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Question #49107
min E=px 3⁄4 x^4+py 3⁄5 y^3 and x^0,6 y^0,4≥U_p
A) Does the above model support the monotonic transformation? Why?
B) Explain the relationship and difference between the expenditure and income functions. Explain the utility function and state the relationship between expenditure and utility functions.
A) A monotonic transformation is a transformation that preserves inequalities of its arguments. That is, if T is a monotonic transformation, then: (i) iff x>y, then Tx>Ty, and iff x<y, then Tx<Ty. So, we can state, that the above model supports the monotonic transformation.
B) The relationship between income and expenditure is the consumption schedule or consumption function in economics. When disposable income rises, consumption increases. The fraction of each dollar spent is the marginal propensity to consume. Consumption may exceed disposable income for low-income individuals. As the disposable income increases, the average propensity to consume falls. In other words, the consumer spends a smaller percentage of the extra dollars. Consumption increases with increased income, but short-term increases affect consumption less than long-term increases. For an income increase of a year or less duration, consumers tend to change spending habits less than for permanent increases in income.

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