2. Think about a consumer with a utility function of U(x,y) =2xy+1, his budget constraint is px*x +py*y = m. а. Please derive the Marshallian demand functions. What would happen to the demand of each good if m increases(assume price positive)? Are they normal good or inferior good? Please derive the indirect utility function. b. С. Dloace dorivo th e oxnon uro function
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- 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.1..Calculate the optimal quantity of each of two goods (x and y) and the consumers’ total utility given Px=1, Py=2, I=80, and U(x,y) = x1/2y. How would you represent this graphically? What is value of the utility received by consumer at optimal consumption? Explain all your steps. N.B. You can attach your explanations1.Let x and y denote the amount of goods X and Y. Find the demand functions of X (do not need to find that of Y) when your preferences are represented by the utility function U = x^2y. Is X normal good? Can you confirm law of demand for X? What is the relationship of X with Y? Answer all of them by using the demand curve you derived. 2.Let x and y denote the amount of goods X and Y. Find the demand functions of X (do not need to find that of Y) when your preferences are represented by the utility function U = x + xy + y. Is X normal good? Can you confirm law of demand for X? What is the relationship of X with Y? Answer all of them by using the demand curve you derived 3.There are two goods F and C. Let MU and P denote marginal utility and price of each good. SupposeMUF = 3, MUC = 4, PF = 2, PC = 2.Are you maximizing your satisfaction? If not, what would you do to increase your satisfaction? Explain.
- 1. An agent consumes quantity (X1,X2) of goods 1 and 2. Here is his utility function: U (x1,x2) = x13x2, his budget constraint is: p1x1+p2x2=m. (a) Calculate the agent's Marshallian demand (x*, x*2). (b) Derive the agent's expenditure function. (c) Roy's identity for good 1 states that: aV(pl,p2, m)/ х1* 3 дV (р1, р2, т) am Verify this equation (you need not verify it for good 2).1. A consumer has a utility function defined over two goods X and Y. Let the quantity of Good X be x ≥ 0 and the quantity of Good Y be y ≥ 0. The utility function is given below: u(x, y) = xy + 2y. Assume that the consumer has income m and that prices are px and Py.5. Suppose the utility function for goods x and y is given by U (x, y) = xY + y (i). 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. (ii). Calculate the expenditure function for x and y. (iii). 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.
- There are two goods in an economy: apples (a) and bananas (b). Price of anapple is $1 and price of a banana is $2. Your income is $10. Suppose your utility function isu(a, b) = 2a2 b+5a. (8 points) How many apples and bananas will you consume?b. (4 points) Are a and b normal or inferior goods?c. (4 points) Are a and b substitutes or complements?d. (4 points) Draw the Engel curve for apples for the income levels ranging from $10, $20,$30 and so on.1) Explain the following: i. UTILITY ii. UTILITY FUNCTION iii. LAW OF DIMINISHING MARGINAL UTILITY. iv. Given a consumer has a money budget M = 360 and utility function U(X, Y)=X^(3/4)Y^(1/4). If she consumes two goods x and y with prices given by Px=10 and Py=30. Find the QUANTITIES of X and Y that MAXIMIZE her utility.1.There are two goods F and C. Let MU and P denote marginal utility and price of each good. SupposeMUF = 2,MUC = 1,PF = 1,PC = 2.Are you maximizing your satisfaction? If not, what would you do to increase your satisfaction? Explain. 2.What is the substitution effect? Can it cause the quantity to decrease given a decrease in price? Explain 3.What is the income effect? Can it cause the quantity to decrease given a decrease in price? Explain
- Moe's income is $320 per week and he spends it on two goods, X and Y. Good X costs $8 and good Y costs $4 per unit. His utility function is U = 4.5XY. (a) Calculate Moe's utility-maximizing purchases of X and Y. (b) Calculate Moe's constrained utility- maximum if his income decreases by $2.00? (c) If the price of Y doubles, with no change in the price of X, by how much would his income have to increase to enable him to maintain his initial level of utility (as in part (a) above)?a. Determine the demand functions of x and y in the case of a Cobb-Douglas type utility function, in the following cases: α=0.40;β=0.60 Graph the demand functions of the two goods (price as a function of quantity) assuming the individual's income is $500 - Determine what is the quantity demanded of x and y, if the price of good x is USD 1, the price of good y is USD 4, and income is USD 500 - Now, explain what happens to the quantity demanded if the prices of the goods are doubles holding income constant.1.a Assume that a person’s utility function is given by the following function: ??=3?^(2/3)?^(1/3) Assume also that the price of X is £3, and the price of Y is £3 and that the budget is £45. What is the optimal amount of goods X and Y that should be purchased with this budget? b) Assume now that the price of good X is PD, while all other conditions remain the same. Find the optimal amount of good X that should be purchased for a generic price PD. In other words, find the individual demand function for good X. 1.b Assume now that the price of good X is PD, while all other conditions remain the same. Find the optimal amount of good X that should be purchased for a generic price PD. In other words, find the individual demand function for good X.