Lecture4

# Lecture4 - ECON 301 LECTURE#4 Market Demand for Labour The...

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1 ECON 301 – LECTURE #4 Market Demand for Labour The market demand curve for labour is obtained by the usual horizontal summation technique. This involves adding up all of the individual firm’s demands for labour along the horizontal axis. Now, suppose we have a production function f (L) = ln(1+L). What is the firm’s demand for labour, in general? Using the firm’s profit function we can find the profit maximizing labour input… Max {P ln(1 + L) – wL} FOC __P __ = w ! P / w = 1 + L ! L = (P – w) 1 + L w In general, we can say that for any number of inputs i = 1, 2, … , n P · MP i = w i ! P · MP L = w ! P · MP K = r ! P · MP LAND = t (rental rate of land), etc. \$ L d 1 d 2 d 3 d 4 Market Demand Curve for Labour

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2 Labour Supply The supply of labour is derived from the consumer’s problem of choosing between work and PLAY!!! Work (BOOOO!!!!) yields income, while play (OH YEAHHHHH!!!) gives us utility in the form of leisure. We formulate this problem of the consumer’s income-leisure choice as follows: [1] The consumer has a utility function defined on income, M, and leisure, " (where leisure, " = 24 – L in a day). U = U ( ! , M) The indifference curve corresponding to a given utility level # connects all combinations of income and leisure (M , " ) that satisfy the equation U ( ! , M) = " Within this income-leisure choice framework, the marginal rate of substitution refers to the change in income as a result of a marginal change in leisure MRS = \$ M \$" M ! Indifference Curve U ( ! , M) = "
3 [2] Suppose the consumer has a time endowment of T bar = 24 hours per day to spend either on work to produce income or on play to produce pleasure. Given the market wage, w, if she allocates a time amount " for play then the value of her leisure would be w " (which is the income lost by playing around) or the opportunity cost of choosing not to work. The income earned from work would be M = w · (T bar ! ) The budget constraint for the income-leisure choice can be written as: w ! + M = w T bar The budget line is thus a straight line with slope –w as described by the equation M = w T bar – w ! [3] The consumer choice problem can now be formulated as the standard constrained utility maximization problem: Maximize U ( ! , M) Subject to w ! + M = w T bar M ! T bar wT bar Budget Line w ! + M = wT bar

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4 Remember, at the consumer equilibrium point, the indifference curve must be tangent to the budget line. [4] Solving for the optimal quantities for leisure, " *, and income, M*, we can derive the optimal amount of labour, L*, supplied by the consumer at a given market wage. L* = T bar ! * In general, if we can write the amount of labour supply as a function of the market wage, w, then we have the following individual supply of labour by the consumer: L = L(w) How do we go about this? Let’s use an example to illustrate… Recall that consumers are endowed with time. Essentially, there are two uses of time in this model.
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