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Q1: Suppose Labor and Capital are substitutes and the price of capital falls. All else equal, we should expect the labor select (
Q2: An individual has a utility function over Leisure and Income such that ?=?1/2?1/2 This individual has a budget constraint ?=?⋅(24−?)+?
The best possible wage this individual can earn in the labor market is $2 per hour. This individual is $30 in debt (they have negative non-labor income).
If this individual is earning a utility level of 4, which of the following are true?
Group of answer choices
The worker could be supplying 1 unit of Labor
The worker could be earning $10
The worker could be supplying 8 units of labor
The worker is maximizing their utility given their budget
The worker's Marginal Rate of Substitution at the point where the budget constraint intersects the indifference curve is equal to -2
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- Q.7 A consumer's utility function is given by the expression: U = (0.6Xx5 + 0.4Y5). • Determine the marginal utility functions for each commodity. Does marginal utility decrease when consumption increases? Assuming that the price of good X is Rs 15 and the price of Y is Rs 6, write the equation of the budget line and plot it when income is Rs 450. What is its slope? What does it indicate? Calculate the marginal rate of substitution of Y for X and interpret its economic meaning. Write the equation showing consumer's equilibrium condition. Obtain the equilibrium values of X and Y. Find the expressions for change in MUx due to increase in Y and change in MUy due to increase in X.A consumer’s utility function is given by the expression: ( )2 0.5 0.5 U = 0.6X + 0.4Y . • Determine the marginal utility functions for each commodity. Does marginal utility decrease when consumption increases?• Assuming that the price of good X is Rs 15 and the price of Y is Rs 6, write the equation of the budget line and plot it when income is Rs 450. What is its slope? What does it indicate?• Calculate the marginal rate of substitution of Y for X and interpret its economic meaning. Write the equation showing consumer’s equilibrium condition. • Obtain the equilibrium values of X and Y. • Find the expressions for change in MUX due to increase in Y and change in MUY due to increase in XUtility function U(X,Y)=(x^(3/4))(Y^(1/4)) 1)Suppose Px=2, Py=1, and Income is 100. What are the new levels of demand for X and Y? 2) Digrammatically show the income and substitution effect from 3 to 2 on the consumption of x. You must explicitly specify the optimal consumption bundles for the different sets of prices (appropriatly graph and label actual quantities) but you may qualitatively specify anything else deemed relevant. 3)Which effect (substitution or income) will move you along a given indifference curve? And for this question, do you move to the left or right along the given indifference curve and does this increase of decrese MRS. Also, explicitly specify what the MRS is equal to before and after you move along the indiferrence curve.
- Given a consumer has a money budget M = 90 and utility function ? ( ? , ?) = ? 1/4? 1 / 2 If she consumes two goods x and y with prices given by ? = 2 and ? = 4 state the ? ? budget constraint equation. Determine the utility maximizing quantities X and Y for the consumer3. Consider the following utility function, u (21, x2) = min V#1, Varz), where a > 0 Derive the Marshallian demand functions. (Explain your derivation in details.) Does the Marshallian demand increase with price? Are the two consumption goods normal goods? Show two different ways to derive the Hicksian demand functions. (b) Does the Hicksian demand increase with price?Q.7 A consumer's utility function is given by the expression: & = (0.6.x"s + 9.47"s}. Determine the marginal utility functions for each commodity. Does marginal utility decrease when consumption increases? Assuming that the price of good X is Rs 15 and the price of Y is Rs 6, write the equation of the budget line and plot it when income is Rs 450. What is its slope? What does it indicate? Calculate the marginal rate of substitution of Y for X. and interpret its economic meaning. Write the equation showing consumer's equilibrium condition. Obtain the equilibrium values of X and Y. Find the expressions for change in MUx due to increase in Y and change in MUy due to increase in X.
- Q11. Consider a utility function: U (F,C) = FC so MU_F = C and MU_C = F. Suppose as Case A, Total income is $120 and per unit prices of Food (F) and Cloth (C) are $2 and $10, respectively. a. What is the value of MRS at the optimal point and what does this value mean? b. What is the optimal consumption bundle i.e (F*,C*)? c. Plot the budget line and clearly depict the point of optimality in the F (x-axis)-C (y-axis) space.answer please, additional information has been given. Assume you can work as many hours you wish at £12 per hour (net of tax). If you do not work, you have no income. You have no ability to borrow or lend, so your consumption, c, is simply equal to your income. d) Now assume that you receive an income of £140 per week from an unknown benefactor. Show the impact on your feasible set, and show a new optimal choice in which consumption increases but labour supply de Using the concept of the marginal rate of substitution, explain why this is a likely outcome. e) Now assume that, starting from the optimal point in d), your wage increases to £18 per hour. Explain why the impact of this change is ambiguous, and relate to the long-run historical experience of wage growth in rich countries.Answer the following questions using the following information. Columns 1 and 2 in the table below show the marginal utility that Cody gets by purchasing products A and B. Column 3 shows the marginal utility Cody gets from saving Assume that the price of A is $13 the price of B is $10, and Cody has an income of $129. a) Find the following series of MU/$ for each column. Note: Keep as much precision as possible during your calculations. Your final answer should be accurate to at least two decimal places Column 1 Column 2 Column 3 Units of A MU MU/S Units of B MU MU/$ Number of $ saved MU MU/S 68 6.8 1 80 6.15 1. 13 0. 2 71 5.46 2 63 6.3 2 10 0. 3 66 5.08 3 56 5.6 3 7 4 61 4.69 4. 46 46 0. 54 4.15 40 4 45 3.46 31 3.1 6. 1 39 3 22 2.2 0. 29 2.23 8 17 1.7 8 b) What quantities of A and B will Cody purchase in maximizing his utility? Quantity of A: 0 Quantity of B: 0 c) How many dollars will Cody save? Dollars Saved = $0 SAVE AND CLOSE
- 1. Consider the utility function given by u (x1, x2) = x1x3, and budget constraint given by P1x1 + P2x2 = w. (a) Solve the EMP to find the Hicksian demand function, h (p, u). (b) Find the expenditure function e (p, u). (c) Recover h (p, u) from e (p, u). (d) Noting that the indirect utility function corresponding to the UMP for this form is 4w3 v (P1, P2, w): 27p1p3' demonstrate that v (.) and e (.) are inverses of each other. (e) Using only the indirect utility function above, recover the optimal consumption bundle of the UMP (i.e., Walrasian demand function). (f) Using your answer to (e), identify the substitution effect on the quantity demanded of good 1 of a change in the price of good 1. 1; and consider the Hicksian demand curve for good 1 corresponding to , and Walrasian demand curve for good 1 corresponding to w = 1. At what price and quantity for good 1 do they intersect? Which is steeper at this point of intersection? (g) Assume P2 What does that signify? (h) Using your…= Mary has the following utility function: u(x, y) I = 10 and the prices originally are p = 1 and py 3 ln(x) + 2y. Her income is given by = 2 (e) Find the total, substitution and income effects for good x caused by the price change. Consider this price change a “large” price change (Apx = P₁ - Px = 3− 1 = 2).Q9. Consider a utility function: U (F,C) = FC so MU_F = C and MU_C = F.Suppose as Case X, Total income is $100 and per unit prices of Food (F) and Cloth (C) are $2 and $15, respectively. a. What is the value of MRS at the optimal point and what does this value mean? b. What is the optimal consumption bundle i.e (F*,C*)? c. Plot the budget line and clearly depict the point of optimality in the F (x-axis)-C (y-axis) space. d. Now assume a new Case Y, Pc' = $10, holding all else the same, do the same analysis (parts a-c) and contrast your answers to Case X. For part c, you should draw old (Case X) and new (Case Y) budget lines/point of optimality.