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.

Solution Preview

1. The curve will be azymptotic to both axes. It will pass through the points (1/3,3), (1/2,2), (1,1), (2,1/2), (3,1/3), etc.

2. 2 units of x

3. It will connect the points (0,2) and (2,0). It will be tangent to the ...

Solution Summary

This solution shows how to find a household's optimal consumption bundle algebraically and graphically.

... getting on furthest out on indifference curve that touches ...Indifference curves are shown by pink lines on the ... be maximized when it touches budget line at (0 ...

... What is Thurston's optimal consumption choice? ... Then, the budget line is 40P+20G=80 The utility of the sweaters will be U=P+G Indifference curve will be P+G ...

... of substitution (slope of their indifference curves) = (dU/dx1i ... slope of consumer 1's budget line is then ... maximizing point, his indifference curve is tangent to ...

... points correspond to tangency of the highest possible Indifference Curve with the Consumer's budget line. ... 2, there are two kinds of demand curves that can ...

... of bagels and wine is the point where the Indifference Curve is tangential to the budget line. ... Sally's indifference curves are shown as above. ...

budget constraint, indifference curve. ... This is indicated by the budget line in picture q1.jpg. ... bundles are indicated on the graph, with indifference curves drawn ...

... A budget line depicts graphically the set of goods that a person ... at (12,12) we know that her indifference curve is tangent to the budget constraint at ...

... Notice that the budget constraint cuts the vertical ... the direction in which the indifference curves represent higher ... shape of the price offer curve is exactly ...