Suppose Alex has the following utility function defined over goods x and y. U (x, y) = xy +10x a. Write out the expression for his indifference curve with y in terms of x and U. b. Assume Alex's current level of utility is U = 80 and plot the indifference curve for this level of utility for values of x between 2 and 12. c. Suppose Alex has $30 to spend on these two goods and x costs $5 per unit while y costs $1.00 per unit. Add Alex's budget constraint to your graph. Visually determine the combination of these two goods that Alex will purchase. d. Write the expressions for the marginal utilities of each good and the marginal rate of substitution between the two goods. Write out the expression for the slope of the indifference curves. Does the MRSxy equal the negative of the expression for the slope? e. Now suppose that the market conditions change, and the price of good y rises dramatically to py = $5, while all else remains unchanged. Add this budget line to your graph. f. Since Alex is faced with a higher price for y, we know that he will not be able to enjoy the same level of utility as he did before the price increase. How do we know this?

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MRTS reaches a manufacturer when a part of the product is lowered to sustain the manufacturing level when the other part is extended. It is the level of the quantity that is lowered when one extra volume is used, and the output is unchanged.

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Before understanding what is preference and utility analysis, it is very important to understand the terms preference and utility separately.