Quiz 3 Ec21 W2013 Solutions.pdf

Quiz 3 Ec21 W2013 Solutions.pdf - Economics 21 Winter 2013...

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Page 1 of 5 Economics 21 Winter 2013 Quiz 3 SOLUTIONS 1. Short Answer Questions (21 points) a. Define “sunk cost” and explain its relevance for economic decisions. A sunk cost is a cost of production that has already been paid for (incurred) and has no alternative use. I.e., it has an opportunity cost of zero, and should not be counted among the firm’s economic costs when making decisions like whether or not to shut down. b. Define the “Law of Diminishing Marginal Returns”. As you increase one input, at some point the marginal product of that input decreases as output increases, holding other inputs constant. E.g. Suppose that there are two inputs, capital (K) and labor (L). Under the law of diminishing marginal returns, when you hold L constant, you will find that the marginal product from capital will begin to decrease at some point as you keep increasing output. If you are adding more and more sewing machines to the same number of seamstresses, there are not enough seamstresses to operate each machine, and the marginal product of the machine (i.e. the extra output added because of the last machine) starts to fall. c. What is a “price support”? A price support is when a minimum price is supported by the government’s commitment to buy up the excess supply (i.e. via market intervention), as opposed to simply legislating a certain price floor. d. What are the five conditions for “perfect competition”? (1) Free entry and exit (2) Identical products (i.e., homogeneous products) (3) Negligible transaction costs (4) Large number of firms and buyers (5) Perfect information Note that price taking follows from conditions (4) and (2). Note also that perfect competition does not require firms to have identical technologies (i.e. identical cost or production functions).
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Page 2 of 5 e. For each of the functions below circle whether it could be correct or is always wrong, and for the ones marked wrong, explain why. All notation is standard, so: K: units of capital; L: units of labor: Q: output; p: price of output; w: wage rate; r: rental rate of capital; C: total cost. The function Max(a, b) is equal to a if a b, and is equal to b if b a. The ln function denotes the natural log. (1) [ Correct / Wrong ] Unconditional factor demand for capital: K(w, r, L) = (w/r) 0.5 L (2) [ Correct / Wrong ] Conditional factor demand for labor: L(w, r, Q) = Q 1.5 (3) [ Correct / Wrong ] Supply function: S(p, w, r) = Max(0.85 ln(p) – 0.50 ln(w) – 0.35 ln(r), 0) (4) [ Correct / Wrong ] Cost function: C(Q, w, r) = 12.904 Q -2/7 w 5/7 r 4/7 One-line explanation for each function you circled as wrong: (1) Unconditional factor demand should be a function of wages, rent and prices; K(w, r, p) because it takes p, r, and w as given. Note that a factor demand function can never depend on the quantity of the other factor of production (L in this case), because that is an unknown that we have to solve for.
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