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Assume preferences are strictly convex and a consumer has a budget constraint given by:
M = PxX + PyY. Show in a diagram and explain how to find the income and substitution effects of a reduction in the
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- c Serpil's utility function is U(B,C)= B · C , where B = veggie burgers per week and C = packs of cigarettes per week. a) What is her marginal rate of substitution if veggie burgers are on the vertical axis and cigarettes are on the horizontal axis? b) Serpil's income is $120, the price of veggie burger is $2, and that of a pack of cigarettes is S1. How many burgers and how many packs of cigarette does Serpil consume to maximize her utility? Illustrate your answers in a graph.Sally consumes two goods, X and Y. Her utility function is given by the expression U = 2XY3. The current market price for X is $20, while the market price for Y is $10. Sally's current income is $500. a. Write the equation for Sally's budget constraint. What is the slope of her budget line? b. Determine the X,Y combination which maximizes Sally's utility, given her budget constraint.Help me
- James Bond consumes two goods: vodka (x) and martini (y). His preferences are described by the utility function U(x,y) = (1x+9)y. Calculate the value of the marginal rate of substitution in the point (2;2). Please use 2 decimals in your answer.Consider a consumer whose utility function is (screenshot) Assume the consumer has income $120 and initially faces the prices px=$1 and py=$1. How much x and y would they buy? Draw the budget constraint and the demands.Please no written by hand solution
- 1) Max chooses to purchase movie tickets and restaurant meals every week with his $100. If the price of a movie ticket is $20 and the price of a restaurant meal is $25, then the slope of his budget constraint will be, a) 1/5 b) -1/5 c) 4/5 d) -4/5 2) Marginal rate of substitution(MRS) is the rate at which consumer is willing to trade one good for another. It must be true that: a) MRS is the slope of an indifference curve in reference to a particular bundle of goods. b) MRS is not the same along an indifference curve that is of usual shape. c) MRS is same along an indifference curve that is of usual shape. d) Both a) and b).1 FOOD STAMPS Consider a person who has $750 per month in income and has preferences for food (F) and all other goods (X) represented by a utility function, U(F, X) = F⁰.2 X0.8. To simplify analysis, let's assume that both the price of food and the price of all other goods is $1 per unit such that F and X represent expenditure on food and all other goods, respectively. a. Set up a Lagrangian and derive the consumer's demand functions for food and all other goods. As you are solving, make sure you can explain each step in words. b. Now solve for the demand functions using the "substitution approach" whereby we sub- stitute the constraint directly into the objective function. Show that the resulting demand functions are the same as in part (a). c. What is the consumer's optimal bundle given the prices and income? How much utility does the consumer derive from this bundle? Now assume that the government introduces a Food Stamps program that gives this con- sumer $250 that she can only…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.
- A student has a lunch utility function U(S, P) 8S + 3P, where S is number of salads per month and P is number of pizzas per month. The price of a salad is $5, the price of a pizza is 8, and his monthly income for lunch is $80. a) Derive the equation representing the consumer's demand for Salad. Represent the demand for Salad graphically. b) The price of Salad goes up to $25 and the price of Pizza does not change. Compute and represent graphically the new equilibrium of the student. What can you tell about the substitution effect on Salad and pizzaAlice 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.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…
