Consumer A's utility function is U,(x,X2)=x+2x32, Consumer B's utility function is Ug(x,X2)= X+2ln(1+x). If the prices are pi=p2=10, will consumers A and B's income offer curves be the same? O a. No O b. Yes Oc. Not enough information to answer question.
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- Find utility functions given each of the following indifferencecurves [defined by U()=k ]: a. z=k1/x/y/ b. y=0.5x24(x2k)0.5x c. z=y44x(x2yk)2xy22xQ1. Bob has a utility function defined over goods 1 and 2:u(x1; x2) = min{6*x1 + x2, x1 + 2*x2} Consider Bob’s preferences represented by the utility function inQuestion 1. Which of the following is correct?(A) Bob’s preferences are not homothetic.(B) Bob’s preferences are not transitive.(C) Bob’s preferences are not convex.(D) A typical indifference curve for Bob’s preferences is a straight line.(E) None of the above.An agent has utility u(x1, x2) = (x-11+x-12)-1for goods x1 and x2. The prices of the goods are p1 and p2. The agent has income m. a) Show preferences are convex. You can do this graphically or by showing that MRS is decreasing in x1. b) Solve for the agent’s optimal choice of (x1, x2). c) Show the agent’s indirect utility function is given by:V=m(p1/21 + p1/22)2
- Consider a consumer whose utility function is U(q1,q2) = q1*q2. This consumer has $100 and prices of two goods are p1 = $1 and p2 = $2.a) Draw indifference curves corresponding to utility levels 1 and 4.b) Now consider utility function U(q1,q2) = (q1*q2)2. Check that it generates same indifference curve map as initial utility function and JUSTIFY this result.(c) Calculate marginal utilities of both goods and COMMENT on their properties.d) Calculate marginal ratio of substitution (MRS) at points (1,1) ; (1/2,2) ; (2,1/2) ; (2,2) ; (3,1) and (1,3) and INTERPRET results. THANKS.Let t = 3 The consumer has a preference relation defined by the utility function u(x, y) = −(t + 1 − x)2 − (t + 1 − y)2. He has an income of w > 0 and faces prices px and py of goods X and Y respectively. He does not need to exhaust his entire income. The budget set of this consumer is thus given by B={(x,y)∈R2+ :pxx+pyy≤w } A. Is the optimal demand for good 1 everywhere differentiable with respect to w? informal argument is sufficientQ10. Consider a utility function: U (F,C) = FC so MU_F = C and MU_C = F. In Case 1, Total income is $100 , per unit prices of Food (F) are $2 , per unit prices of Cloth (C) are $10In Case 2, Total income is $100 , per unit prices of Food (F) are $2 , per unit prices of Cloth (C) are $15 Find the following for both cases, and contrast Case 2 with Case 1:a. What is the value of MRS at the optimal point and what does this value mean? b. What is the optimal consumption bundle i.e. (F*, C*)? c. Plot the budget line and clearly depict the point of optimality in the F (x-axis)-C (y-axis) space (draw both case budget lines and point of optimality on one diagram)
- 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 onlyA consumer has $600 to spend on good x and y. Her preferences can be represented by theutility function U(x.y)= y+100 In xIf the price of one unit of good x is $10 and the price of one unit of good y is $5, what is the consumer optimal bundle?Q 15. suppose the consumer's utility function is given by U(x,y) =x^1/4 y^3/4 where the equation for this consumer's demand curve for x is?
- Angela's utility function is U(x1; x2) = (x1 + x2)3. Her indierence curves are downward- sloping, parallel straight lines. true or false?Consumer has the following utility function U(x,y) = x1/2y1/2 , where the price of good x is 1$ 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.Assume a utility function U(x,y) = XY, where Px = $2, Py =$1 and Income = $100.a) Determine and graph consumer's optimum.b) Determine Demand Functions of X and Y.c) If income were to increase IN 100%, determine how many additional units of X and Y are consumed.d) What type of goods are X and Y with respect to Income? Also plot Engel curve for both goods.