Mary spends all her budget on statistical software (S) and office supplies(O). Her preferences can be represented by the utility function: U(S, O) =2 ln(S) + 3 ln(O). Suppose that the price of software is pS = 2, the price of officesupplies is pO = 3, and Mary’s income is I = 10. What bundle ofsoftware and office supplies (S, C) maximizes Mary’s utility?

The price of salad is ps = 10, the price of green juice is pg = 5, and Tom’s income is I = 100.

Suppose you had a budget of $20.00 and the prices of a burger and a slice of pizza are $5.00 and $2.00 respectively.  What would be your optimal consumption bundle?

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Define the Marginal Rate of Substitution between two goods (X and Y).If a consumer’s preferences are given by U(X,Y) = X1/4Y 3/4, compute the consumer’s marginalrate of substitution as a function of X and Y. Calculate the MRS if the consumer has chosen toconsumer 12 units of X and 30 units of Y.

Sylvia’s utility function over waffle fries, F, and frozen yogurt, Y is given by U = 2 ∗ F ∗ Y. Her marginal utility from waffle fries is MUF = 2Y, and her marginal utility from frozen yogurt is MUY= 2F. A pack of frozen waffle fries sells for $4. The price of a cup of frozen yogurt is $6. Sylvia has a budget of $120 to allocate to these items each month. a) For Sylvia’s utility functions above, draw a set of indifference curves showing utility levels U = 20, U = 30, and U = 40 b) What is the equation for Sylvia’s budget line? Draw it (with frozen yogurt –Y– on the vertical axis), and label the slope and intercepts. c) What is Sylvia’s marginal rate of substitution? d) If Sylvia maximizes her utility, how much of each food should she consume? Solve for her optimal bundle. Show how to determine this bundle on a diagram using indifference curves and a budget line. e) Briefly explain if each of the four conditions of the utility-maximizing behavior is satisfied with the bundle you…

Assume that a consumer can buy only two goods, X and Y, and has an income of $13,000. The price of X is $60 and the price of Y is $140. What is the slope of the budget line if X is measured horizontally and Y is measured vertically? Note that you will need to include a negative sign in your answer. If needed, round your answer to the nearest two decimal places.

Dev likes to consume scones (Good X) and cups of coffee (Good Y). Her utility functionis: U(x,y) = min{x, 2y}That is, her level of utility for any given bundle (x,y) is the lesser of x and 2y.Suppose the price of scones is $3 and the price of coffee is $2. Dev’s weekly budget is$20. Determine her optimal consumption bundle for a week.

Alice receives an allowance of 500 dollars that she spends on buying snacks (S) and tea (T). The price of each snack is 10 dollars and the price of each tea is 5 dollars. Her utility is given by: U (S, T) = 2S³/4 +T3/4 (a) Find her marginal rate of substitution (MRS) between S and T. (b) Write Alice's budget constraint. (c) Find Alice's optimal consumption and the optimal A. (d) What is her new consumption if the price of tea becomes 10 dollars? Note: numeric solutions for questions (c) and (d) are not integers.

Question 3 A certain household comprises of a couple, Adam (A) and Betty (B). They have lexicographic preferences over two goods G1 and G2 - A wants to consume as much of G1 as possible, before moving on to G2 whereas, for B, it is the opposite, she wants to consume as much of G2 as possible before moving on to G1.¹ Given their varying preferences, they decide to shop separately, after dividing the household income equally. The household income is $8. One difference to the usual setting - there are government restrictions in place so that no individual is allowed to buy more than two units of either good. Hint: Do not use mathematical brute force (like Calculus) to solve this problem. A simple diagram with appropriate budget lines, etc. should suffice. 1) Suppose prices are p= (P₁, P2) = (1,2). Denote the optimal choice of A and B as a= b= (b₁,b₂) respectively. Solve for a and b. (a1, a2) and