2. Let your utility function be U (X, Y) = VX + VY. M This will give a demand function for X, X (Px, PY, M): Px2 +Px PY a. What is the demand function for Y? b. If Px = $1, M= $100,000, and Py starts at $1 then increases, what is the substitution effect and income effect?
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- I need help with my homework assignment that i dont undertsand. Suppose a consumer has a utility function given by U(X,Y) = MIN(X, 2Y). The consumer has $90 to spend (M = $90). The Price of good Y is PY = $1. Using a graph, sketch the consumer’s demand curve for Good X. Make sure to identify three points on the demand curve. Make sure your graph is neat, accurate, and scaled properly.Explain why it is that as the consumer purchases more of a good, her marginal utility falls while her total utility rises.Explain through the optimal choice of a person how their individual demand function arises. Use an example.
- Consider the following utility function belonging to “Consumer A”. UA(x,y,z,v) = x0.1y0.2z0.3v0.4. Suppose that prices of x, y, z and v are 1$, 2$, 3$ and 4$. The consumer’s income is 10$. a. Find the values of x, y,z and v that maximize the consumer’s utility subject to his/her budget constraint. b. Suppose that “Consumer B” has a utility function which is a logarithmic transformation of the consumer A’s utility function, i.e. UB =ln UA. Suppose that prices and income are the same. Would the amounts of x, y, z and v consumed by “Consumer B” be the same as the amounts consumed by “Consumer A”?Ann consumes two goods, a and y. Her utility function is given by: u(x, y) = (x+1)G. The price of a is $4 per unit and the price of y is $ per unit. Ann's income is w. (a) * ) Nrite down an expression for Ann's budget line. (b) v- 'Determine the formula for Ann's marginal utility of a, and the formula for Ann's marginal utility of y. (c) ( » For each income level w > 0 calculate Ann's optimal consumption bundle. (d) For which income levels w is bang-for-buck equalization violated at Ann's optimal consumption bundle? Explain. , Assume that w = 2. Draw Ann's budget line in a figure with r on the hor- izontal axis. Add 2 indifference curves of Ann, including the indifference curve that contains Ann's optimal consumption bundle. Indicate Ann's optimal consumption (e) - bundle.Consumer satisfaction from consuming goods X and Y is as follows:U=10X+14Y-X2-Y2 and consumer income 3X+Y=12Look for:1. The marginal utility function for goods X and Y?2. What are the values of X and Y for maximum utility?3. Prove with the results of X and Y obtained whether optimal customer satisfaction is achieved?
- Pat divides a $900 monthly income between the consumption of food (X) and all else (Y). Pat’s preferences can be described by the following utility function: U = XY. a) If the price of food is $1, and of all else is $2, how much of each good will Pat choose? b) If now the price of food rises to $2, how much of each good will Pat choose? c) Explain this change in terms of income and substitution effects. d) How much would Pat be willing to pay to avoid this price increase?Mariah consumes music downloads (M) and concert tickets (C). Her utility function is giveh by U = 0.5M? + 2C². a. Using calculus, what is the marginal utility of music downloads? b. Using calculus, what is the marginal utility of concert tickets? Write the equation for the MRSMC (i.e., the MRS of C for M; M is increasing, C is С. decreasing). d. Would the bundles of (M = 4 and C = 1) and (M = 2 and C = 2) be on the same %3D %3D %3D %3D indifference curve? How would you know? e. Calculate the MRSMC when M = 4 and C =1 and when M = 2 and C = 2. Explain why the %3D %3D values of MRSMC differ across these two bundles. f. Based on your answers above, are Mariah's indifference curves convex? Explain using the values calculated. er thisTrue/False Marginal utility keeps falling with the each additional consumption of a good or service.
- Question 3: Robert's utility is given by U(x,x)=ln x + ln y, and therefore MUX-1/x and MUX-1/y. Let the prices and income be Px. Py and m. a. Find Robert's demand for x and y b. How is Robert's demand for x affected by an increase in Py? Explain1. Let Amy derive utility each from housing, h, and a consumer good, z, with the following utility function: 1/ U=h¾/3₂¾3 M Her Mashallian demand equations are the following: h= and z=- 3ph 2M 3p₂ Amy lives in a city where everyone works downtown. While her income is $160 per month, her commute cost (bus pass) costs her $40 per month, so she only has $120 to spend on h and z. (we assume no time cost of the commute) The consumer good, z, has a price of $1 and the price of her housing, h, is $2 per unit. a. What is her quantity demanded of h and z and what level of utility is she currently enjoying? She is considering moving to a location further from work to a house where her commuting cost would be $60 per month (so she will have $100 to spend on z and h). The market adjusts ph and housing sizes across the city so that utility is the same at every location around the city. b. What is the equation for the appropriate demand function for housing in this city? C. What the price of housing…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.
