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In the long run
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All inputs are variable
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The short run is defined as that period of time during which
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One or more inputs cannot be freely varied
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If equal amounts of a variable input are sequentially added to the fixed input in a typical production function,
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Increments to output will eventually decrease with increase in the variable input
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The law of diminishing returns to an input says that if other inputs are fixed
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Change in output will eventually decrease with increases in the variable input
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The average product of a variable input
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Is defined as the total product divided by the quantity of the variable input
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Geometrically, the marginal product
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At any point is the slope of the total product curve at the point
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In a short-run production function before diminishing returns set in,
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Both MPL and APL will have positive slopes and MPL will lie above APL
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Say you are the owner of a Pizza place. You know that when you produce 10 pizzas, the average product of each of your workers is 10, and the marginal product of your last worker is 15. From this information you know that:
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The average product is increasing
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When the marginal product curve lies below the average product curve,
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The average product curve must be falling
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The rate at which one input can be exchanged for another without altering output is called
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The marginal rate of technical substitution
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Say you own a Mexican place that produces, among other things, Mexican burritos. Your production of burritos is given by the equation Q = 5K1/2L1/2, where Q is the amount of burritos, K is the amount of capital and L is the amount of labor. How many workers you would need to use in order to minimize the cost of producing 100 burritos when the capital is, K, is 100?
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4
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A production function for which proportional changes in all inputs leads to a less-thanproportional change in output is said to exhibit
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Decreasing returns to scale
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For any constant returns production function, the isoquants for Q = 1, Q = 2, Q = 3, etc. will
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Be equally spaced, in that the distance between Q = 1 and Q = 2 is the same as Q = 2 and Q = 3, etc.
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Returns to scale refers to
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What happens to output when all inputs are varied in some proportion
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On the next exam for this course you can study for a maximum of four hours. If you don't study at all you will get a score of 70. One hour would give you an 80, the second hour increased your score to 89, the third to 92. If you studied the fourth hour your score would be 87. In which hour did diminishing returns set in?
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The second because your gain is less than the previous hour
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Which of the following production functions exhibits decreasing returns to scale?
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Q = Kl/4Ll/3
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Suppose that at a firm's current level of production the marginal product of capital is equal to 10 units, while the marginal rate of technical substitution between capital and labor is 2. Given this, we know the marginal product of labor must be:
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20
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In the production of bicycles an increase of 2 percent in the level of capital and labor respectively will generate an increase of 1 percent in the production of bicycles. From this information we know that the production of bicycles exhibits:
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Decreasing returns to scale
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A daily production function for staplers is Q = 5L- 2L3. Show all your work for the following questions. a) What is the marginal product equation for labor? b) What is the APL function?
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a) MPL= 5 - 6L2 b) APL= 5 - 2L2
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In the production function Q = 10L1/2K1/2calculate the marginal product equations of both inputs
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MPL= 5L-1/2K1/2 MPK= 5L½K-1/2