Suppose u(x) = max{arı, ßr₂} for parameters a, ß > 0. (a) Will this consumer will spend all their money (i.e. choose z" so that px = m)? Why or why not? (b) Show that either i - of the two goods. 0 or r2 = 0 that is, the consumer buys only one (c) Solve the consumer's problem. What is ? [Hint 1: The first question, and the previous part of this question, might be helpful here. Hint 2: The price ratio might be relevant to the consumer's behavior.] בין

Please help me to solve the questions below.

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QUESTION 1 x0.80Qy(1-0.80); and the budget 153 = 11Qx + 12Qy find the CHANGE in optimal consumption of X if the price of X increases by a factor of 1.9. as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 1.2, 1.14 = 1.1). Qx For the utility function U = Please enter your response

Happy Goluki likes tea (good 1) and cookies (good 2). Her preferences are represented by the utility function U(q₁,92) = (q₁)⁰.5+(q₂)0.5, where q₁ is the number of cups of tea and q2 is the number of cookies. Goluki is given I = $180, which she is allowed to spend as she wishes on tea and cookies. a) Calculate Goluki's optimal bundle if the price of tea is p₁=$1 and the price of cookies is p2=$2. Call this bundle A and show it on a graph (put tea on the horizontal axis). b) Suppose that the price of tea increases to $5 (I know, I can't believe it either, but Melbourne does have some very fancy tea places) and the price of cookies stays the same. Calculate Goluki's new optimal bundle of tea and cookies (call it bundle B). Show it on a graph from part a). c) If at new prices (pnew-$5 and p2=$2) Goluki has just enough income to achieve the same utility as in part (a), what bundle will she buy? Calculate this new bundle D and show it on the graph from part a). Calculate the income required…

PROBLEM (4) You have the Cobb-Douglas utility function u(x, y) = xy over apples (x) and plums (y) and you have $120 budget to spend and can carry at most 480 ounces in weight in your backpack going back to the dorm. Each apple costs $1 and weighs 8 ounces, and each plum costs $3 and weighs 4 ounces. You can only leave the store with a bundle of fruits you can afford and carry. (a) Drawing the relevant lines, intercepts, marking the points and hence identifying the feasible set of bundles, calculate the optimal bundle. (b) Forget about (a). If you were to choose a backpack before going on this shopping trip, for the weight constraint not to be an issue for you, how many ounces of weight capacity would you need for your backpack? HINT: That is, for this weight capacity of the backpack, you'd be able to carry the best bundle you can afford, i.e, the weight constraint is not binding for your decision. (c) Forget about (b). In (a), just before going out for shopping with your backpack to…

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.

There are two shows on Netflix that Jeff can watch, Show 1 and Show 2. x₁ measures the number of episodes watched of Show 1 and x₂ measures the number of episodes watched of Show 2. Jeff's preferences can be represented by u(x₁, x₂) = x² + ax². Jeff has 11 hours available for watching Netflix today. Each episode of Show 1 lasts 30 minutes, while each episode of Show 2 lasts one hour. For all question parts, round to three decimal places if necessary. For parts (a) - (f), let a = 1. Draw Jeff's indifference curves for the utility levels u = 4, 9, 16. Draw a straight line between the bundles (x₁, x₂) = (4, 0) and (x₁, x2) = (0, 4). Now, use your picture to determine whether the following two statements are true or false. Answer "1" for true. Answer "0" for false. a) Statement 1: Jeff's preferences are strongly monotone. 1 b) Statement 2: Jeff's preferences are strictly convex. 0 c) Find the bundle at which one of Jeff's indifference curves is tangent to the budget line. (x₁, x^2) = ( d)…

Ding Ding is a cat philosopher. He spends his time on two activities. Sleep and thinking. Both activities produce pleasure to Ding Ding. How effective Ding Ding is in each activity varies day by day. But on a given day, if he spend “s” effective hours in sleeping and “t” effective hours in thinking, his utility is u(s,t)=s^2+t. you can assume that time is continuous in answering the following question.   (A) Let us first ignore that there are only 24 hours each day. Label “s” on the x-axis and “t” on the y-axis in a diagram. Draw two indifference curves u(s,t)=s^2+t=24^2=576, and u(s,t)= s^2+t=12^2=144. On each indifference curve, you have to mark at least the coordinates of four points to illustrate the shape of it.   (B) Describe in words how these two indifference curves in (a) relate to each other.

Given the utility function U (x1, x2) = x³x2.7 select all that are true. a) 30% of the budget is spent on good 1. ○b) V (p, I) = 30.370.7 I 10 P1P2 c) If P2 = 2 and I = 60, then $18 is spent on good 21. d) If P1 = 9, P2 = 2, and I = 60 then the consumer enjoys 1.81 utils of utility. e) Half the budget is spent on good 1 and the other half is spent on 2.