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- Alice is going to Wonderland and needs supplies. She has $100 and can buy only walnuts and raisins. The price of walnuts is $20 per kg and of raisins is $10 per kg. Alice's preferences are described by the utility function u(x1,x2)=min{0.5*x1+2*x2,x1}, where x1 is the quantity of walnuts, and x2 is the quantity of raisins. Given her budget constraint and preferences, if Alice were offered a choice only among the bundles listed below, which one would she buy? Выберите один ответ: a. x1=3, x2=4 b. x1=2, x2=0.5 c. x1=4, x2=3 d. x1=1, x2=8Suppose an individual has the following utility function: U(x,y)=−4(x−5.5)^2 −2(y−3.5)^2 Further assume that the price of good x, px = $6, the price of good y, py = $8 and the individual has an income m = $65 a) Draw an indifference curve (one IC is enough) that represents this person’s prefer- ences. Please label the graph properly including values for x and y. b) Intuitively, and without formally solving, can you guess the maximized values x* and y*for the above utility function. Explain your answer. c) Derive the optimal values x*and y*by formally solving the above utility function subject to the above constraint. You can use any of the utility maximization techniques we learned in class. d) Compare your answers in parts b) and c). Based on the utility function that is given in this problem as well as the budget constraint, can you explain the differences between the answers you found in parts b) and c) (if any). Be as detailed as possible with your explanation.assume that the data in the following table are an indifference curve for a consumer: what is the value of the MRS and the slope (Px/Py) at consumer equilibrium? explain and draw graphs to derive demand curve for x. Choice Unit x Unit y A 10 2 B 6 4 C 4 6 D 2 12
- A convex indifference curve implies what type of behavior? diminishing marginal utility complementary goods perfect substitutes inferior goodsGiven above are some of the indifference curves for a student who consumes Burritos and Pizzas and the relevant budget line. Equilibrium is defined as the maximum utility or satisfaction given the consumer’s budget. The consumer has more indifference curves above I3, below I1, and between I1 and I2 and between I2 and I3. Out of all the indifference curves the consumer has, only I1, I2, and I3 are shown. The given budget line touches I2 at the point where I2 touches the y-axis (Burritos axis). a) If the price of Pizzas decreased and the price of Burritos remained unchanged, would the quantity of Burritos consumed at equilibrium increase or decrease compared to the equilibrium point A in the graph given above? (b) If the price of Pizzas increased and the price of Burritos remained the same, would the consumer equilibrium point be different from point A or the same as point A in the graph given above?A consumer has a budget set aside for entertainment during the year, and they spend the budget on concerts and plays. The consumer has a strong preference for attending concerts over plays: the two activities are substitutes, but not very strong substitutes. Sketch the indifference curves for this consumer on a graph, with concert tickets on the vertical axis and play tickets on the horizontal axis. Briefly explain why the consumer might ultimately choose to purchase a large number of play tickets, even though they have a strong preference for concerts. Include a budget line on your graph to illustrate this case.
- The MRS of food (vertical axis) for shelter (horizontal axis) measures the amount of food that must be received in order to absorb the loss of 1 unit of shelter without losing utility. If that value is 3, if the price of food is 5, and if the shelter price is 10, then the consumer is not maximizing his utility. Sketch a budget line, assuming the consumer has $100 to spend, and draw in a possible indifference curve that illustrates the situation described here. Then, on the same graph, show with a simple sketch what could be done to correct the problem.Another instance when people are likely not to spend a dime (or a minute) on an item is when they have a dislike for mixing the item with other items available. In this case, we say the consumer has ‘non-convex preferences’ and indifference curves are bowed out from the origin. In plain language, the consumer has a preference for binging. We often feel this way towards our favorite social media app. Consider a kid who has four hours a day to spend on social media. They enjoy spending time on Snapchat (x) or spending time on Twitter (y). a) Write the kid’s time constraint and illustrate it in a graph where you measure time spent on Snapchat along the horizontal axis and time spent on Twitter along the vertical axis. This kid’s utility from time spent on Snapchat and time spent on Twitter is U(x,y) = 4x2+ y2. b) In your graph, draw a couple of the kid’s indifference curves. Notice how the kid’s |MRSY,X| increases along each curve as he spends more time on Snapchat and less time on…A consumer currently spends a given budget on two goods, X and Y, in such quantities that the marginal utility of X is 10 and the marginal utility of Y is 8. The unit price of X is $5 and the unit price of Y is $2. The utility-maximizing rule suggests that this consumer should
- 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 functionSuppose the marginal utility of a Coke is 15 utils, and its price is $1.50. The marginal utility of a pizza is 20 utils, and its price is $5. To achieve consumer equilibrium, you need to spendUtility maximization with a budget constraint. A hypothetical consumer spends all tgheir income on ramen noodles (N) and wild rice (W). N is the quantity of noodles; W is the quantity of wild rice. Their income is $1,600 per month. the price of noodles is $2 per package and the price of wild rice is $20 per pound. The utility function is U=sqrt(N*W). the MRS = -N/W. The budget constraint is: 1,600 = 2*N + 20*W Graph Qty of noodles (N) on vertical axis and Qty of wild rice (W) on horizontal axis. SOLVE: a. Graph the budget constraint. label all points. What is the slope of the budget constraint? b. Find the optimal quantities of noodles(# of packages) and the wild rice (# of pounds) given the budget constraint. graph these optimal quantities. draw your indifference curve on the same graph. c. Show on your graph what happens when the price of wild rice increases to $40 per pound. Find your new optimal quantities of noodles and wild rice. label all points on graph. label the…