Suppose we observe an individual making the following choices at three different prices: Do these choices satisfy the SARP? Choose one: yes no Prices Choices px = (5,1) X = (6,6) p = (6,6) Y = (2,8) p² = (2,7) Z = (7,2)

Greg has the following utility function: u=2057 20.43. He has an income of $96.00, and he faces these prices: (P1, P2) (9.00, 9.00). Suppose that the price of an increases by $1.00. Calculate the equivalent variation for this price change. =

For the following utility function find the MRS at (x, y) = (2, 3) a) U(x, y) =2x +y b) U(x, y) =x^3 y^2 c) U(x, y) =min(x, 2y)  Solve subparts (c )correctly

For each of the following utility functions get the marginal utility of consumption of each of the goods. 1/2 1/2 (a) u(a,b) = a b (b) u(x, y) = x³/4y1/4 (c) u(a, b) = n(a) + In(x) (d) u(x, y) = ln(x) + ln(y) (e) u(a, b) = 2xa +Xb

Consider the following utility functions. G(x,y) = -1/[ min (6x,2y)+1] H(x,y) = min (6x,6y)² L(x,y) = min (6x,2y) - 10000000000 3 U(x,y) = min (3x, y)³ W(x,y) = min (6x, y)³ + 2 Z(x,y) = min (x,2y) Which of the above functions, if any, is homogeneous of degree 3? Select one or more: a. None. b. Z c. L d. G e. U f. W g. H

Violet buys pies (x) and champagne (y) with her income of $400 and her utility function over pies (x) and champagne (y) (assumed to be divisible goods, where any real number unit pie or champagne is feasible) is Cobb-Douglas and given by u(x, y) = xy. The price of champagne is pY = $10 per bottle. (a) Pies cost pX = $10 per pie if she buys between zero and 20 pies; if she buys more than 20 pies, each additional pie is half-price, i.e., pX = $5. Draw her budget set, carefully labelling all relevant points. calculate the quantities of pies and champagne she will consume when she maximizes her preferences. (b) (HARDER! We haven’t covered this scenario in class) Pies cost pX = $10 per pie if she buys between zero and 20 pies; if she buys more than 20 pies, each pie purchased is half-price, i.e., pX = $5. The discount applies to all units purchased, not the additional ones! Draw her budget set, carefully labelling all relevant points. Calculate the quantities of pies and champagne she will…

You have $3,000 to spend on entertainment this year (lucky you!). The price of a day trip (T) is $40 and the price of a pizza and a movie (M) is $20. Suppose that your utility function is U(TM) T1/3M2/3. a. What combination of T and M will you choose? b. Suppose that the price of day trips rises to $50. How will this change your decision?

Your own a chocolate producing company which can advertise on both television (T) and internet(I). The effect of TV and online commercials on sales is again given byS(T,I) = 500 + 48T−6T2+ 112I−6I2+ 4TI. You have a budget of $25 that you can spend on T and I. The price of aTV commercial is $12per unit and the price of an online commercial is also $12 per unit. 1. Determine the optimal level of TV commercials T and online commercials  I if you have to spend all of your budget. You should provide two methods to solve this, by direct substitution and by setting up the Lagrangian. Is the Lagrange multiplier positive or negative? Give an intuitive interpretation of why this is the case? 2. Now determine the optimal level of TV commercials T and online commercials I if you DO NOT have to spend all of your budget. Do you obtain the same answer as subquestion 5.1? What is the Lagrange multiplier equal to in this case? Discuss.

not use ai please

Steve's utility function is U = q, +4 q,, where q, = veggie burgers per week and q, = packs of cigarettes per week. The price of a veggie burger is p,-$1.00. If Steve's optimal choice is (q,, 92) = (3,5), then the price of cigarrets is $