Microeconomics (9th Edition) (Pearson Series in Economics)
9th Edition
ISBN: 9780134184241
Author: Robert Pindyck, Daniel Rubinfeld
Publisher: PEARSON
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Chapter 4.A, Problem 3E
To determine
The change in
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A consumer has the following demand function for good 1: x1 = (1/4)(m/p1) The original price of the good is $2 and the consumer’s income is $200. Calculate the substitution effect, the income effect and the total effect for this consumer, when the price of good changes to $1.
Harry consumes 2 goods, X and Y and he spends N$60 per month. The price of good X is N$4
and the price of good Y is N$10. Harry's utility function is U(X, Y) = XY.
(i) What is Harry's marginal rate of substitution? (5)
(ii) What is the expression for Harry's budget constraint? (3)
(iii) What is the slope of Harry's budget constraint? (2)
(iv)Find the values of good X and Y maximizes Harry's utility. Show all your work. (6)
(v) Illustrate Harry's utility maximizing combination on a clearly labelled graph. (4)
(vi) Suppose the price of good X increased to N$6. Illustrate Harry's income and substitution
effects on a well labelled graph. Show your work. (10)
(vii) Suppose Genie is consuming two goods, coffee and beer. She spends all her income on
a combination of coffee and beer where MUcoffee/Peoffee is 5 and MUbeer/Pbeer is 3.
Explain why this combination is not maximizing her satisfaction. What should she do
to maximize her utility? (5)
0.8 A consumer's utility function is given by the expression:
U = (0.6X0.5 +0.4Y0.5) ².
Determine the marginal utility functions for each commodity.
Does marginal utility decrease when consumption increases?
Assuming that the price of good X is Rs 15 and the price of
Y is Rs 6, write the equation of the budget line and plot it
when income is Rs 450. What is its slope? What does it
indicate?
Calculate the marginal rate of substitution of Y for X and
interpret its economic meaning. Write the equation showing
consumer's equilibrium condition.
Obtain the equilibrium values of X and Y.
Find the expressions for change in MUx due to increase in Y
and change in MUy due to increase in X.
Chapter 4 Solutions
Microeconomics (9th Edition) (Pearson Series in Economics)
Ch. 4.A - Prob. 1ECh. 4.A - Prob. 2ECh. 4.A - Prob. 3ECh. 4.A - Prob. 4ECh. 4.A - Prob. 5ECh. 4 - Prob. 1RQCh. 4 - Prob. 2RQCh. 4 - Prob. 3RQCh. 4 - Prob. 4RQCh. 4 - Prob. 5RQ
Ch. 4 - Prob. 6RQCh. 4 - Prob. 7RQCh. 4 - Prob. 8RQCh. 4 - Prob. 9RQCh. 4 - Prob. 10RQCh. 4 - Prob. 11RQCh. 4 - Prob. 12RQCh. 4 - Prob. 1ECh. 4 - Prob. 2ECh. 4 - Prob. 3ECh. 4 - Prob. 4ECh. 4 - Prob. 5ECh. 4 - Prob. 6ECh. 4 - Prob. 7ECh. 4 - Judy has decided to allocate exactly 500 to...Ch. 4 - The ACME Corporation determines that at current...Ch. 4 - Prob. 10ECh. 4 - Prob. 11ECh. 4 - Prob. 12ECh. 4 - Prob. 13ECh. 4 - Prob. 14ECh. 4 - Prob. 15ECh. 4 - Prob. 16E
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- Recent research confirms that the demand for cigarettes is not only inelastic, but it also indicates that smokers with incomes in the lower half of all incomes respond to a given price increase by reducing their purchases by amounts that are more than four times as large as the purchase reductions made by smokers in the upper half of all incomes. How can the income and substitution effects of a price change help explain this finding?arrow_forwardFor the utility function, U = 2x1/2 + y What are the income and substitution effect of price changes in Px and Py respectively?arrow_forwardConsider the following utility function that expresses the preferences of any consumer for good x and good U(x, y) Min {2x, y) Consider that the price of x is $4, the price of y is $2, and the income R is $100. Reply: a) What is the marginal rate of substitution for x? b) What is the marginal rate of substitution for y? c) What is the expression of demand ( demand function) of x? d) What is the demand expression (demand function) for y? e) What is the basket composition that maximizes this consumer's satisfaction given the given restriction? f) What is the utility achieved with this basket?arrow_forward
- Suppose that we have a utility function involving two goods that is linear of the form U(x, y) = ax + by. Calculate the expenditure function for this utility function. Hint: The expenditure function will have kinks at various price ratios.arrow_forwardAlice 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.arrow_forwardSuppose the weighted marginal utility for two goods x and y at a position of consumer equilibrium 70. If the price of good x is r10 and the relevant marginal utility for y is 140 what is the price of good y and the relevant marginal utility for xarrow_forward
- Please answer this question with steps thank youarrow_forwardA 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 pizzaarrow_forwardDefine 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.arrow_forward
- Individual that consumes two goods (X and Y) and has a CES Utility Function of the form: U = 100(X^(0.75) + Y^(0.75)). Income of 1000, the price of Good X is 10 and the Price of Good Y is 20 a) Find the Marginal Rate of Substitution as a function of the quantities consumed of Good X and Good Y. b) Write out the Lagrangian for this problem. c) Solve to find the demand for Good X, the demand for Good Y, and the highest level of utility for this individual. d) Now consider an increase in the price of Good X to 20. What is the demand for Good X and Good Y? What is the Utility of the consumer following the price change? e) Considering the change in demand for each good between parts c) and d), how much is due to the substitution effect and how much is due to the income effect? f) Show your answers on a graph.arrow_forwardPlease answer fastarrow_forwardUtility = XY + 3X. If prices of X and Y are Birr 4 and Birr 2 respectively; and if a consumer has an income of Birr 80: Find the consumer equilibrium point. Find value of marginal rate of substitution at equilibrium pointarrow_forward
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