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Indifference Curves and budget lines

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Given the following information, DESCRIBE the budget line for the consumer: Be sure to state what the axes are and provide numbers for the vertical and horizontal intercepts. Also what is the slope of the line? Explain what the budget line represents.

Income =$1000/ month
Price of 1 pound of steak = $4.00
Price of 1 pound of potatoes = $0.50

Now, "overlay" several indifference curves onto the picture. Describe the shape of these curves -- why are they that shape. How can you find the utility-maximization point. Describe why other points on some indifference curves do not represent utility-maximization. NOTE: You are not required to submit graphs as part of any answer. You can explain any relationship that are contained in almost every graph.

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Total Income = 1000
Steak = $4

Budget Line:
1000 = 4Steak + 0.5Potatoes

X axis will represent the number of pounds of Steak
Y axis will represent the number of pounds of potatoes

So if we assume pounds of steak to be X and pounds of potatoes to be Y, we get
1000 = 4x ...

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Indifference Curve, Budget Line & Optimal Utility

A household's utility over two consumption goods x and y is U= U(x,y) = xy.

1. Describe the household's indifference curve for U = 1 for values of x and y less than 3 (ie. the curve containing all combinations of x and y such that U(x,y)=1.

Now assume that the household's wealth is w=4 and that the prices of the goods are px = 2 and py = 2.
2. How many units of x can the household consume at most if it does not consume any y?
3. Describe the household's budget line and its relationship to the indifference curve.
4. What is the household's optimal consumption bundle?
5. What is the Marginal Rate of Substitution (MRS) between the two goods?

Note the budget constraint can be written as 2x + 2y = 4

6. Solve this budget constraint for y and substitute it into the utility function to obtain an expression for utility that depends on x only.
7. Maximize this utility to obtain the optimal amount of x. (Take the derivative of this expression with respect to x, set the derivative equal to zero, solve for x)
8, Find the optimal amount of y by using the result for x.
9. How does this optimal consumption bundle compare to the one found graphically.

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