Question

Suppose that (L_1) represents workers without a high school degree, and (L_2) represents workers with a high school degree. Suppose that there is a 12% increase in the population of (L_1) workers (i.e., (L_1/L_2) increases by 12%). How μch do relative wages ((W_1/W_2)) decrease by when the production function is Cobb-Douglas? (Express in percentage points)

a) 6%

b) 8%

c) 10%

d) 12%

Answer 1

In a Cobb-Douglas production function, an increase in the population of workers without a high school degree (L1) leads to a decrease in relative wages. The exact decrease depends on the share of L1 workers in the production function (α).

Step-by-step explanation:

In a Cobb-Douglas production function, the relative wages decrease when there is an increase in the population of workers without a high school degree (L1). The decrease in relative wages is determined by the ratio of the increase in the population of L1 workers to the population of workers with a high school degree (L2). In this case, the increase in L1 workers is 12%.

Using the formula for the Cobb-Douglas production function, the decrease in relative wages can be calculated as:

Relative Wage Decrease = (L1/L2) * (1 - α)

Where α is the share of L1 workers in the production function (0 < α < 1).

Since the percentage increase in L1/L2 is 12%, the relative wages would decrease by 12 * (1 - α) percentage points. However, the value of α is not provided in the question, so the exact decrease in relative wages cannot be determined without additional information.