Quiz 3: Labor Demand
Given, Output to be produced (Q) units Price of capital (k) per machine, per week Wage rate (w) per worker So, the slope of the isocost Marginal rate of technical substitution between labour and capital is the slope of the isoquant. = Now, the inputs (labor and capital) are perfect substitutes of each other. Therefore, the isoquant curve is linear, which implies that the firm can use only labour or only capital to produce 100 units of input, depending upon which proves least costly for the firm. Let's solve this problem with the help of the below figure: Figure-1 In the above figure, labour is shown on the x axis, and capital on the y axis. The Isoquant line is PP, and the slope of the isoquant line is 1/3. The Isocost line is PC, and its slope is 2/5. Now the slope of the isocost line is steeper than that of the isoquant (2/5 1/3), therefore, it would cost minimum to the firm if it hires only capital at point P on y axis to produce 100 units of output. Now, let's see what firm the does when the wage rate (w) is $225 , while others things remains same. So, the slope of the isocost Slope of the isoquant Figure-2 In the above figure, the Isoquant line is PP , and the Isocost line is CP. The slope of the isoquant is more than isocost line (1/3) (3/10). Therefore, it would cost minimum to the firm if it hires only labour at point C on x axis to produce 100 units of output. Let's find out the elasticity of labour demand as the wage falls from $300 to $225. Elasticity of labour is calculated by dividing the percentage change in labour with percentage change in wages: = Now, as the wage rate falls from $300 to $225, the demand for labour will move to positive number from zero. Thus, = Therefore, as the wage falls from $300 to $225, the elasticity of labor demand becomes infinity.
a) Let's describe how the ratio of the federal minimum wage to the average hourly manufacturing wage changed from the 1950s to 1990s: In the year 1950, the ratio of federal minimum wage to the average hourly manufacturing wage was 54%, which was a sudden jump from 30% in the year 1949. This sudden jump occurred due to the rise in the federal minimum wage in the year 1950. Then this ratio kept fluctuating till the year 1968, when it reaches its maximum and becomes 55.6%. From the year 1950 to 1968 the federal minimum wage remained below $1, but increased at regular intervals. From the year 1968 to 1974 the minimum wage rate remained same at around $1.5, and as a result the ratio kept falling during this period. It is because the average manufacturing wage rate was increasing continuously. The period from 1974 to 1982 saw a considerable increase in federal minimum wage, which increased from $1.5 to $3.35. However during this period the ratio kept fluctuating from 40% to 42%. There is one point worth noting that from the period of 1950 to 1980, the ratio never fell below 40%. But the period from 1982 to 1989 saw a considerable fall in the ratio, even though the federal minimum wage remained as high as $3.35 during entire period. For example the ratio of minimum wage to the average manufacturing was 42% in the year 1981 when the federal minimum wage was $3.35, and this ratio fell to 32% in the year 1989 though the federal minimum wage remained same at $3.35. This apparent shift in fundamental economic behaviour in the United States is because of the strong argument put forth by the proponents of federal minimum wage. The proponents were of the view that in the absence of the minimum wage, the income of the workers would fall below the intolerable level, therefore enactment and continuous increase in level of the federal minimum wage rate is must. b) Let's explain the underlying dynamics of the minimum wage and the average manufacturing wage from the period 1968 to 1974, and from 1980 to 1990. As it is clear from the figure that in both the periods (1968 to 1974, and 1980 to 1990) the ratio of minimum wage and the average manufacturing wage fell sharply, but still the underlying dynamics minimum wage and average manufacturing were different in both the periods. As we analyse both the periods we observe that during the period 1968 to 1974, the ratio between minimum wage and average manufacturing wage remained above 40%, though it fell sharply from highest 55.6% to 40%. During this period the federal minimum wage remained same at $1.3. The high ratio indicates that there was not much difference between federal minimum wage and average manufacturing wage. On the other hand, during the period 1980 to 1990, the ratio between minimum wage and average manufacturing wage came below 40% and fell sharply from 42% to 32%, though the federal minimum wage remained same at $3.35. This ratio indicates that the difference between federal minimum wage and average manufacturing wage have increased with time. It means the average manufacturing wage have increased at a much higher rate than federal minimum wage during the period 1980 to 1990 as compared to the period 1964 to 1974.
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