Paul's utility function is Cobb-Douglas. U = B0.2Z0.8, where his income is Y, the price of B is Pg, and the price of Z is Pz. What is Paul's Engel curve for B and Engel curve for Z? What does the shape of Engel curve say about Z? a) b) What is Paul's income consumption curve when PR = 1 and P, = 1? Calculate and graph it on Paul's consumption diagram. What does the shape of income consumption curve say about B and Z? c) What is Paul's demand for B when Y = 100, P, = 1? Calculate and graph it. How would this curve change if Paul's income increases?

Paul's utility function is Cobb-Douglas. U = B0.2Z0.8, where his income is Y, the price of B is Pg, and the price of Z is Pz. What is Paul's Engel curve for B and Engel curve for Z? What does the shape of Engel curve say about Z? a) b) What is Paul's income consumption curve when PR = 1 and P, = 1? Calculate and graph it on Paul's consumption diagram. What does the shape of income consumption curve say about B and Z? c) What is Paul's demand for B when Y = 100, P, = 1? Calculate and graph it. How would this curve change if Paul's income increases?

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter10: Consumer Choice Theory

Section: Chapter Questions

Problem 6P

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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?
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…
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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.
Ann consumes two goods, a and y. Her utility function is given by: u(x, y) = (x+1)G. The price of a is $4 per unit and the price of y is $ per unit. Ann's income is w. (a) * ) Nrite down an expression for Ann's budget line. (b) v- 'Determine the formula for Ann's marginal utility of a, and the formula for Ann's marginal utility of y. (c) ( » For each income level w > 0 calculate Ann's optimal consumption bundle. (d) For which income levels w is bang-for-buck equalization violated at Ann's optimal consumption bundle? Explain. , Assume that w = 2. Draw Ann's budget line in a figure with r on the hor- izontal axis. Add 2 indifference curves of Ann, including the indifference curve that contains Ann's optimal consumption bundle. Indicate Ann's optimal consumption (e) - bundle.
A consumer has a utility function U(X,Y ) = X1/2 Y1/2 . Prices of the goods are pX = £10 and pY = £5, respectively, and the consumer has income M = £200 to spend on X and Y. Currently, she buys 2 units of good X and spends the rest of her income on good Y.a) Determine this consumer’s current utility level. b) Computetheconsumer’smarginalutilitiesofgoodsXandY. c) Explain why the consumer’s current consumption of goods X and Y is not optimal. Should she substitute X for Y or vice versa? The consumer’s marginal rate of substitution is MRS = Y/X.d) Determine this consumer’s optimal consumption of both goods. e) By how much does the consumer’s utility increase when she consumes the optimal bundle?
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Q.7 A consumer's utility function is given by the expression: U = (0.6Xx5 + 0.4Y5). • 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.
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Q.7 A consumer's utility function is given by the expression: & = (0.6.x"s + 9.47"s}. 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.
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1 Alice has a monthly lunch budget of 360 dollars which she spends on either burgers (B) or pizza (Z). The price of each pizza is 16. dollars and the price of each burger is 8 dollars. Alice's utility is given by: u(B, Z) = B'/2 +4Z!/2 + 47!/2 a) Find Alice's budget constraint. Set up the Lagrangian and find her optimal consumption. What is her new consumption if the price of burgers becomes 16 dollars?