Rita has the following quasilinear utility function: U(q1,92) = q,0.5 + q2. Suppose that the price of good 1 is 3 and that the price of good 2 is 34. If Rita's optimal bundle includes a positive amount of both goods, then her income has to be bigger than
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- A consumer’s preferences over pizza (x) and steak (y) are given by u(x,y) = x^2y (HINT: MUx = 2xy and MUy = x2) and his income is I = $120 and py = $1. (a) Calculate his optimal bundle when pX = $8 (call this bundle A) and separately when pX = $1 (call this point C). (b) Finding the decomposition bundle B, calculate the income and substitution effects on the amount of pizza of a decrease in the price of pizza from pX = $8 down to pX = $1. (c) Forget about the decomposition bundle and the two effects. In (a), the price of pizza decreases, hence the agent ends up better off. Let’s quantify how much “better off” the agent becomes after this price drop, in dollars. For this, instead of the price drop, suppose the agent is given some money $m and he optimize utility with this additional gift included to his budget. What should m be, so that his optimal utility with his expanded budget is exactly equal to his utility at the bundle C (the bundle he chooses optimally when pizza price drops to…A consumer has $600 to spend on good x and y. Her preferences can be represented by the utility function U(x,y)= y+100 In x If the price of one unit of good x is Ș10 and the price of one unit of good y is $5, what is the consumer optimal bundle?Lan's utility function is U (x,y) =6.9 x².9y7.4. If the price of good X is 8.3 and Lan's optimal bundle has x*-9 units of good X and y*=1.1 units of good Y, what is the price of good Y?
- Assume an individual’s preference for Fanta (Good x) and Fritters (Good y) are given by the following utility function: U(x,y)=20= x^0.5y^0.5 REQUIRED: i) Derive the equation for the indifference curve for this utility functionFor the following utility function, for good 1, derive and draw the Engel curve, x1(m) and the demand curve, x1(p1): U(x1, x2)=x11/3 x22/3 .Consider the following utility function: U= 100x0.50,0.50 A consumer faces prices of P, = $2 and P, =$1. Assuming that graphically good X is on the horizontal axis and good Y is on the vertical axis, suppose the consumer chooses to consume 6 units of good X and 11 units of good Y. Then the marginal rate of substitution is equal to: MRS = 1.83. (Enter your response rounded to two decimal places. Do not forget to include the negative sign.) Use absolute values. The consumer should consume to maximize utility. more Y and less X the same amount of X and Y more X and less Y O étv MacBook Air 80 esc F1 F2 F3 F4 F5 F6 F7 F8 # $ % & 1 2 7 Q W E T Y tab S D F G caps lock C V M ft control option command つ つ エ B N
- A consumer’s utility only depends on the consumption of goods A and B according to the following Cobb-Douglass utility function: U(A, B) = A1/4 B 3/4. The price of goods A and B are $20 and $40, respectively. The consumer has a budget of $1200 that he can use to consume the two goods. a. Write down the budget constraint and plot it. b. Calculate the optimal bundle and maximized utility for the consumer. c. A new tax of $10 is imposed on the price of good B. Compute the new optimal bundle of good A and B for the same consumer. What is the utility loss due to the tax? d. Show that the consumer would prefer a lump sum income tax that raises the same revenue as the tax on good B. 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.Suppose the utility function of U(x1, x2) = x11/2x21/2 and the budget constraint of p1x1+p2x2=m. Let’s assume that p1=$1.5, p2=$2, and m=$60. Find the optimal bundle. Also, specify the optimal bundle.Donald derives utility from only two goods, carrots (X) and donuts (Y). His utility 0.1 0.9 function is as follows: U(X,Y) =X Y Donald has an income (M) of $900 and the price of carrots (P,) and donuts (P,) are $45 and $90 respectively Based on this information, what does the slope of the indifference curve for Donald tell us. Select one: A. For each additional quantity of carrot consumed, Donald must give up 0.25 of donuts to maintain the same level of satisfaction B. For each additional quantity of donuts consumed, Donald must give up 1/2 of carrots to maintain the same level of satisfaction C. For each additional quantity of carrot consumed, Donald must give up 1/2 of donuts to maintain the same level of satisfaction D. For each additional quantity of carrot consumed, Donald must give up 1/9 of donuts to maintain the same level of satisfaction E. For each additional quantity of donuts constumed. Donald must give up 1/2 of carrots to maintain the same level of satisfaction. F. For…
- Kim spends all her weekly income of R200 on two goods, X and Y. The prices of the two goods are R5 per unit for X and R2 per unit for Y. She has a utility function expressed as: U(X, Y) = 5XY Express the budget equation mathematically. Determine the utility-maximising bundle of X and Y. Calculate the total utility that will be generated per unit of time for this individual.A consumer’s preferences over pizza (x) and steak (y) are given by u(x,y) = x2y (HINT: MUx = 2xy and MUy = x2) and his income is I = $120 and py = $1. (a) Calculate his optimal bundle when pX = $8 (call this bundle A) and separately when pX = $1 (call this point C). (b) Finding the decomposition bundle B, calculate the income and substitution effects on the amount of pizza of a decrease in the price of pizza from pX = $8 down to pX = $1. (c) Forget about the decomposition bundle and the two effects. In (a), the price of pizza decreases, hence the agent ends up better off. Let’s quantify how much “better off” the agent becomes after this price drop, in dollars. For this, instead of the price drop, suppose the agent is given some money $m and he optimize utility with this additional gift included to his budget. What should m be, so that his optimal utility with his expanded budget is exactly equal to his utility at the bundle C (the bundle he chooses optimally when pizza price drops to…Consider a consumer with preferences over two goods X (represented on the horizontal axis) and Y (repre- sented on the vertical axis). Assume that the consumer's indifference curves are strictly convex to the origin. The consumer's income equals $20, px = $2, and py = $4. At the bundle (x = 4, y = 3), the absolute value of the consumer's MRS (the marginal rate of substitution of good Y for good X) equals 1. Select the correct answer from the options below. O To maximize utility the consumer should buy less of good X and more of good Y. To maximize utility the consumer should buy more of good X and less of good Y. O The bundle x=4 and y=3 maximizes the consumer's utility.