Let consumer have CES utility function u(q1, q2) = (q1^0.5 + q2^0.5)^2 with income Y=10, and prices p1=2, p2=3. Compute optimal demand for both goods. Solve q1 and q2
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Let consumer have CES utility function u(q1, q2) = (q1^0.5 + q2^0.5)^2 with income Y=10, and prices p1=2, p2=3. Compute optimal demand for both goods. Solve q1 and q2
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- Consumer has the following utility function U(x,y) = x1/2y1/2 , where the price of good x is 1$ per unit, the price of good y is 4$ per unit, and the consumer’s income is 800$. Find the utility maximizing consumption levels of x and y.Utility Maximization A consumer faces income constraints and has CES preferences of the following form: U(x, y) =x y Find the consumer’s demand for x as a function of prices and incomeDetermine the optimum demand for goods 1 and 2 for consumers who have the utility function u(x)=x1x2. Show that the solution will be the same whether using the slope approach (i.e the slope of the indifference curve is the same as the slope of the budget line) or using the Lagrange approach.
- Find the maximizing utility for the person consuming two commodities from the following information: Income: 10 OMRPrice of Qx= 2 OMR, Price of Qy= 1 OMRConsider the following indirect utility function:ʋ(P,y) = y(P1r + P2r)-1/r Wherer = ρ/(ρ-1, Pi are parametric prices, and y is the consumer’s budget a) Solve for the Marshallian demand functions xi (P, y) and verify that these functions are homogenous of degree zero (Hint: you can also use Roy’s Identity). b) Derive the Hicksian demand functions xih (P,u)Given utility function and prices of the good along with income U = x2 + y2 +2x + 2y P x = 1 P y = 1 M = 4 Find out ordinary demand functions and expenditure function.
- A consumer's preferences are represented by the utility function If the budget constraint is P1X1 + P2X2 = M, determine the demand functions q1(P1, P2, M) and Q2(P1, P2, M). Determine also the indirect utility function V(P1,P2,M).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.If the utility function for a consumer is defined by U=f(X,Y)=3√(X^2Y), Given that the consumer's income is 900 currency units and unit price of goods X and Y are 20 and 30 currency units respectively, find the combination of X and Y which optimize the consumer satisfaction.
- The 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 the consumer solves the following UMP: max (x1)^2 + (x2)^2 , s.t. p1x1 + p2x2 ≤ w where p1,p2 > 0. a) Plot the indifference curves b) Find the Marshallian demand functions. Show graphically the utility maximizing choices.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?