1. If the utility function is U(x1, x2)U(x1,x2) given the budget constraint p1x1 + p2x2 < = M. 2. For the following utility function U(x1,x2)U(x1,x2), when p1 = 10, p2 = 5, and M = 200, determine the equilibrium quantity demanded for both goods.
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- 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.A consumer consumes two agricultural products: Red Meat, and Tomatoes according to the following utility function: U = RT That is, the total utility is the multiplication of the quantity consumed of the two products. Given that consumer's income is 210, price of R is 10, and the price of Tis 2, a)Write down the budget constraint (budget line equation) for this consumer. b)Determine the quantities that the consumer should consume of each of the two products c)Calculate the value of the lagrangian multiplier and derive the demand function for Red Meat and for tomatoes.The question is in the attached image. Thank you!
- 23. Tom's utility function is U (x; y) = 3x+4y: His budget constraint is ax + by = 1, a,b,I > 0 a) Derive the demand function of x. b) Derive the demand function of y. c) Please draw the demand curve for y. d) If the price of x increases from a to c; what would the value of the Hickis substitution effect of x be?3 8. Let be the utility function U(x, y) =(xi + 2ya), , where x and y are the quantities consumed of two goods. (a) Show that the functional equation U(x,y) U(2, 2) defines y as a function of x in a neighborhood of point (2, 2). (b) If the quantity consumed of good x increases by 1 unit, by how much does the quantity have to increase or decrease? Consumed of the good and to keep utility constant? (c) If the quantity consumed of good x increases by 1%, by how much does the quantity have to increase or decrease? Consumed of the good and to keep utility constant?
- Suppose the weighted marginal utility for two goods x and y at a position of consumer equilibrium 70. If the price of good x is r10 and the relevant marginal utility for y is 140 what is the price of good y and the relevant marginal utility for xa)Assume that the typical consumer always spends a small share of her overall budget on Vietnamese meals and use the utility maximization conditions to find the demand for Vietnamese food of the typical consumer (keep in mind that since utility is quasi-linear, you can find demand without information about the consumer’s weekly budget). b) Sum across consumers to find the weekly market demand for Vietnamese meals in NYC.Consider a consumer whose utility function is (screenshot) Assume the consumer has income $120 and initially faces the prices px=$1 and py=$1. How much x and y would they buy? Draw the budget constraint and the demands.
- Question is in attached image, Thank you!Let a1 and x2 denote the quantities consumed. The consumer's preferences are represented by the utility function: U (r1, 22) = V+ VT2. Suppose the consumer has income m =100 and that the prices for the two goods are pi -2 and p2=8. Calculate the optimal quantity demanded for good 1.Pete 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.
