2. Suppose there are n identical consumers, each with a utility function u(x, y): = ax = x²+y.Each consumer has different disposable income w. The price of good x is p dollars, and theprice of composite good y is equal to 1 dollar. Assume a > 0 and b > 0. (Hint: Question 1)(a) Calculate the marginal utility of good x and good y. Then, calculate the marginal rateof substitution between good x and good y.(b) Calculate the individual demand of consumer 1 for good x.(c) Calculate the aggregate demand for good x.(d) Draw a graph showing the market demand curve for good x.(e) Discuss whether an increase in disposable income for each consumer lead to an increasein the consumption of good x? This increase in disposable income can result fromvarious factors, such as a decrease in taxes, government stipends, or other forms ofincome support.(f) Discuss the effect on demand for good x if there is an increase in the price of good x.This increase in the price of good x can result from various factors, such as productioncost increases, supply shortages, increased demand for inputs, tax increases for the good,or regulatory changes.

The objective of the question is to understand the consumer behavior in terms of utility, demand,…

Answered: 2. Suppose there are n identical…

ENGR.ECONOMIC ANALYSIS

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Publisher:NEWNAN

Chapter1: Making Economics Decisions

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b. A consumer purchases two goods, the amounts of which are x and y. Her marginal utility of consuming good x is Ux , while that of consuming good ? is Uy. If the two marginal utility functions are given by Ux = y2 + 2xy and Uy = 4xy + 3x2 − 3 and the consumer is known to stay on the same utility curve, find the total utility function of this consumer buying the two goods
Consider the single-good utility function u(x) = 3x². du(x) a) Find the marginal utility of x, MUx = dx b) Plot the utility function and marginal utility function on two separate graphs. c) Does this utility function satisfy the law of diminishing marginal utility? Explain.
1. Consider a consumer who consumes two goods. The utility function is given by u(x1, x₂) /2x1+1+√√√x₂, - where x > 0 denotes the amount of good i = the price of good 1 is 3, the price of good 2 is p2 > 0, and the income is 12. 1,2 consumed. Unless stated otherwise, (1) Calculate the marginal rate of substitution (measuring the value of good 1) at the consumption plan (x₁, x₂) = (3, 4). (2) Calculate the consumption plan that is optimal for the consumer. (3) Let v(p₂) denote the utility level at the optimal consumption plan. Calculate its derivative with respect to p2, i.e., v'(P2), at p2 = 3. (4) Suppose that p2 = 1 and the utility level is 10. Calculate the compensated demand for each good.
3*. Ms Smith likes to drink wine; in particular, a french bordeaux (f) at $40 per bottle and a California varietal wine (c) priced at $8. She allocates $600 to these two each month; and her utility is: U(ƒ, c) = ƒ²/³ c¹/³ (a) Write out her (constrained) utility maximization problem. Solve for the optimal consumption of wine f and c.
Give only typing answer with explanation and conclusion to all parts Martina’s preferences are represented by u(x , x ) = x2 + x3 , where x > 0, x > 0. (1) What is the marginal utility of good 1 at (x1, x2)? (2, 3)? (2) What is the marginal utility of good 2 at (x1, x2)? (3, 2)? (3) What is the marginal rate of substitution of good 2 for good 1 at (x1, x2)? (2, 2)? (4) Redo (1),(2),(3) for another representation v(x1,x2)=ln(x^1/2 +x^(1/3).)
A consumer consumption bundle contains good X and Y. Suppose the price of good X goes up and a consumer goes on consuming the exact same amount of X as before. Check the correct statement(s).A) Both X and Y are inferior. B) X is an inferior good.C) In the special case where X is Leisure, and Y is "all other goods", X is an inferior good.D) The consumption of Y decreases.E) It is impossible that the consumption of X remains unchanged when the price of × goes up.F) The substitution effect is negative
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
A consumer has utility (see image) on ice creams (x) and cakes (y). (a) Are the indifference curves bowed towards the origin? (b) Derive his demand function (as a function of prices px, py and budget I) for ice cream (x). (c)(Looking at the demand function you found in (b), Is ice cream a normal good? Are ice cream and cakes substitutes or complements? Calculate the income elasticity of market demand at the point px = 2, py = 1 and I = 12.
Consider a consumer whose preferences are given by the utility function U (x, y) = (x + 1)² (y + 1)where x and y are the quantities he consumes of goods x and y and the prices of good x and good y are p, and p, respectively and his income is m. Assume that p, is twice of p,. The demand function of good x (p,, m) is (а) т Зр, 2m (b) Зр, (c) 3p. 2m (d) 3p, (e) None of the above.
Description 1. Suppose the utility function for goods x and y is given by utility = U(x, y ) = xy + y. a. Calculate the uncompensated (Marshallian) demand functions for x and y, and describe how the demand curves for x and y are shifted by changes in I or the price of the other good. b. Calculate the expenditure function for x and y. c. Use the expenditure function calculated in part (b) to compute the compensated demand functions for goods x and y. Describe how the compensated demand curves for x and y are shifted by changes in income or by changes in the price of the other good.
3) The utility function of a consumer who consumes quantities x and y of two goods is defined by the expression U(x, y)=√xy subject to the constraint 7x+3y=84 where $84 is the consumer's overall budget. Assuming marginal utilities U,,U>0, maximize the utility function of the consumer. What are the optimal values of x, y and U(x,y) ?

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