Chapter 4 Key Fall 07

Chapter 4 Key Fall 07 - Chapter 4 Homework Due: September...

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Chapter 4 Homework Due: September 14, 2007 1. Suppose a consumer only purchases strawberries and bananas. The price of strawberries is $4 per pound and the price of bananas is $1 per pound. The consumer has an income of $100. a. Write the budget constraint and draw it in the space provided. What is the cost of strawberries and bananas? (remember opportunity cost) The constraint is 100 = 4S + B where S is pounds of strawberries and B is pounds of bananas. bananas strawberries 25 100 The slope is the opportunity cost of bananas and the inverse of the slope is the opportunity cost of strawberries. Therefore, the one pound of bananas cost one quarter of a pound of strawberry and one pound of strawberries cost 4 pounds of bananas. 1
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b. Suppose the price of bananas increases to $2 per pound. Draw the new budget constraint. What has happened to the cost of bananas and strawberries? bananas strawberries 25 100 50 The budget constraint rotates inward around the y axis. The slope is now one half. Therefore, a pound of bananas costs one half of a pound of strawberry while one pound of strawberry costs 2 pounds of bananas. Bananas are now more expensive while strawberries are less expensive. Always remember that if one price changes, the relative price of all goods change. 2
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Let income I = $80, P x = 1, P y = 3 and utility U = x + y. a. Compute the optimal consumption bundle for this consumer. The slope of the budget line is 1/3. The indifference curve is downward sloping with a slope of 1. We know it is downward sloping because utility increases with more x or y. Therefore, the assumption of more is preferred to less is satisfied for both and the indifference curve slopes downward. However, the slope of the indifference curve is constant. The marginal utility of both x and y are 1 which makes the MRS equal to 1. Therefore, the indifference curve is downward sloping and linear. This is a case of perfect substitutes. Given the slope of the budget constraint is 1/3, the MRS will always be greater no matter how many units of x are consumed. Therefore, the consumer will choose only x and no y and will be in a corner solution. Another way to look at the problem is to realize that when we increase x or y by one unit, utility increases by one unit. In other words one unit of x yields the same level of additional satisfaction as one unit of y. However, y costs 3 times x. As a result, the bang for the buck is always greater when spent on x rather than y. 3
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Chapter 4 Key Fall 07 - Chapter 4 Homework Due: September...

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