Because Income depends on work effort and work effort depends on nutrition, suppose the relationship between income (Y) and total food availability (F) in a poor household is given by: Y = 10F + 20F2 – 0.6F3 a) If food availability in a two-person household is 20, would it be “rational” to share the food? Explain. b) If food availability in a two-person household is 30, would it be “rational” to share the food? Explain.

Juanita lives in New York City and enjoys drinking lattes and eating scones. The price of a latte is held constant at $4 throughout this problem. On the following diagram, the purple curves (I₁ and I2) represent two of Juanita's indifference curves. The lines BL₁ and BL2 show two budget lines. Points X and Y show Juanita's consumer equilibriums subject to these budget lines. QUANTITY OF LATTES 20 18 16 14 6 4 2 0 0 2 4 6 8 10 12 14 QUANTITY OF SCONES BL₁ 16 18 20 Given the previous graph and knowing the price of a latte is $4, Juanita's budget is $ ?

Q3. Consider a utility function: U (F,C) = FC so MU_F = C and MU_C = F. Suppose as Case 1, Total income is $100 and per unit prices of Food (F) and Cloth (C) are $2 and $10, respectively. 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. Now assume a new Case 3, where instead of one time income change, Pc' = $15, holding all else the same as in Case 1, do the same analysis (parts a-c) and contrast your answers to Case 1. For part c, you should draw old (Case 1) and new (Case 3) budget lines/point of optimality.

Using the homogeneity of indirect utility, which of the following cannot be an indirect utility function? (a) V: = (b) V: = (c) V: = [2 PzPy I Pz+Py p²+p² (d) V = 1 Pz

(In this question we denote income by Y, not by W as in the lecture notes). The following figure shows the consumption of x and y for two market situations. We can conclude that: x is a normal good for all market situations. py is greater than px. It is not conclusive. x is an inferior good for some market situation. y is an inferior good for some market situation.

Question 22: Kathy gets utility from three things: the number of flowers in her local park (F), reading books in this park (R), and eating sushi (S). Four utility functions that might describe Kathy's preferences are shown below. In each case, discuss whether reading in the park (R) is non-essential and whether reading (R) and the number of flowers in the park (F) are weak complements. [medium] (a) U(F, R, S) = 2FR+S (b) U(F, R, S) = /2FR+S (c) U(F, R, S) = (V2FR)S (d) U(F, R, S) = v2F + RS

can you please provide a explanation with any mathematical working out

Question 22: Kathy gets utility from three things: the number of flowers in her local park (F), reading books in this park (R), and eating sushi (S). Four utility functions that might describe Kathy's preferences are shown below. In each case, discuss whether reading in the park (R) is non-essential and whether reading (R) and the number of flowers in the park (F) are weak complements. [medium] (a) U(F, R, S) = 2FR+ S (b) U(F, R, S) = /2FR+ S (c) U(F, R, S) = (V2FR)S (d) U(F, R, S) = /2F+ RS

Let u(x) be a utility function that represents the preferences of a household. We say that the function v(x) is a monotonic transformation of u if f(·) is a strictly increasing function and v(x) = f(u(x)). (a) Show that if v(x) is a monotonic transformation of u, it represents the same preferences. (b) Can you explain why taking a monotonic transformation of a utility function does not change the marginal rate of substitution? (c) What kind of preferences are represented by a utility function of the form U(x1,x2) =  ? What about the function U(x1,x2) = 13x1+13x2?

Beans and doughnuts: The consumer receives positive benefits from the consumption of beans (B) and donuts (K). Utility function of the consumer is the following: U(B,K) = 100∙B^0.25 · K^0.75 The price of beans (can) is ISK 2,000. but the price of a donut (box) is ISK 4,000. Consumption restrictions are placed on the consumer since his income is ISK 400,000. Put on all form donuts on the x-axis and beans on the y-axis. a) Show an equation for the bean's success rate for a single donut in light of the utility function. Draw the equivalence curve on a picture and explain what the equation is performance ratio is stated at each point on the equivalence curve. Explain with the concept of the efficiency ratio of the curvature of the equivalent curve. b) Find the most efficient consumption combination and draw on the diagram. c) The government decides to support the consumption of beans so its price drops to 1,000. Who is the most economical consumption combination based on the changed price…