Anna has an income of 1000 euros and utility function U(x,y)=x²y³. The prices of the two goods are P₁=5 and Py-20. Define the budget constraint and represent it graphically.
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- Kate’s utility function includes coffee (c) and sugar (s). She only consumes coffee and sugar together, and she only consumes in the ratio of one unit (cup) of coffee with two units (spoons) of sugar. Her utility function is What is her marginal utility of sugar if she has 4 cups of coffee and 6 spoons of sugar? Remember that unit are infinitely divisible (you can have parts of units). (a) 0 (b) 1 (c) ½ (d) 2Utility maximization with a budget constraint. A hypothetical consumer spends all tgheir income on ramen noodles (N) and wild rice (W). N is the quantity of noodles; W is the quantity of wild rice. Their income is $1,600 per month. the price of noodles is $2 per package and the price of wild rice is $20 per pound. The utility function is U=sqrt(N*W). the MRS = -N/W. The budget constraint is: 1,600 = 2*N + 20*W Graph Qty of noodles (N) on vertical axis and Qty of wild rice (W) on horizontal axis. SOLVE: a. Graph the budget constraint. label all points. What is the slope of the budget constraint? b. Find the optimal quantities of noodles(# of packages) and the wild rice (# of pounds) given the budget constraint. graph these optimal quantities. draw your indifference curve on the same graph. c. Show on your graph what happens when the price of wild rice increases to $40 per pound. Find your new optimal quantities of noodles and wild rice. label all points on graph. label the…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.
- If the utility function of an individual takes the form: U = U ( x 1, x2) = (x1 + 2) 2 (x2 + 3) 3 Where U is total utility, and x1 and x2 are the quantities of two commoditiies consumed: (a) Find the marginal-utility function of each of the two commodities (b) Find the value of the marginal utility of the first commodity when 3 units of each commodity are consumed.Questions 1. Will's utility from vacations (91) and meals (92) is given by the function U(V, M) = 91 x 92. Last year, the price of vacations was $200 and the price of meals was $50. This year, the price of meals rose to $75, while the price of vacations remained the same. Both years, Will had an income of $1500. (a) What is the compensating variation for the price change in meals? (b) What is the equivalent variation for the price change in meals?QUESTION 1 For the utility function U = Qx0.73Qy(1-0.73) find the trade-off rate between good X and good Y at Qx= 3 and Qy=12 Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 1.2, 1.14 = 1.1).
- Q1: (I)Asma eats only apples and almonds. Her level of income is $36, Price of apple (Pa) is $2 per kg and price of almond (Pl) is $6 per kg. The preferences of Asma are represented by the following utility function Utility U= 10*Qa + 40*Ql where Qa and Ql are Asam’s consumption of Apples and almonds. (a) which kind of preferences Asma has? (b) Find Utility per dollar spent on apple and almond (c) Find Marginal rate of substitution and interpret it (d) Find utility maximizing values of apples and almond and show graphically(Review Question) Sarah consumes both wine ) and cheese (y) and considers them perfect substitutes. She always gets twice as much utility from consuming wine as she does cheese. What equation would represent her utility function? U-(2xy) U=x+2y U=2x+y U=min(x,2y)(3) Graph the demand curves associated with the utility function u(x, y) = x0-.25 ,0.75 and budget constraint p1x + P2y = 100. 1
- Alice receives an allowance of 500 dollars that she spends on buying snacks (S) and tea (T). The price of each snack is 10 dollars and the price of each tea is 5 dollars. Her utility is given by: U (S, T) = 2S³/4 +T3/4 (a) Find her marginal rate of substitution (MRS) between S and T. (b) Write Alice's budget constraint. (c) Find Alice's optimal consumption and the optimal A. (d) What is her new consumption if the price of tea becomes 10 dollars? Note: numeric solutions for questions (c) and (d) are not integers.Consider the following utility function. U=U(X,Y)=X0.2Y0.8 Find the marginal utilities. Determine their signs. Provide the economic interpretation of the signs of these marginal utilities. Determine whether the law of diminishing marginal utility holds for both goods.Define Economic utility