6. 6 A) If a consumer has a certain income and at this level of income the consumer prefers to purchase 50 units of y and 0 units of X, if the price of good Y is $10, then the consumers income is $10 units of Y. disposable income = $10 y = $10 50 = $500. B) If the same consumer wished to purchase 40 units of X and 0 units of Y, the price of good X would be disposable income divided by the number of units to be purchased.
Cost of good X = disposable income / units of X = $500/40 = $12. 5 C) The equation for the budget line is calculated using the prices for each good and the disposable income. The disposable income is equal to the cost of good X multiplied by the amount of X purchased, plus the cost of good Y multiplied by the amount of Y purchased. To find the equation of the budget line, solve for Y.
$500 = $10 Y+$12. 5 X$10 Y = $500-$12. 5 XY = $500/$50-$12. 5/$10 XY = $50-$1. 25 XD) The consumer would choose the point where the budget line is tangent to the highest possible utility or indifference curve.
This would be the utility function II. The lines are tangent at X = 20 and Y = 25. This combination maximizes consumption with available income. E) The marginal rate of substitution measures the number of units of Y a consumer will give up per additional level of X, holding the utility constant.
This is the point of utility maximization. Where the budget line and the indifference curve are tangent. The highest level of utility with the given budget line is achieved with X bar units of X and Year units of Y. MRS = Absolute Value of -aY/aX (this is the absolute value of the slope of the indifference curve).
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MRS = |-12. 50/10.
00| = 1. 25 F) At point A- the consumer can give up one unit of X for 1, 25 more units of Y and utility will not change. Consumers can buy Px/Py more units of Y if 1 less unit of X is purchased on this budget line. This is more Y than is needed to be indifferent (Px/Py>MRS).
Giving up one unit of X to get 1. 25 more units of Y must increase utility.
At point B- Consumers would give up 1. 25 units of Y to get 1 more unit of X and remain on the budget line, utility remaining unchanged. Px/Py.