Which of the following is NOT a statement of the tangency condition? Select one: O O O a. MRSxy= Px/Py b. MUX/Px = MUY/Py c. MRSxy=MUX/MUy d. slope of the budget line is equal to the slope of the indifference curve
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- Why is the consumer’s MRS equal to the price ratio at the optimal consumption point? Givea graphical interpretation of this fact in XY space (hint: what do we know about the indifferencecurves and the budget line?).Refer to the indifference curve/budget line diagram below in Figure 7. Given that a consumer initially faces budget line (BL1) and ICI, and thus, by choosing consumption point c, is able to achieve the optimal utility level. If the price of x (Px) decreases, then the substitution effect (SE) is the movement from _-. effect (IE) is the movement from and the income y a IC2 d IC: BLI Figure 7 O a. from b to a; and a to d. O b. from a to b; and b to c. O c. No correct answwers. O d. from c to d; and d to a.Suppose that the following utility function is given U(X,Y) = -X-ywhich of the following is correct? X is a good and Y is a bad and indifference curve is negatively sloped. Both X and Y are goods and indifference curve is negatively sloped. Both X and Y are bads and indifference curve is negatively sloped, OYisa good and X is a bad and indifference.curve is positively sloped.
- The marginal rate of substitution is the slope of an indifference curve. O True O FalseQuestion 17 When considering her budget, the highest indifference curve that a consumer can reach is the one that is tangent to the budget constraint indifference curve farthest from the origin indifference curve that intersects the budget constraint in at least two places None of the above is correct O OIf a consumer is always indifferent between an additional one grapefruit or an additional two oranges, then when oranges are on the horizontal axis the indifference curves: O A) will be straight lines with a slope of -1/2. B) will be straight lines with a slope of -1. O C) will be straight lines with a slope of +1/2. D) will be right angles whose corners occur on a ray from the origin with a slope of +2. O E) none of the above Suppose that a firm's production function is given by Q = K²L. Further suppose that w = $10 andr = $20. Suppose that the firm wants to produce 27,000 units of output in the most efficient way possible. The firm's minimum cost of production is
- 4. Assume the prices of r and y are 1 and income is 10. For the following two utility functions, find the quantities of r and y consumed at the con- sumer's optimum. (Here, it may be helpful to solve by drawing out some indifference curves.) (a) U(r, y) = Min(x, 2y) (b) U(x, y) = 2x + y (c) Suppose the price of a rises to 3. What are the new optima in each case. What are the substitution effects?Determine which, if any, of Properties 4-1 through 4-4 are violated by the indifference curves show in the following diagram. Product Y Product X __" U 1 All properties hold except Propert 4-3 (Diminishing Marginal Rate of Substitution) and Property 4-2 (More Is Better). All properties hold except Property 4-4 (Transitivity). All properties hold except Property 4-1 (Completeness) and Property 4-4 (Transitivity). O All properties hold except Property 4-3 (Diminishing Marginal Rate of Substitution).(a) Suppose we have preferences U(X, Y) = 10X²/³ Y¹/3, Create a table and graph/sketch the indifference curve through the bundle X = 30 and Y = 30.< (b) The Marginal Rate of Substitution is MRSxy=-2Y/X. For the bundle (X= 30, Y = 30), calculate and then interpret what the value of the MRS means.< (c) Cobb-Douglas preferences are strictly convex. What does this imply about the MRS as we move along the indifference curve? Explain/discuss (you may want to draw a picture). < (d) What are the two conditions (equations) that identify the optimum given these preferences and the consumer's budget constraint? Sketch this in a figure and explain.< (e)_From (d) we can show that optimal demands are: X=½ M/PX and Y = ½ M/Px. (you do not have to derive these, just use the equations I have given you.) Calculate optimal demands (X*, Y*) and utility if Px = 10, Px= 5 and income M = 1200. < (f)_Suppose Px falls to Px = 8 but Py and M are unchanged (Px = 5 and M = 1200). Calculate the new optimal demands…
- Indifference curves: O eliminate the need to place numerical values on utility. O facilitated a move from cardinal utility to ordinal utility. O show all the choices that represent the same level of utility. Ⓒall of the above.Assume Pat spends all of her allowance to purchase 4 apples and 4 candy bars. Pat's marginal utility of the fourth apple is 20 utils, and her marginal utility of the fourth candy bar is 40 utils. If an apple costs $1.00 and a candy bar $0.50, to maximize utility Pat should(A) purchase more apples and more candy bars(B) maintain the current purchase of 4 apples and 4 candy bars(C) purchase more apples and fewer candy bars(D) purchase fewer apples and more candy bars(E) purchase fewer apples and fewer candy barsNo written by hand solution I mainly need the indifference curves drawn please. Julian’s utility function is U(x, y) = (x + 2y)^2 . In every graph for this question, set y in the vertical axis and x in the horizontal axis. (a) Obtain the marginal rate of substitution. Obtain the equation of the indifference curves for U = 16 and U = 36 (solving for y as a function of x). Draw these indifference curves.