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1) Eor each of the utility functions below, find the optimal consumption bundle if pi-3 and...
Find the optimal bundle for the following utility functions and for budget line (P1X1+P2X2=m) a) U(X1,X2)=X1X2 b) U(X1,X2)=X1^2X2^3 c) U(X1,X2)=X1^2+2X2 d)U(X1,X2)= ln (x1^3X2^4) e) U(X1,X2)= 2X1+X2 f) U(X1,X2)= min (2X1,X2)
My utility is given by u(x1, x2) = 2x194x2-2 + In(x1) + [min{x1, x2)] + 2x2 + x1!! True, False, or Cannot Be Determined: When P1 = $2,P2 = $4, and I = $100, my optimal consumption bundle is (x1,x2) = (25,15).
My utility is given by u(x1, X2)-240.4X21.2 + 1n(%) + [min{x, xjf + 2x2 + x11.1 True, False, or Cannot Be Determined: When P1 $2,P2-$4, and I-$100, my optimal consumption bundle is (xi,xż) (25, 15)
h. U(1, 2 For the utility function above, find the consumer's optimal consumption bundle when prices of goods 1 and 2 are pl and p2, and the consumer has an income m. 1. 2. For the utility function above, find the consumer's optimal consumption bundle when prices of goods 1 and 2 are pl and p2, and the consumer has an endowment (el, e2) of the two goods. For each of your answers in question 2, write down the consumer...
2) Eor each of the production functions below, find the cost function and conditional factor demands if w1-2 and w2-4. What is the amount of x1 and x2 that minimizes the cost of producing 4 units of output? a. f(x)- XiX22 b. fx)- 2xi+x2 c. f(x)-min(x,2x2) d. u(x)- max(xi,X2)
2. Find the optimal bundle for utility given by u(x1, 2) bу рі — 1, р2 — 3 and m min x1, 32 and a budget described 300 3. Find the optimal bundle for utility given by u(x, y) 40 In x 200. (Note that x is inside the ln function but y is not.) nd a budget described by Y X Ра — 2, р, — 4, and m
how to solve this?! Section III Longer Problems (4 points each - 68 points total). Show your work. 1. Consider Mary's utility function u(x1, +2) = [min{2x1, x2}]} (a) Draw Mary's indifference curve that yields u = 1 and u = 2. Mark the kink clearly. (b) Derive Mary's optimal demand function for each of the goods, i.e., find ai (P. P. m) and (P1, P2, m). (C) If Pi = 1, P2 = 1 and m 6, what is...
1.) Liz has utility given by u(x2,x1)=x1^7x2^8. If P1=$10, P2=$20, and I = $150, find Liz’s optimal consumption of good 1. (Hint: you can use the 5 step method or one of the demand functions derived in class to find the answer). 2.) Using the information from question 1, find Liz’s optimal consumption of good 2 3.) Lyndsay has utility given by u(x2,x1)=min{x1/3,x2/7}. If P1=$1, P2=$1, and I=$10, find Lyndsay’s optimal consumption of good 1. (Hint: this is Leontief utility)....
d. U (1, ) (1a)(b-a For the utility function above, find the consumer's optimal consumption bundle when prices of goods 1 and 2 are pl and p2, and the consumer has an income m 1. 2. For the utility function above, find the consumer's optimal consumption bundle when prices of goods 1 and 2 are pl and p2, and the consumer has an endowment (el, e2) of the two goods For each of your answers in question 2, write down...
2. 2.1 Draw the indifference curves for the utility function U(21, 22) = x1 + 3x2. 2.2 What is the marginal rate of substitution evaluated at an arbitrary consumption bundle (21, 22)? 2.3 Suppose that p1 = 5, P2 = 2, and M = 10. Find the utility-maximizing consump- tion bundle (among those that satisfy the budge constraint) for this agent. You should be able to do this without using any calculus: it should be clear from your indifference curves....