Suppose Maryís utility function is given as U(X; Y ) = 2X + Y . Mary has and income of 60 dollars. If the price of X is Px = 1 and the price of Y is PY = 3, how many units of X and Y should Mary consume in order to maximize her utility. Show your result on a graph (Plot the indi§erence curve and the budget constraint and show the utility maximizing point).

The marginal utility for shoes and coffee is given below for five individuals. A pair of shoes costs $2, and a cup of coffee costs $1. Which of these consumers are optimizing over their choices? Explain  For those who are not, how should they adjust their spending? Explain  “Pasta is Miguel’s favorite meal therefore the law of diminishing marginal utility does not apply”. Do you agree with this statement?  It is known that the indifference curve is convex. What does this tell you about the relationship between the goods?  The income effect and the substitution effect work in the same direction for a normal good. Explain how this differs for an inferior good.

Jackie has a budget of $36 per month to spend on snacks. She can spend this budget on bags of potato chips (C) and Hershey chocolate bars (H). Potato chips cost $4 per bag, while Hershey bars cost $1 per bar. The utility that Jackie receives from consuming potato chips and Hershey bars is represented by the following utility function: U=3C2 H. Given that Jackie seeks to maximize her utility, find the number of potato chip bags and Hershey chocolate bars that Jackie will purchase each month.

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Yam has the following utility function for Apples (X1) and Ice Cream (X2), U(X1,X2) = Min{3X1,X2}. Yam likes to get more of both Apples and Ice Cream. Suppose Yam has an income of M = $160 budgeted to be spend on these two goods and the prices of Apples and Ice Cream are p1 =$2, p2 =$1. Yam's optimal consumption of Apples is and Ice Cream is (Please put your answer in numerical values with no comma or decimal place.) Suppose a quantity tax of $1 is imposed on Ice Cream. Yam's after tax optimal consumption of Apples is and Ice Cream is (Please put your answer in numerical values with no comma or decimal place.) Suppose instead of the quantity tax, the government choose to impose a lump-sum tax of $20. After the imposition of the lump-sum tax, Yam's optimal consumption of Apples is and Ice Cream is (Please put your answer in numerical values with no comma or decimal place.) If government would have to impose one of these 2 kinds of taxes, which of these types of tax would be better…

Question 3 Utility Maximization Marge has the utility function U(F,H)=20F?H where F is the quantity of footwear and H is the quantity of hats she consumes. Suppose the price of footwear is $20 and the price of hats is $5, while Marge has an income of $200/week. 1. Calculate Marge's MRS as a function of the quantities F and H. 2. BONUS: Write down the Lagrangian function for Marge's utility maximization problem. 3. Solve for Marge's optimal consumption bundle of footwear and hats, You can either use the Lagrangian from part b or use any other method you likeli

Utility maximization with a budget constraint. A hypothetical consumer spends all tgheir income on ramen noodles (N) and wild rice (W). N is the quantity of noodles; W is the quantity of wild rice. Their income is $1,600 per month. the price of noodles is $2 per package and the price of wild rice is $20 per pound. The utility function is U=sqrt(N*W).   the MRS = -N/W.   The budget constraint is: 1,600 = 2*N + 20*W   Graph Qty of noodles (N) on vertical axis and Qty of wild rice (W) on horizontal axis.   SOLVE: a. Graph the budget constraint. label all points. What is the slope of the budget constraint? b. Find the optimal quantities of noodles(# of packages) and the wild rice (# of pounds) given the budget constraint. graph these optimal quantities. draw your indifference curve on the same graph. c. Show on your graph what happens when the price of wild rice increases to $40 per pound. Find your new optimal quantities of noodles and wild rice. label all points on graph. label the…

8. Fabian consumes X and Y and the following utility function represents his utility: U = 2XY a. With a utility function of U = 2XY, Fabian's MU, = 2Y and his MU, = 2x ,where MU is marginal utility. Write an equation for Fabian's marginal rate of substitution (MRS). b. Suppose Fabian's income is $120 and Px = S6 and Py-$2, where Px is the price of X and Py is the price of Y. Write an equation for Fabian's budget constraint. c. Write the equation that equates the slope of Fabian's budget constraint to the slope of Fabian's indifference curve: d. If Fabian is spending all of his income, how much X and how much Y will he choose? Use the equations you wrote in part's b and c to answer this question. e. What will Fabian's utility be with this combination of X and Y? f. Now suppose the price of X increases to P.=10. Write the equation that equates the slope of Fabian's budget constraint to the slope of Fabian's indifference curve. How will this change the optimal combination of X and Y? What…