An agent consumes quantity (x1,X2) of goods 1 and 2. Here is his utility function: U(x1, x2) = Vx1 + 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?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,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 y
- Consider 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 ySuppose 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.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 prices
- 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.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.Assume there is consumer, his utility function is u(x,y) =8 * x0.5+y , and his budget constraint is px*x +y = m, which implies py = 1. Please derive the Marshallian demand function of x. Please derive the indirect utility function. Please derive the expenditure function
- 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 Now suppose that instead both goods are priced as follows: There is a discount of 50% on the price of good 1 on each additional unit in excess of 3 units, and there is a discount of 50% on the price of good 2 on each additional unit in excess of 3 units. Draw the new budget constraint and derive it analytically.Utility Function: U(X,Y)=X1/2Y1/2 Budget Constraint: 2X+2Y=16 If the price of good X changes to Px=3, what is the Equivalent variation?A consumer is in equilibrium and is spending income in such a way that the marginal utility of product X is 40 units and that of Y is 32 units. If the unit price of X is $5, then the price of Y must be: