question #104 Fred currently has $800 to spend on Goods X and Y. The price of good X is $20/unit, and the price of good Y is $12 per Fred's preferences over good X and Y are represented by the utility function U(x, y) = x²y³ a. What is Fred's best bundle? b. If Fred can only buy good Y in blocks of 15 units, what is his best bundle?
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- Donald derives utility from only two goods, carrots (X) and donuts (Y). His utility function is as follows: U(X,Y) =X0.1 Y0.9 . Donald has an income (M) of $900 and the price of carrots (PX) and donuts (PY) are $45 and $90 respectively. How will the bundle change when the price of carrot increased by $25 and the price of donut and income remain constant? Select one: A. Donald will now consume 3 units of carrot and 2 units of donuts B. Donald will now consume 2 units of carrot and 6 units of donuts C. Donald will now consume 2 units of carrot and 3 units of donuts D. Donald will now consume 1 unit of carrot and 1 unit of donuts E. Donald will now consume 2 units of carrot and 2 units of donutsMary's indifference map and budget constraint for goods X and Y are shown below. If Mary spends all her money on X and Y, which bundle will she choose to maximize her utility? Good Y с A E B A D B U3 U₂ U₁ E Good XSuppose that Mr. Umais spends his entire income on good X and Y. The marginal utility of each commodity is recorded in the table below. If the price of X is Rs. 100 and price of Y is 500 and mr. Umais has an income of Rs. 1000 per month. How many units of each good should he purchase? Units of X and Y MU x MU y 1 20 50 2 18 45 3 16 40 4 13 35 5 10 30 6 6 25 7 4 20 8 2 15 a. (X, Y) = (5, 0) b. (X, Y) = (5, 5) c. (X, Y) = (0, 5) d. cannot be determined
- 21. A consumer has a utility function defined over two goods X and Y. Let the quantity of Good X be x ≥ 0 and the quantity of Good Y be y ≥ 0. The utility function is given below: u(x, y) = xy + 2y. Assume that the consumer has income m and that prices are på and py. (a) Explain whether the preferences underlying this utility function satisfy completeness and transitivity. (b) Explain whether the preferences underlying this utility function satisfy monotonicity and convexity. (c) Find the consumer's Marshallian demands for Good X and Good Y at prices px > 0 and Py > 0. (d) Show that goods X and Y are normal goods and explain whether either good is a substitute for the other. (e) Assume that px 10, Py = 5 and m = 100. Suppose that px increases to px = 15, how much of the change in demand for Good X is via the substitution effect and how much is via the income effect? Note: You may assume an interior solution (i.e. x > 0 and y> 0). =7. MRS and utility maximization Suppose your classmate Felix loves to eat dessert-so much so that he allocates his entire weekly budget to apple crisp and pie. The price of one bowl of apple crisp is $1.75, and the price of a piece of coconut crème pie is $7.00. At his current level of consumption, Felix's marginal rate of substitution (MRS) of apple crisp for pie is 5. In other words, Felix is willing to sacrifice five bowls of apple crisp for one piece of pie per week. Does Felix's current consumption bundle maximize his utility? That is, does it make him as well off as possible? If not, how should he change it to maximize his utility? Felix could increase his utility by buying more apple crisp and less pie per week. Felix could increase his utility by buying less apple crisp and more pie per week. Felix's current bundle maximizes his utility, and he should keep it unchanged.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=8
- Solve these consumer choice problems: a. Suppose a consumer has a utility function u(x, y) = xy + 7y facing prices p,=S1 and p,=$2 and income I = $10. Draw a diagram and find the consumer's optimal consumption of goods x and y. b. Suppose that you are in a situation where you can afford purchasing 3 units of good x and 4 units of good y. You discover that another affordable bundle of 5 units of good x and 2 units of good y causes you to reach the same level of utility. Assume that your utility function and budget line are both well behaved. Are you maximizing your utility by consuming your original bundle? Why or why not? Propose an alternative, affordable bundle that would yield a higher utility level than either of the original bundles.4. Tim wants to maximise his utility given his utility function of U (A, B) = A² B¹. He faces the following prices and income: PA = 25; PB = 20; M = 250. However, a change in the price of good A to PA 22 will change his optimal bundle. If he is only interested in being able to consume his original bundle of goods, how much income would he need after the price change? = (a) Tim would require £54 less income (b) Tim would require £18.33 more income (c) Tim would require £10 less income (d) Tim would require £16.66 more income (e) Tim would require £16.66 less income5. Jonas purchases only two goods, starfruit (S) and kiwi (K). He has an income of $60 and can buy starfruit at $2 per pound and kiwi at $3 per pound. His utility function is U(S,K)=3S+4K. That is, his (constant) marginal utility for starfruit is 3 and his marginal utility for kiwi is 4. What bundle of starfruit and kiwi should he purchase to maximize his utility? Why?
- 1. In a simple but delicious world, Joey eats only sandwiches, s, and jam, j. He has a Cobb-Douglas utility function U(j, s) = Nj1-asª, where 0 0. The price of jam is pj, the price of sandwiches is Ps, and Joey has a monthly budget Y to spend on lunch. a. Explain why you can safely use a simpler Cobb-Douglas utility function, V(j, s), to represent Joey's preferences, which is the same as U(j, s) except for replacing N with 1. b. Transform V(j,s) by taking natural logs and bringing down exponents. Explain why it is useful to do this for a Cobb-Douglas utility function, but not for a quasi-linear utility function. Use In(V(j, s)) and the substitution method to derive the formulas for Joey's optimal amount of jam, j*, and sandwiches, s*, to buy and consume per month. Simplify your answers so that you arrive at the С. (1-a)Y aY formulas j* = and s* Ps d. What fraction of his income does Joey spend on jam, and what fraction on sandwiches?II. Your preferences are represented by the utility function U(x₁, x₂) = (x² − x²)0.5 for x₁ > 0, x₂ > 0, and x² > x². 1. Find your marginal utility function for each good.Question 3 (Demand). Carlos really likes pizza. His utility function for Little Caesar's (xi) and Woodstock's (x.) is given by: U(xi, x2) = x;+2x2 The price of x,is $10 and Carlos spends $50 on pizza. a) Graph the demand curve for x1, with pi (the price of x) on the y-axis and x, on the x-axis. (Hint: There will be a range of prices where the demand for x, will be 0). Explain you graph. Page 2