ajaz_eco204_2009_chapter_4.5

ajaz_eco204_2009_chapter_4.5 - University of Toronto...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
University of Toronto, Department of Economics, ECO 204 2009 2010 S. Ajaz Hussain ECO 204 2009 2010 S. Ajaz Hussain (Draft) Chapter 4.5: Short Run Production Function, Returns, Short Run CMP, and user cost of capital 1 Please help improve the course by sending me an e mail about typos or suggestions for improvements The focus of this chapter is on the optimal choice of inputs required to produce an exogenously given target level of output in the short run (when at least one input is fixed). We denote fixed inputs by lowercase letters (for example: ݈, ݇ ) and variable inputs by U PPERCASE letters (for example: ܮ, ܭ ). For tractability, for the majority of this chapter, we assume that labor and capital are the only inputs where capital is fixed and labor is variable so that the short run production function takes the form: ܳ ൌ ܣ ݂ሺܮ, ݇ሻ Again, it should be stressed that treating labor as a variable input and capital as a fixed input is an assumption. In some settings, labor is fixed and capital variable (for example: Ecoman is fixed and class rooms variable) so that: ܳ ൌ ܣ ݂ሺ݈, ܭሻ In this chapter, we will model the optimal choice of variable inputs and derive the cost function ܥሺݍሻ , the cost of producing the target output ݍ . In contrast to earlier chapters, the cost function will now consist of total fixed cost (cost of the fixed inputs) plus total variable cost (cost of the optimal variable inputs): ܥሺݍሻ ൌ ܶܨܥ ൅ ܸܶܥሺݍሻ 1 Note to self: next semester: model technology in 4.1 and introduce choice of inputs for an inputs price making firm. 1 ECO 204 (Draft) Chapter 4.5
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
University of Toronto, Department of Economics, ECO 204 2009 2010 S. Ajaz Hussain Let us begin by looking at “returns”, the short run counterpart of the long run “returns to scale”. 1. Returns From chapter 4.1, recall that returns to scale ‐‐ a long run concept – tells us the impact output when all inputs are doubled: there are increasing returns to scale if doubling all inputs more than doubles output; there are constant returns to scale if doubling all inputs doubles output; and there are decreasing returns to scale if doubling all inputs less than doubles output. The short run counterpart of returns to scale is “returns”: there are increasing returns if doubling all variable inputs more than doubles output; there are constant returns if doubling all variable inputs doubles output; and there are decreasing returns if doubling all variable inputs less than doubles output. Formally, returns can be expressed as: ܳ ൌ ܣ ݂ሺFixed inputs, V riable inputsሻ a Suppose the company is currently producing output by using ܮ workers and ݇ machines: ݍ ܳ ൌ ܣ ݂ሺܮ, ݇ሻ Returns can be re expressed as: Increasing Returns Output with doubled variable inputs > Double initial output with initial inputs ܣ ݂ሺ2ܮ, ݇ሻ ൐ 2ܣ݂ሺܮ, ݇ሻ Constant Returns Output with doubled variable inputs = Double initial output with initial inputs ܣ ݂ሺ2ܮ, ݇ሻ ൌ 2 ܣ݂ሺܮ, ݇ሻ Decreasing Returns
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern