Utility maximization under constraint Lucas gets utility (satisfaction) from two goods, A and B, according to the utility function U(C, D) = 25[C-3+4D-³]-4+25. While Lucas would like to consume as much as possible he is limited by his income. Maximize Lucas' utility subject to the budget constraint using the Lagrangean method.

Do not understand please help me figure this out

I am not sure how to start solving the M'. Need some guidance on this so I can also plot in a graph. TY

Utility maximization under constraint, substitution and income effect, CV and EV Josh gets utility (satisfaction) from two goods, A and B, according to the utility function U(A, B) = 4[A-4 + B-4-4 + 40. While Josh would like to consume as much as possible he is limited by his income. a. Maximize Josh's utility subject to the budget constraint using the Lagrangean method b. Suppose PA increases. Show graphically the income, substitution effect and total effect and explain c. Suppose PA increases. Show the graphs for CV and EV and explain. One graph for CV and one graph for EV

Ronald is an Economics students who likes to spend his leisure time of sixty hours a month doingone of two activities: watching movies at Dendy Cinemas Newtown (x), and indoor-climbing(y). A trip to the movies takes 3 hours, and each visit to the climbing gym lasts 5 hours.Further, suppose that Ronald has a fixed monthly monetary budget to spend on leisure activities. He currently exhausts this entire budget by watching two movies and visiting the climbinggym fifteen times. With this monthly budget, he would also have been able to afford exactlyseven movies and six visits to the climbing gym.Assume that both goods are perfectly divisible.(b) Show, using algebra, that Ronald’s two budget lines intersect at the bundle (x, y) =(5.5, 8.7).

Two individuals, Blair and Anton, derive utility from leisure and from the other goods (OG) they consume. Observing their leisure and OG choices when wage increases, we conclude that Blair has backward-bending labour supply and Anton has upward slopping labour supply. Therefore, Select all that applies a) Leisure is a normal good for Anton but an inferior good for Blair. b) Anton has only an income effect, while Blair has only a substitution effect. O C) Anton's income effect is larger than Blair's income effect, but Anton's substitution effect is smaller than Blair's substitution effect. O d) Anton's substitution effect is larger than his income effect, but Blair's income effect is larger than her substitution effect. O e) Anton's income and substitution effects are negative while Blair's income and substitution effects are positive.

Focus on parts e-h

- Assume an individual has quasilinear preferences of the form U(x1,x2) = 3x1¹2 + 2x2. If the price of Good 1 is $1 and the price of Good 2 is $2, how many additional units will the individual consume of Good 2 if her income increases by $1, assuming we're at an interior optimum? A. B. C. D. The individual's consumption of Good 2 will increase by 1/2 unit. The individual's consumption of Good 2 will increase by 1 unit. The individual's consumption of Good 2 will decrease. The individual's consumption of Good 2 will not change.

8. Fabian consumes X and Y and the following utility function represents his utility: U = 2XY a. With a utility function of U = 2XY, Fabian's MU, = 2Y and his MU, = 2x ,where MU is marginal utility. Write an equation for Fabian's marginal rate of substitution (MRS). b. Suppose Fabian's income is $120 and Px = S6 and Py-$2, where Px is the price of X and Py is the price of Y. Write an equation for Fabian's budget constraint. c. Write the equation that equates the slope of Fabian's budget constraint to the slope of Fabian's indifference curve: d. If Fabian is spending all of his income, how much X and how much Y will he choose? Use the equations you wrote in part's b and c to answer this question. e. What will Fabian's utility be with this combination of X and Y? f. Now suppose the price of X increases to P.=10. Write the equation that equates the slope of Fabian's budget constraint to the slope of Fabian's indifference curve. How will this change the optimal combination of X and Y? What…

12 There are two goods and John's preferences can be represented by u: R²0 R given by u(x) = x₁³x2³. His income and price of the two goods are given by (M, P1, 20 P2) = (12, 1, 2). Which 2 of the following 8 options are false: In John's optimal bundle, he consumes the same amount of good 1 as good 2. If we change John's utility function to u(x) = x + then John's optimal bundle remains unchanged. At John's optimal bundle, the slope of the budget constraint equals the slope of the indifference curve. In John's optimal bundle, he spends the same amount on good 1 as good 2. John's preferences satisfy local non-satiation. At John's optimal bundle, his bang per buck of good 1 equals his bang per buck of good If we change John's utility function to u(x) = In (17 +x₁x₂) then John's optimal bundle remains unchanged. If we change the budget set to (M, P1, P2) = (24, 2, 4) then John's optimal bundle remains unchanged.