A consumer has 4 units of x and 1 unit of y. The price of x is 3, and the price of y is 6. Suppose the consumer has a utility function: U(x,y)=x (a) Is the consumer a net buyer or a net seller of x? Is the consumer a net buyer or a net seller of y?
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- Bill is the only person on an island, and he has an endowment of 20 units of coconuts (C) and 5 units of water (W). His utility function is: U(C, W) = In(C)+2 ln(W) a) Find the marginal utility of C and W. b) Find the marginal rate of substitution when Bill consumes all of his endowment.Suppose that there are two goods (X and Y ). The price of X is $2 per unit, and the price of Y is $1 per unit. There are two consumers (A and B). The utility functions for the consumers are UA (X, Y): = X0.5y-0.5 UB (X,Y)= X0.8y-0.2 Consumer A has an income of $100, and Consumer B has an income of $300. PAGE 2 (a) Use Lagrangians to solve the constrained utility-maximization problems for Consumer A and Consumer B. (b) Calculate the marginal rate of substitution for each consumer at his or her optimal consumption bundles. (c) Suppose that there is another consumer (let's call her C). You don't know anything about her utility function or her income. All you know is that she consumes both goods. What do you know about C's marginal rate of substitution at her optimal consumption bundle? Why?(A) Suppose an individual who derives utility u(x, y) from consuming a units of the good X and y units of the good Y. Prices of goods X and Y are respectively p = 1 and Py = p. Furthermore, the individual has a budget m. What is the demand for Y if the utility function is: u(x, y) = min{x, ay}. (a) y(p, m) = am (b) y(p, m) = = (c) y(p, m)= (d) y(p, m) = = am a+p m a+p m 1+p (B) Same setup as (A) with u(x, y) = ax + y and ap Pr. The quantity demanded of good X is q. Which of the following is true ? (a) The substitution effect increases q but the income effect decreases q and over- come the substitution effect. Overall q decreases. (b) The substitution effect decreases q but the income effect increases q come the substitution effect. Overall q increases. and over- (c) Both the income and substitution effects increase q. Overall q increases. (d) Both the income and substitution effects decrease q. Overall q decreases. (D) Suppose an inferior good X (not Giffen). Its price increases from…
- Suppose that a consumer's utility function is given by u(x, y) = x(a+y), where x is consumption measured in $ and y is a good that can take either 0 or 1 and a is some number. Suppose that a=26 and the consumer has $51 to spend on x and y. Find the reservation price for y. (Answer up to 2 decimal places.)Suppose a consumer’s utility function is given by U(X,Y) = X1/2*Y1/2. Also, the consumer has $72 to spend, the price of Good X, PX = $1, and the price of Good Y, PY = $1. a)How much X and Y should the consumer purchase in order to maximize her utility? b)How much total utility does the consumer receive? c) Now suppose PX increases to $9. What is the new bundle of X and Y that the consumer will demand?Suppose a consumer had a utility function given by: U=X0.5Y. If the price of Good X (Px) is $1 and the price of Good Y is $2 then what is the utility maximizing quantity of Good Y the consumer will purchase with a budget of $24?
- Suppose that there are two goods (X and Y). The price of X is $2 per unit, and the price of Y IS SI per unit. There are two consumers (A and B). The utility functions for the consumers are U A(X,Y) = X0.5 yo.5 UB (X,Y) = X 0.8 yo.2 %3D Consumer A has an income of $100, and Consumer B has an income of $300. a. Use a Lagrangian to solve the constrained utility-maximization problem for Consumer A. b. Use a Lagrangian to solve the constrained utility-maximization problem for Consumer B. C. Calculate the marginal rate of substitution of Y for X (X is increasing and Y is decreasing; MRSXY) for consumer A at his or her optimal consumption bundles. d. Calculate the marginal rate of substitution of Y for X for consumer B at his or her optimal consumption bundles. e. Suppose that there is another consumer (let's call her C). You don't know anything about her utility function or her income. All you know is that she consumes both goods. What do you know about C's marginal rate of substitution at…A consumer has a utility function U(X,Y ) = X1/2 Y1/2 . Prices of the goods are pX = £10 and pY = £5, respectively, and the consumer has income M = £200 to spend on X and Y. Currently, she buys 2 units of good X and spends the rest of her income on good Y.a) Determine this consumer’s current utility level. b) Compute the consumer’s marginal utilities of goods X and Y. c) Explain why the consumer’s current consumption of goods X and Y is not optimal. Should she substitute X for Y or vice versa? The consumer’s marginal rate of substitution is MRS = Y/X.d) Determine this consumer’s optimal consumption of both goods. e) By how much does the consumer’s utility increase when she consumes the optimal bundle?Bread and doughnuts: The consumer receives positive benefits from the consumption of beans (B) and donuts (K). Utility function of the consumer is the following: U(B,K) = 100∙B0.25 · K0.75 The price of beans (can) is ISK 2,000. but the price of a donut (box) is ISK 4,000. Consumption restrictions are placed on the consumer since his income is ISK 400,000. Put on all form donuts on the x-axis and beans on the y-axis. a) Show an equation for the bean's success rate for a single donut in light of the utility function. Draw the equivalence curve on a picture and explain what the equation is performance ratio is stated at each point on the equivalence curve. Explain with the concept of the efficiency ratio of the curvature of the equivalent curve. b) Find the most efficient consumption combination and draw on the diagram. c) The government decides to support the consumption of beans so its price drops to 1,000. Who is the most economical consumption combination based on the changed price…
- Suppose that an agent has utility function u(x,y)=x+2y. What information is necessary to calculate the agent’s optimal consumption of x? price of y only price of x only income only price of x, price of y, and income price of x and y onlyMaya is doing her undergrad at Queen's University. She loves donuts and chocolate chip cookies (CCC). Her utility function is given by u(x, y) = √8x +5 + 2y, where x denotes her consumption of donuts and y denotes her consumption of CCC. Her budget is $10/day. The price of a donut is $1. (a) When the price of CCC is $1, what is Maya's optimal choice of donuts and CCC? (b) When the price of CCC is $8, what is Maya's optimal choice of donuts and CCC? (c) When the price of CCC increases from $1 to $8, calculate Maya's substitution effect and income effect. (d) According to your calculation in part (c), is CCC a normal good or an inferior good? Explain. Is CCC an ordinary good or a Giffen good? Explain.Individual that consumes two goods (X and Y) and has a CES Utility Function of the form: U = 100(X^(0.75) + Y^(0.75)). Income of 1000, the price of Good X is 10 and the Price of Good Y is 20 a) Find the Marginal Rate of Substitution as a function of the quantities consumed of Good X and Good Y. b) Write out the Lagrangian for this problem. c) Solve to find the demand for Good X, the demand for Good Y, and the highest level of utility for this individual. d) Now consider an increase in the price of Good X to 20. What is the demand for Good X and Good Y? What is the Utility of the consumer following the price change? e) Considering the change in demand for each good between parts c) and d), how much is due to the substitution effect and how much is due to the income effect? f) Show your answers on a graph.
