Lea's utility function is U = x y0.4 where x denotes her consumption of good X, y denotes her consumption of good Y. The price of good X charged by the sellers of good X is Px = 6, the price of good Y is Py = 6 and Lea's income is M = 411. How many units of good X will Lea buy to maximize her utility?
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- Suppose your utility for goods x1 and x2 is represented by the following utility function: U(x1,x2)= x11/5 x24/5 a) What is your marginal rate of substitution, MRS12? b) If the price for good x1 is p1 = 2, the price for good x2 is p2 = 4, and your available income is m = 20, write down your budget constraint. c) Using the prices and income given at b) above, find your optimal consumption choice bundle (Marshallian demand) and its corresponding utility level. d) Illustrate your optimal consumption choice on a graph. e) For the prices given in b), what income would you need to achieve a utility level of 25? PLEASE ONLY ANSWER PART C, D AND ESally consumes two goods, X and Y. Her utility function is given by the expression U = 2XY3. The current market price for X is $20, while the market price for Y is $10. Sally's current income is $500. a. Write the equation for Sally's budget constraint. What is the slope of her budget line? b. Determine the X,Y combination which maximizes Sally's utility, given her budget constraint.Joyce drinks both coffee (x) and tea (y). Her preferences over these two goods can be represented by the utility function U(x,y) =x + 3y^1/2 where x represents the number of pounds of coffee and y represents the number of cups of tea. a) Given her preferences, find her demand functions for coffee (x) and tea (y). b) Suppose that the price of a pound of coffee is $4 and that she has $56 to spend on coffee and tea. Write her demand curve for tea. Illustrate her demand curve. c) Suppose that the price of a cup of tea is $1 (the price of coffee and income remain $4 and $56, resp.). Use your demand functions to find her best bundle. In an indifference curve diagram illustrate her best bundle at these prices. For the remainder of the question, assume that her income rises to $60 and that the prices of coffee and tea are unchanged at = $4 and =1.
- Rick consumes 2 goods, Chicken McNuggets (M) with Szechuan sauce (S). His utility function is U(M, S) = M2/3 S1/3 and his income is m. The price of Chicken McNuggets is p, and the price of Szechuan sauce is 1. Suppose m=100 and p=2. How much of each good does Rick consume? On the same graph from part (e), show Rick’s budget constraint and indifference curve passing through his new chosen consumption bundle.Dan's utility function is U(x,y) =9.5 x2.4y4.9. Dan's income is 129.1 dollars, the price of good X is 4.8 and the price of good Y is 6.3, What is the slope of Dan's income expansion path, dy/dx, on a graph where good X appears on the horizontal axis and good Y appears on the vertical axis. Remember not to enter ratios below, such as 3/4, 2/9 etc. Instead enter the number in decimal form.An individual consumes two goods, X and Y, and receives utility according to a Cobb-Douglas production function of the form: U(X,Y)= X1/3Y2/3. Give that MUX= 13(MUYMUX)2/3 and MUY= 23(MUXMUY)1/3 find the consumers optimal demand functions for X and Y in terms of PX, PY, and I. Explain why I could have solved the problem above using the utility function U(X,Y)= XY2 and would have obtained the same answer. What is it about utility that makes this possible? Economists define the ‘certainty equivalent’ of a risky stream of income as the amount of guaranteed money an individual would accept instead of taking a risk. The certainty equivalent varies between individuals based on their risk preference.
- Suppose we are able to model the total utility function for the consumption of two goods, good x and good z. The utility function is structured as U(x, z) = 3x2 + z2 - 2xz. The consumer is faced with the prices of goods x and z. The price for each unit of good x and z is $1 each. The consumer has an income $1 (in thousands). How many units of each good should the consumer consume so as to maximize his/her utility?A consumer has an income of $400 and is deciding between two products: X and Y. Assume that the X product is the horizontal axis product. The price of X is $10 and the price of Y is $2. Assume the consumer currently wants to consume 50 units of product Y to maximize his utility. a) Write out the equation to this consumers budget line. What is the slope to this budget constraint? b) How much of X and Y will the consumer consume to maximize his utility subject to his budget constraint. C) Now assume the price of X changes to $5 and price of Y and Income stays the same. At the new price, the consumer wants to buy 60 units of product X to maximize her utility given her budget. How much X and Y will the consumer consume to maximize utility. g in the before and after the change of the budget constraint and indifference graph on the same graph space. Show all necessary points. Label clearly. ead oubstitutiofs. Draw d) Write out the expression of the utiiity maximizing ruie here.?Julie, who has $64, consumes only two goods: whistles (w), which cost $6 each and xylophones (x), which cost $7 each. Her preferences over these two goods can be represented by the utility function u(w, x) = 3w0.75 0.25 a) What is the optimal number of whistles for Julie to consume given this scenario? b) What is the level of utility Julie attains at this level of consumption? c) Suppose now that the price of whistles rises from $6 to $7. What is the magnitude of this price effect on whistles?
- Rick consumes 2 goods, Chicken McNuggets (M) with Szechuan sauce (S). His utility function is U(M, S) = M2/3S1/3 and his income is m. The price of Chicken McNuggets is p, and the price of Szechuan sauce is 1. d. Use the equation from part (c) and the budget constraint from part (a) to find Rick’s demand for each of the two goods. e. Suppose m=100 and p=1. How much of each good does Rick consume? Draw a graph showing Rick’s budget constraint and indifference curve passing through his chosen consumption bundle. f. Suppose m=100 and p=2. How much of each good does Rick consume? On the same graph from part (e), show Rick’s budget constraint and indifference curve passing through his new chosen consumption bundle.Suppose that, by law, a person is required to consume a fixed amount of good X, say X0. Assuming X is a normal good, explain how this law reduces utility for both high and low income people.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?