Part 4 5 6 needed David’s utility function for good X and Y is given by U (x, y) = x2 y3 . Where Px, Py and I are the price of good X, price of good Y and consumer income respectively. i. Write the budget equation of the consumer and draw the line of this equation. ii. Using the budget line drawn in (i) show the effect of a 100 percent increase in the price of good X hold the price of good Y and income constant. iii. Using the budget line drawn in (i) show the effect of a 100 percent increase in his income holding the price of both goods constant. iv. What combination of X and Y maximizes the consumer’s utility at I=100, Px = 4 and Py = 5. v. Calculate the marginal rate of substitution between X and Y at equilibrium and interpret your results vi. Suppose all prices double and income is held constant, what is the effect of this on the optimal combination of X and Y? vii. What happens to the optimal combination of X and Y if price of good X decreases to 2 whiles the price of good Y and income remain unchanged?
Part 4 5 6 needed David’s utility function for good X and Y is given by U (x, y) = x2 y3 . Where Px, Py and I are the price of good X, price of good Y and consumer income respectively. i. Write the budget equation of the consumer and draw the line of this equation. ii. Using the budget line drawn in (i) show the effect of a 100 percent increase in the price of good X hold the price of good Y and income constant. iii. Using the budget line drawn in (i) show the effect of a 100 percent increase in his income holding the price of both goods constant. iv. What combination of X and Y maximizes the consumer’s utility at I=100, Px = 4 and Py = 5. v. Calculate the marginal rate of substitution between X and Y at equilibrium and interpret your results vi. Suppose all prices double and income is held constant, what is the effect of this on the optimal combination of X and Y? vii. What happens to the optimal combination of X and Y if price of good X decreases to 2 whiles the price of good Y and income remain unchanged?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Part 4 5 6 needed
David’s utility function for good X and Y is given by U (x, y) = x2 y3 . Where Px, Py and I are the price of good X, price of good Y and consumer income respectively.
i. Write the budget equation of the consumer and draw the line of this equation.
ii. Using the budget line drawn in (i) show the effect of a 100 percent increase in the price of good X hold the price of good Y and income constant.
iii. Using the budget line drawn in (i) show the effect of a 100 percent increase in his income holding the price of both goods constant.
iv. What combination of X and Y maximizes the consumer’s utility at I=100, Px = 4 and Py = 5.
v. Calculate the marginal rate of substitution between X and Y at equilibrium and interpret your results
vi. Suppose all prices double and income is held constant, what is the effect of this on the optimal combination of X and Y?
vii. What happens to the optimal combination of X and Y if price of good X decreases to 2 whiles the price of good Y and income remain unchanged?
Expert Solution
Step 1
The graphical representation of the utility function is known as the indifference curve.
The indifference curve shows the combination of two goods that give the same utility to the consumer.
If the utility function is Cobb Douglus, then indifference curve is convex in shape and consumer consume some units of both the good.
If the utility function is linear, then indifference curve is downwad sloping straight line and consumer consumeonly one good.
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