(a) Suppose we have preferences U(X, Y) = min [X, 3Y]. Graph/sketch the indifference curve through the bundle (X=30, Y = 30). What is the utility of (30, 30) and explain why the indifference curves look the way they do. (b) What does the Marginal Rate of Substitution tell us about preferences? < (c) Why is the Marginal Rate of Substitution not applicable in this example? <

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3. We claimed in the text that if preferences were monotonic, then a diag- onal line through the origin would intersect each indifference curve exactly once. Can you prove this rigorously? (Hint: what would happen if it intersected some indifference curve twice?)

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10. which of the utility function U=5x+3y^2. the indifference curves for this utility function.  @) will have a constant marginal rate of substitution of x for y as x increases.  B) will have an increasing marginal rate of substitution of x for y as x increases.  please explain

(a)_Suppose we have preferences U(X, Y) = X² Y².. What is the utility at the bundle X = 5 and Y = 20? Create a table then graph/sketch the indifference curve through (5, 20). Interpret the MRS (with MRS = Y/X) at this bundle. < (b) _Let prices be Px = $5, Py = $5 and income M = $1000. Draw/sketch the budget constraint. Explain what the slope of the budget line means in economic terms.< (c) State the consumer's utility maximization problem and express this in words. What are the two conditions (equations) that identify the optimum? Sketch this in a figure and explain.< (d) Use the information in (a) and (c) to show that demands are: X = ½ M/PX and Y = ½ M/PY.< (e) For the income and prices in (b), what is optimal X, Y, and utility? Show your work. (f) Suppose Px falls to $4 and Py rises to $7 but income stays at $1000. Does consumer utility rise or fall? Show and explain. < (g) Calculate the Compensating Variation that ensures the consumer is no worse off nor better off with these price…

Please tell me which of the multiple choices in question 1.6)1.7)1.8) are correct.State only the correct ones please.   1.6) The marginal rate of substitution (MRS) can be defined as: Select one or more: a. The amount of one good that the consumer is willing to trade for one unit of the other. b. The ratio of the amounts of two goods. c. The change in the consumer’s utility when one good is substituted for another. d. The absolute value of the slope of the indifference curve.   1.7)   (SEE ATTACHED PICTURE) The diagram shows that: Select one or more: a. If Angela works 24 hours a day she can still survive. b. There is a technically feasible allocation where Angela does not work. c. A new technology that produced more grain would give a larger technically feasible set. d. If Angela needed less grain to survive the technically feasible set would be smaller.

Suppose you have a $20 gift card and want to buy Blue and Red yarn. The utility function from yards of blue (B) and red (R) yarn can be expressed as follows: U(B,R) = 3B+R Red yarn costs $4 per yard. blue yarn costs $4 per yard. A) Graph the budget constraint and the indifference curves that can be reached. How many yards of each type of yarn will he purchase at these prices with his gift card?

A consumer has $100 to spend on craft beer and Schweinefleischaft (pork shanks). Suppose craft beercosts $10 per 4-pack if the customer purchases up to five 4-packs. After that, it is $5 per 4-pack. SupposeSchweinefleischaft is $5 per order of pork shanks.(a) Draw the budget constraint for this consumer, with craft beer on the horizontal axis and Schweine-fleischaft on the vertical axis.(b) Will the consumer ever purchase exactly five 4-packs of craft beer? Explain why, using both thegraph in part (a) and words.

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