. Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.A consumer consumes two goods and her utility is form by Cobb-Douglas utility function. Her MRS is 0.9 * (q2/q1) Using these information find Marginal utility levels of first amd second goodsKari requests two goods: X and Y. The utility function is given by: U(XY)=X-Y. Prices of X and Y is Px and Py, and budget is of m dollars. A) Set up the budget constraint and draw the budget line in an x-y diagram. B) Whats the expression for the slope in the budget line? C) Show the condition for optimal fit using Lagranges method D) Show the optimal fit graphically and relate the figure to task C
- Mrs. Griffiths earns $5000 a week and spends her entire income on dresses and handbags, since these are the only two items that provide her utility. Furthermore, Mrs. Griffiths insists that for every dress she buys, she must also buy a handbag. What is the algebraic equation for Mrs. Griffiths budget constraint if dresses cost $25 each and handbags cost $14 each? How many of each good will she buy and represent this on a budget line with handbags on the horizontal axis Assume for this question only that when the price of dresses decreases, less of that good is demanded. Illustrate the income and substitution effect of this price decreasea. Is the “more is better” assumption satisfied for both goods? Explain.b. What type of function is this? Explain.c. Provide expressions for the marginal utilities of x and y and does the marginal utility of x increase, remain constant, or diminish as the consumer buysmore units of x? Explain. Does the marginal utility of y increase, remain constant, or diminish as the consumer buysmore units of y? Explain.d. Provide an expression for the marginal rate of substitution of x for y.e. Is MRSx,y diminishing, constant, or increasing as the consumer substitutes more x for y alongan indifference curve? Explain.f. On a graph with x on the horizontal axis and y on the vertical axis, draw the indifferencecurves for U1 and U2 where U2 has a higher value than U1a. Is the “more is better” assumption satisfied for both goods? Explain.b. What type of function is this? Explain.c. Provide expressions for the marginal utilities of x and y and does the marginal utility of x increase, remain constant, or diminish as the consumer buysmore units of x? Explain. Does the marginal utility of y increase, remain constant, or diminish as the consumer buysmore units of y? Explain.d. Provide an expression for the marginal rate of substitution of x for y.e. Is MRSx,y diminishing, constant, or increasing as the consumer substitutes more x for y alongan indifference curve? Explain.f. On a graph with x on the horizontal axis and y on the vertical axis, draw the indifferencecurves for U1 and U2 where U2 has a higher value than U1 instructions: answer d,e, and f only