sam's utility over x and y is given by the U= 10x.y. The marginal utility of each good is given by : MUx=5y and MUy=5x. a) Draw sam's indifference curve representing a utility level of 100. b) is sam's preferences well behaved? why or why not?
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sam's utility over x and y is given by the U= 10x.y. The
a) Draw sam's indifference curve representing a utility level of 100.
b) is sam's preferences well behaved? why or why not?
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- Biwei’s utility function U=4XY, where X is consumption of beer and Y is consumption of pizza. For this utility function, the marginal utility of X is MUx = 4Y; the marginal utility of Y is MUY = 4X. 1) Suppose Y = 3. Calculate Biwei’s utility for X = 2, 3, 10, and 11. For a given level of Y, does good X display diminishing marginal utility? 2) Suppose X = 3. Calculate Biwei’s utility for Y = 2, 3, 10, and 11. For a given level of X, does good Y display diminishing marginal utility?The price of goods A and B are 20 and 10 respectively. given that the marginal utility of commodity A is 10. what is the marginal utility of B if the consumer is at equilibrium.Suppose there are two goods, x and y. If one good has a negative price, and the other good has a positive price, then the slope of the budget constraint will be positive. is this true or false?
- I. You only consume two goods and your preferences are represented by utility function U(x₁, x₂) = (x0.5 + x2.5)² for x₁ > 2 and x₂ > 0. 1. Find your marginal utility for each good. Simplify your answers. Based on your answers, are your preferences strictly monotonic? Why or why not? 2. Do your preferences obey the law of diminishing marginal utility for each good? Why or why not? If not, what is the behavior of your marginal utility for each good? Use calculus and words to answer this question.compute the marginal utility of good X (MUX) and the marginal utility of good Y (MUY).a. U=U ( X ,Y )=3 X1 /2+5Y1/ 2Pete consumes goods 1 and 2. Pete thinks that 3 units of good 1 is always a perfect substitute for 4 units of good 2. Which of the following utility functions is the only one that would not represent Pete's preferences? A B D E U (x₁,x₂) = 40x₁+30x - 10000 2 U(x₁,x₂) = 4x₁+3x₂+ 1000 2 U (x₁,x₂) = min {4x₁, 3x₂} U(x,x)=16x² +24xx₂+9x² More than one of the above does not represent Pete's preferences.
- Donald derives utility from only two goods, carrots (X) and donuts (Y). His utility function is as follows: U(X, Y) = XY. Donald has an income (M) of $120 and the price of carrots (PX) and donuts (PY) are both $1. a) Find the marginal utility that Donald receives from carrots (MUX) and from donuts(MUY) b) Determine the marginal rate of substitution of X for Y (MRSXY)c) How does MRSXY change as the firm uses more X, holding utility constant.d) What is Donald's budget line and relative price (PX/ PY )e) What quantities of carrots and donuts will maximize Donald's utility?Utility is given by the function U(x,y) = x0(y + 4)0.3. a. Calculate the marginal utility of x in terms of x and y. Simplify. b. Calculate the marginal utility of y in terms of x and y. Simplify. c. Calculate the marginal rate of substitution in terms of x and y. Simplify.Tom consumes only beer (B) and whisky (W). His utility function is U(B,W) = 2B + 5W, where B is the quantity of beer and W is the quantity of whisky. The price of beer is PB = 2, the price of whisky is PW = 5, and Tom’s income is M = 20 dollars. (a) Obtain the equation of Tom’s indifference curve for the utility U > 0 with beer in the horizontal axis and whisky in the vertical axis. What is the magnitude of the slope of Tom’s indifference curves? Explain the economic meaning of this magnitude. Are Tom’s indifference curves vertically parallel? Explain. (b) Obtain the equation of Tom’s budget line. What is the magnitude of the slope of the budget line? What is the economic interpretation of this magnitude? Does Tom consume beer at the current prices (indicated above)? Explain in detail. (c) Are Tom’s preferences quasi-linear? Are they homothetic? Justify each of your answers. (d) Tom’s brother, Jerry, has a utility function given by
- Tom consumes only beer (B) and whisky (W). His utility function is U(B,W) = 2B + 5W, where B is the quantity of beer and W is the quantity of whisky. The price of beer is PB = 2, the price of whisky is PW = 5, and Tom’s income is M = 20 dollars. (a) Obtain the equation of Tom’s indifference curve for the utility U > 0 with beer in the horizontal axis and whisky in the vertical axis. What is the magnitude of the slope of Tom’s indifference curves? Explain the economic meaning of this magnitude. Are Tom’s indifference curves vertically parallel? Explain. (b) Obtain the equation of Tom’s budget line. What is the magnitude of the slope of the budget line? What is the economic interpretation of this magnitude? Does Tom consume beer at the current prices (indicated above)? Explain in detail. (c) Are Tom’s preferences quasi-linear? Are they homothetic? Justify each of your answers. (d) Tom’s brother, Jerry, has a utility function given by V (B, W ) = max{B, W }. (d.1) Are Jerry’s…U(x, y) = xayb A consumer maximises utility subject to a budget constraint M = Pxx+Pyy Where px is the price of good x, py is the price of good y and M is the budget available. a. Derive an expression for the marginal utility of x. Under what condition is the marginal utility diminishing. b. Derive an expression for the marginal utility of y. Under what condition is the marginal utility diminishing.Question 2: Kevin's utility function is given by U=3x+2y. a. Find Kevin's demand functions for X and Y b. Show graphically Kevin's optimal point when m=120, Px=2, Py=1. Explain in words why he chooses this point. c. Draw the Engle curve for x.