Consumption is equal to total wage income plus dividend income minus taxes This

Consumption is equal to total wage income plus

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Consumption is equal to total wage income ( 𝑤? ? ), plus dividend income ( ? ), minus taxes ( ? ). This budget constraint (BC) is given by: ? = 𝑤? ? + ? ? Accounting for the time constraint we end up with ? = 𝑤 ? + ? ? ? = − 𝑤? + 𝑤ℎ + ? ? Slope of BC is 𝑤 , and intercept is 𝑤ℎ + ? T
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Representative Consumer’s Budget Constraint when taxes is greater than dividend income ( T> π ) This figure shows the consumers budget constraint, line AB, for the case in which taxes are greater than the consumer’s dividend income. In this case ? ? is negative. The slope of the budget constraint is – w , and the constraint shifts with the quantity of non-wage real disposable income, π - T. All points in the shaded area and on the budget constraint can be purchased by the consumer. The vertical intercept is the maximum quantity of consumption attainable for the consumer, which is what is achieved if the consumer works h hours and consumes no leisure. The horizontal intercept is the maximum number of hours of leisure that the consumer can take and still be able to pay the lump sum tax. Representative Consumer’s Budget Constraint when dividend income is greater than taxes ( T< π )
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This figure shows the consumers budget constraint when taxes are less than dividend income, in which case ? ? is positive. This implies that the budget constraint is kinked. Consumption bundles in the shaded area and on the budget constraint are feasible for the consumer; all other consumption bundles are not feasible. The kink in the budget constraint can be seen to be as a result of the fact that the consumer cannot consume more than h hours of leisure. Thus, at point B we have ? = h, which implies that the number of hours worked by the consumer is zero. Points along BD all involve the consumer working zero hours and consuming some amount C ? ? — that is, the consumer always has the option of throwing away some of his dividend income. Even though the consumer does not work at point B we have C = ? ? > 0, as dividend income exceeds taxes. Consumer Optimization To determine what choice of consumption and leisure the consumer makes, we assume that the consumer is rational. This means the consumer knows his or her own preferences and budget constraint and can evaluate which feasible consumption bundle is best . Therefore, the consumer can make an informed optimization decision and can therefore optimize his behaviour. The consumer chooses the consumption bundle that is on his or her highest indifference curve, while satisfying his or her budget constraint. Optimization in this case implies that the marginal rate of substitution of leisure for consumption equals the real wage. The consumption bundle represented
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by point H, where an indifference curve is tangent to the budget constraint, is the optimal consumption bundle for the consumer. Points inside the budget constraint, such as J, cannot be optimal (more is preferred to less), and points such as E and F, where an indifference curve cuts the budget constraint, also cannot be optimal. A consumer would ot choose point J as it is
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