An agent consumes quantity (x1,x2) of goods 1 and 2. Here is his utility function: U(x1, x2) = √x1 + 2 ∗ x2, his budget constraint is p1x1+p2x2 = m. a. Calculate the agent’s Marshallian demand (x*1 , x*2 ). b. When would the agent’s consumer’s problem have a corner solution?
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An agent consumes quantity (x1,x2) of goods 1 and 2. Here is his utility function: U(x1, x2) = √x1 + 2 ∗ x2, his budget constraint is p1x1+p2x2 = m.
a. Calculate the agent’s Marshallian demand (x*1 , x*2 ).
b. When would the agent’s consumer’s problem have a corner solution?
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- Suppose a consumer’s utility function is u = x_1^(3/2) x_2^(3/2) . She spends her budget of £27 for two goods. The prices of both goods are p1 = 6 and p2 = 6. Derive the Marshallian demand functions for ?1 and ?2 as functions of both prices and income. Then find the optimal consumption point for the given budget constraint.Consider the utility function U(x,y)=5x +2y. An agent with a budget constraint of 10x + 5y = 20 will choose which of the following bundles in order to maximize his/her utility? 1 unit of x and 2 units of y 10 units of x 2 units of y 2 units of x 4 units of yConsider the utility function U(x,y)=3x +6y. An agent with a budget constraint of 15x + 5y = 30 will choose which of the following bundles in order to maximize his/her utility? 2 units of x and 0 units of y 2/3 units of x and 4 units of y 1 unit of x and 3 units of y 0 units of x and 6 unit of y 1/2 unit of x and 1 unit of y
- An economy described in an edgeworth box consists of 2 goods, namely X and Y and two consumers, namely A and B. Initially A has goods X and Y equal to 12 and 2 respectively, with the utility function UA (XA, YA) = XAYA . Meanwhile, B initially has goods X and Y equal to 8 and 18, respectively, with the utility function UB (XB, YB) = XBYB. It is known that the price of item X is IDR 50,000 and the price of item Y is IDR 50,000. a. Draw the economy above, in an edgeworth box representing the endowment positions of individuals A and B complete with their respective utility curves. Don't forget to include all relevant symbols and numbers on the vertical and horizontal axes. b. Is initial ownership an efficient allocation? By evaluating the endowment and MRS of individuals A and B, will there be an exchange? c. Determine the competitive balance allocation! (hint: considering the ratio of the price of goods X and Y)Consider the utility function u(x) =√x1+ √x2 ; and a standard budget constraint: p1x1+p2x2=I. a.Are the preferences convex? b. Are the preferences represented by this function homothetic? c. Verify that the demand function is homogeneous of degree 0 in prices and income.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 only
- An agent consumes quantity (x1,x2) of goods 1 and 2. Here is his utility function:U(x1, x2) = x13x2, his budget constraint is: p1x1+p2x2=m. 1. Show the expenditure function is homogeneous of degree 1 in pricesThe preferences of a typical Californian can be represented by the following utility function: U (x1 , x2 ) = α ln(x1) + (1 − α) ln(x2) Here, x1 and x2 are the quantities of electricity and gasoline, respectively. The consumer faces prices given by p1 and p2 and has income m. Currently, the government has decided to impose a consumption restriction so that any person in the state is allowed to consume at most 50 units of electricity (x1 ≤ 50). Call this restriction a rationing constraint. (a) If α=0.25, m=100,and p1 =p2 =1, find the optimal consumption bundle of gasoline and electricity. Is the electricity rationing constraint binding (meaning does x1∗ = 50)? (b) Suppose that α = 0.75, but the other parameters are the same. What is the optimal consumption bundle? Is the rationing constraint on electricity consumption binding? (c) Now, assume that there is no rationing constraint. Assume m = 100 and p1 = p2 = 1, but α remains as a generic parameter. Solve for the optimal quantity…Suppose a consumer has a budget of $200 to spend on two goods, X and Y, whose prices are $20 and $10, respectively. If the consumer is observed to buy 5 units of X and 10 units of Y, where the respective Marginal Utilities of X and Y are, 50 and 40 utils, is the consumer in equilibrium? Explain why or why not. If the consumer is not in equilibrium under conditions in d), suggest another combination that would possibly achieve equilibrium. Explain your answer.
- A consumer utility function is U=(x1,x2) Where X1 is the quantity of good 1 that is bought, X2 is the quantity of good 2 that is bought. The price of good 1 is $10 and the price for good 2 is $2. If the consumer's income is $100 what will the consumer's optimal utility level be? b. Using Lagrange multilplier method. optimise the utility function x0.25 y0.25 subject to the budget constraint 24=x/10+yA utility maximizing consumer purchases two commodities, Q1 & Q2. The consumer’s utility function is described by the following expression: U = Q1 Q2 + Q1 + 2Q2. The prices of the commodities are P1 = $2 and P2 = $5. Suppose the income of the consumer is $51 (a)Form the Lagrangian function that defines the combination of both commodities the consumer could buy subject to the budget constraint imposed by the prices of the commodities and the income of the consumer. (b)Find the combination of both commodities that maximizes the utility of the consumer. (c)Write and evaluate the Bordered Hessian for this utility maximization problem.Between 1990 and 2000, a particular consumer's income increased by 25%, while the price of X and all other goods increased by 10%. It was observed that the consumer's consumption of X and all other goods both increased by 15%. A. The consumer did not regard X and all other goods as perfect complements. B. The consumer's preference cannot be represented by a Cobb-Douglas utility function. C. The consumer's preference can be represented by a Cobb-Douglas utility function. D. The consumer's preference cannot be represented by a quasilinear utility function. E. More than one of the above options is true. The answer for this question is D and I understand why D is correct. However, for options B and C, can someone explain how I should rule them out?