Find utility functions given each of the following indifferencecurves [defined by
a.
b.
c.
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Check out a sample textbook solution- Donald likes fishing (X1) and hanging out in his hammock (X2). His utility function for these two activities is u(x1, x2) = 3X12X24. (A) Calculate MU1, the marginal utility of fishing. (B) Calculate MU2, the marginal utility of hanging out in his hammock. (C) Calculate MRS, the rate at which he is willing to substitute hanging out in his hammock for fishing. (D)Last week, Donald fished 2 hours a day, and hung out in his hammock 4 hours a day. Using your formula for MRS from (c) find his MRS last week. (E) This week, Donald is fishing eight hours a day, and hanging out in his ham mock two hours a day. Calculate his MRS this week. Has his MRS increased or decreased? Explain why? (F) Is Donald happier or sadder this week compared to last week? Explain.arrow_forwardWhich of the following utility functions represent preferences which do not satisfy monotonicity? 1 U= - x+y 1 U= - 5ху Ou=xy O u= yarrow_forwardb) Define indifference curve and discuss the characteristics of an indifferencecurve.arrow_forward
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- Consider the following utility functions: (1) u(x₁, x₂) = x₁ + 2x2. (2) u(x1, 1₂) = 2125 12.75 (3) u(x₁,1₂)=-1²-1₂. (4) u(x1, 1₂) min{x1, 2x2). For utility functions (1) to (3), give the equations of the indifference curves correspond- ing to utility level k, where 22 is expressed as a function of 2₁ and k. For utility functions (1) to (4), draw two indifference curves for each function. That is, draw four graphs (one for each utility function) and two indifference curves on each graph.arrow_forwardDraw indifference curves for the following utility functions. a) u(x, y) = x+ 2y b) u(x, y) = min{x, 3y}arrow_forwardAnna has an income of 1000 euros and utility function U(x,y)=x²y³. The prices of the two goods are P₁=5 and Py-20. a) Define the budget constraint and represent it graphically. (arrow_forward
- Consider the following utility function. U=U(X,Y)=X0.2Y0.8 Find the marginal utilities. Determine their signs. Provide the economic interpretation of the signs of these marginal utilities. Determine whether the law of diminishing marginal utility holds for both goods.arrow_forwardDraw an indifference map for each of the following functions. U(x,y) = x2y3U (x, y) = 2x + 3yU (x, y) =x + ln(y)U (x, y) = min{2x, 3y}U (x, y) = max{3x, 2y}arrow_forwardA 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+yarrow_forward
- Economics (MindTap Course List)EconomicsISBN:9781337617383Author:Roger A. ArnoldPublisher:Cengage Learning