Question 2. [Utility Maximization and Cross Price Effects]Suppose the utility function for goods x and y is given byutility = U(x, y) = xy + xa)$) Calculate the uncompensated (Marshallian) demand functions for x and y, and explainhow I(= income) or other good's price would affect the demand for x and y.b) (i) Calculate the indirect utility function and the expenditure function for x and y.c)s) Calculate the compensated (Hicksian) demand functions for x and y using theexpenditure function from b) above and Shephard's lemma, and explain the effects of income orother good's price on the demand for x and y.

Utility maximization refers to making economic decisions that guarantee the greatest level of…

Suppose the utility function for goods x and y is given by utility = U(x, y) = xy + x a) Calculate the uncompensated (Marshallian) demand functions for x and y, and explain how I( income) or other good's price would affect the demand for x and y. b) () Calculate the indirect utility function and the expenditure function for x and y. c) ( s) Calculate the compensated (Hicksian) demand functions for x and y using the expenditure function from b) above and Shephard's lemma, and explain the effects of income or other good's price on the demand for x and y.

Suppose the utility function for goods x and y is given by utility = U(x, y) = xy + x a) Calculate the uncompensated (Marshallian) demand functions for x and y, and explain how I( income) or other good's price would affect the demand for x and y. b) () Calculate the indirect utility function and the expenditure function for x and y. c) ( s) Calculate the compensated (Hicksian) demand functions for x and y using the expenditure function from b) above and Shephard's lemma, and explain the effects of income or other good's price on the demand for x and y.

Principles of Economics 2e

2nd Edition

ISBN:9781947172364

Author:Steven A. Greenlaw; David Shapiro

Publisher:Steven A. Greenlaw; David Shapiro

Chapter6: Consumer Choices

Section: Chapter Questions

Problem 10RQ: What is the rule relating the ratio of marginal utility to prices of two goods at the optimal...

See similar textbooks

Similar questions

Quèstion 21 "Considering that Salah is tending to buy X and Y, reaching equilibrium may be achieved if." O He consumed the same quantities from X and Y Marginal utility of expenditure for good X equals marginal utility of expenditure for good Y O Marginal utility for good X equals marginal utility for good Y O Total utility for good X equals total utility for good Y
What is the rule relating the ratio of marginal utility to prices of two goods at the optimal choice? Explain why, if this rule does not hold, the choice cannot be utility-maximizing
2. [This question shows that our marginal utility calculations for consumer behav- ior essentially do not depend on which utility we use to represent preferences, even though the marginal utilities themselves do.] Suppose u: X→ R is differentiable at some r E X, with strictly positive marginal utilities. Let f: R→ R be a function with strictly positive derivative; let u fou. (In particular, u and u represent the same preferences because f is strictly increasing.) = (a) Show by example that the marginal utility for good 1 could be different under u and under u. (b) Show that the ratio MU() is the same for utility u as it is for utility u. MU₂ (1)
12)Suppose a consumer has $100 to spend on two goods, shoes and shirts. If the price of a pair of shoes is $20 per pair and the price of a shirt is $15 each, which of the following combinations is unaffordable to the consumer? A) 0 pairs of shoes and 0 shirts B) 2 pairs of shoes and 4 shirts C) 5 pairs of shoes and 0 shirts D) 0 pairs of shoes and 7 shirts E) 2 pairs of shoes and 3 shirts
1.(a) Derive own-price elasticity of demand (eii), income elasticity of demand (hi) and cross-price elasticity of demand (eij) for the Cobb-Douglas Utility Function. (b) With respect to Cobb Douglas preferences, what happens to the demand for each of two products (x and y) when the price of product y increases, as a result of: (i) the substitution effect; (ii) the income effect; and, (iii) the overall price effect?
QUESTION 14 If two goods are substitutes, then a(n) A increase in the demand for one of them will cause its price to fall B. increase the supply of one of them will cause its price to rise C. increase in the price of one of them will cause the demand for the other to increase D. increase in the price of one of them will cause the supply of the other to increase decrease in the price of one of them will cause the demand for the other to increase E. QUESTION 15 If the supply of coffee falls due to bad weather conditions in coffee-exporting countries, then the A price and quantity will rise B. price and quantity will fall C. price will fall and quantity will rise price will rise and quantity will fall quantity will fall, but price may rise or fall
6. Determinants of price elasticity of demand Consider some determinants of the price elasticity of demand: The availability of substitutes • The market used to measure demand • The share of budget spent on the product • The time horizon being considered A good without any close substitutes is likely to have relatively the price of the good rises. The price elasticity of demand for a good also depends on how broadly the good is defined. Organize the goods found in the following table by indicating which is likely to have the most elastic demand, which is likely to have the least elastic demand, and which will have a demand elasticity that falls in between. Categories Most Elastic In Between Least Elastic Beverages Wine Merlot demand, because consumers cannot easily switch to a substitute good if Price elasticity for a good also depends on the share of a consumer's budget spent on a good. Other things being equal, which of the following goods has the most elastic demand? TV and Internet…
2. Which of the following statements is (are) correct? (x) If the coefficient of cross-price elasticity of demand is 1.4, then the two goods are substitutes and the response to a price change is elastic. (y) If the coefficient of cross-price elasticity of demand is equal to one, then the two goods are substitutes and a price increase of ten percent for one good will cause the quantity purchased of the other good to increase by ten percent. (z) If the coefficient of cross-price elasticity of demand for a particular good is equal to negative 0.85, then the two goods are complements and the response to a price change of the other good is elastic. A. (x), (y) and (z) C. (x) and (y) only (y) and (z) only (x) and (z) only Е. (х) only D.
5. The elasticity of substitution will be a lower number: (a) The less curved is the indifference curve (b) The more curved is the indifference curve (c) The greater the income elasticity of demand of the good on the horizontal axis (d) The greater the degree of substitutability between the two goods (e) If tastes are both homothetic and quasilinear
Question 13 The marginal rate of substitution between two goods always equals the O price of one good divided by the price of the other All of the above are correct marginal utility of one good divided by the marginal utility of the other good marginal utility of one times the marginal utility of the other
14. Determinants of Supply and Demand Consider the market for electric cars. Assume electric cars are a normal good. For each of the following events, identify which of the determinants of demand or supply are affected. If demand is unaffected by this event because it creates only a supply change, select the "None" option under the "Demand Determinant column. Similarly, if supply is unaffected by this event because it creates only a demand change, select the "None" option under the "Supply Determinant" column. Event Demand Determinant Supply Determinant Engineers develop new automated machinery for the production of electric cars. People increase their concern for the environment. An economic boom raises people's wealth. A strike by aluminum workers raises the price of aluminum. The price of gas-powered cars falls. Show the effect of the following event on the market for electric cars: Engineers develop new automated machinery for the production of electric cars. Supply Demand Supply…
10. (ch5) For Sara, ramen noodles are a normal good, however Sean considers ramen noodles to be inferior. If Sara and Sean have the same amount of income, Sean's demand for ramen noodles will be less price elastic than Sara's. Please explain why in detail using the substitution effect and income effect graphs. I