Question

2. Suppose you have a cubic cost function and a quadratic revenue function, describe the process of determining the values of units produced which maximize profits, minimize costs, and maximize total revenue: Begin answer here:                           

3. Given the following production function: Q = 100 K^-0.50 L^1.5 M^-1.0­­ , where Q is output; K, capital; and L, Labor requirements, and M, materials
   1. Find and interpret the results of ∂Q∂K=    Begin answer here:                           
   2. Find and interpret the results of   ∂Q∂L= Begin answer here:                           
   3. Suppose the above function was estimated for output in the automobile industry in 1995 and you wish to update the date model with time series data from January 1980 to August 2020. Propose two methods for estimating the model provide an analysis of the preferred method and explain why. Begin answer here:                   
   4. Derive the output elasticity for the materials input. Begin answer here:                   

4. Given a multivariate function specification where Q = 100 K^-0.50 L^1.5 M^-1.0­­ , describe how you estimate a regression what information can you derive form the results. Be as specific as possible.

Answer 1

Solution first part:

Given the following production function: Q = 100 K^-0.50 L^1.5 M^-1.0­­ , where Q is output; K, capital; and L, Labor requirements, and M, materials

The Marginal cost of producing 1unit of additional output with an unit increase in capital.

The Marginal cost of producing 1unit of additional output with an unit increase in labour.

Solution second part:

Taking log on both sides we can convert the function as linear function. After that we can use time series models of AR, MA in the equation.

The interpretation can be drawn by calculating the treand line, future demand of the quantitity produced and amount of inputs like, Labour, Capital. IWe can also conclude the more influencing factors for production of the outputs.