Midterm 2

Midterm 2 - Econ 410: Micro Theory Spring 2010 Basak Altan...

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Unformatted text preview: Econ 410: Micro Theory Spring 2010 Basak Altan NAMEz—Dlslc-n (3 m" r , "\ 1- ,K\ PLEDGE. MIDTERM EXAM 2 — A Instructions: - Please sign the pledge. By signing it, you agree to work alone. - Please write legibly and show all your work. - Calculators are not allowed. 1. U4 \. ’zl L. [0 3. 2H 7‘1” GOOD LUCK © 2, u I, Part I (30 Points, 3 Points Each) / \/1. If capital cannot easily be substituted for labor, then the marginal rate of technical substitution of labor for capital is A l t . ) c ose 0 one Mpfié 4‘ [VIRF B) negative. very large. .4713 3 '13» _:~, L01“ c D) close to Zero. . Suppose capital and labor are perfect complements for a particular production process. If the price of labor increases, holding the price of capital and the level of output constant, the firm should (fix RAD use the same amounts of capital and labor. @mse more capital and less labor. C) eliminate all use of labor. D) use more labor and less capital. /Economies of scale exist when firms have A) decreasing returns to scale. B) constant marginal cost. C) constant returns to scale. ED) increasing returns to scale. / Which of the following will not be true of a perfectly competitive market? A) Buyers and sellers take the market price as given when making purchasing or production decisions. Different consumers may pay different prices for the same product. Each individual buyer or seller has an imperceptible effect on the market price. D) A new firm may incur a cost upon entering a market, but has access to the same technology and inputs as established firms. . Suppose capital and labor are perfect substitutes for a particular production process. If h, the price of labor increases, holding the price of capital and the level of output constant, A" the firm may i l \x‘ A) use the same amounts of capital and labor. (E) Either use more capital and less labor or use the same amounts of both inputs. 2'..\ a“ [I I. - use more labor and less capital. D) use more capital and less labor. 6 Which of the following factors may explain diseconomies of scale? M Specialization of labor. .. B)j Indivisible inputs. K . . . C)" ManagerIal d1seconom1es. ID) Increasing returns to scale of inputs. ./ Explain the truthfulness of the following statements \/ I. A characteristic of a perfectly competitive market is that products are undifferentiated. That is, consumers perceive products to be identical. II. Equal access to resources is a condition in which all firms, including prospective entrants, have access to the same technology and inputs. A) Both 1 and II are false B) I is false; II is true. Both I and II are true 15) I is true; 11 is false. §./A production manager notices that when she triples all of her inputs simultaneously, her V output doubles. The production manager determines that for this range of output, the productionfunction exhibits A) undefined returns to scale. B) increasing returns to scale. C) constant returns to scale. decreasing returns to scale. / X. \y/Compensating variation is the change in income necessary to restore the consumer to the initial level of utility. /B) the difference in the consumer's income between the purchase of the original basket and the new basket at the old prices. 2)“ always the area under the demand curve and above the price paid. D) the change in income necessary to hold the consumer at the final level of utility as price changes. l . The concept of equivalent variation means A) the income effect. B) the substitution effect. C) the change in income necessary to restore the consumer to the initial level of utility as price changes. @the change in income necessary to hold the consumer at the final level of utility as price changes. Part II (70 Points) 1 I Problem 1 (28 points) Suppose in some market that a typical firm’s production function of two inputs, labor and capital, given by Q = L2K2 . The wage rate is represented by w and the rent rate is represented by I'. 5 a- (6 points) Identify the type of returns to scale this production function represents? Z Z G L K i 2 (1; (Au (m 7. 7 “ G : X L2 A IA “ .n-F' l WK «5) '2 X o... iflO’h‘Sx-aé ff ‘It‘x-(fljugfl 566‘qu / ’1 b c- (6 points) Derive the long-run demand for capital. _ f ‘5‘ L ‘I I t 1,. ./ (al A x \ \‘x L/‘ Ll d- (4 points) Derive the long-run total production cost. ’F—Z;L)L*f#\ x “7’3? war—m A ~r(%fi) 2' e- (6 points) Does this cost structure exhibit scale economies? Explain. i \ ‘1 ("r ( gt. \‘ I -' Cg k‘ECfiU‘X’ 1* Rank: " c2. CCLK lMt: *L'FEQQ Garmkh \ (. A3 {AireaLSéS/AC decrEa-Jti [ a Problem 2 (18 points) The market for sweet potatoes consists of 1,000 identical firms. Each firm has a short—run total cost curve of STC = 100 + 100q + 100q2, where q is output. Suppose all fixed costs are sunk. 3 a- (6 points) Calculate the equation of an individual firm's short run supply curve in this market? _ . . u f I ._ a, I — ; ‘- . We ,4 zz‘w ' ' W”: I [1x {:3 -” -f_._.;'____:?‘ up, 72 .L I. ; )‘f‘fl .s fwd“: i F. D) Q '3 4 /LJ U I . - 5.1695") fl— , -'—' Sl‘wfi—dowfl P-l 5"! E 7x30 ‘1 9x I; b- (6poz'nts} Calculate the equation of the industry short run supply curve in this market? r' " ' n I? who“? WT?” II ,.--‘ __ -_________.———- _ ——— r‘/”m“ 5’79, 5’00. p- “l .____ _ _ km ,? rm 0: ,rn 5&3 (2‘ c- (6 points) When the market demand is Qd =5000-5P, find the equilibrium price and quantity produced by each firm. r" ..» - iii-F" . - WK :7}; 572’ f: $55) "5 73" 2'1 Problem 3 (24 pomts) Each firm in a perfectly competitive market has long run average cost represented as AC(q) = 100q-10+100q'l . The long run marginal cost is MC=200q-10. The market demand is Qd = 2150- SP. a- (8 points) Find the long run equilibrium output per firm, q*. z: ---»-: N b- (8 points) Find the long run equilibrium price, P*. Bf” I" P; 2000). K0 \\ :34— NR7 ,. c- (8 points) Find the number of firms in the industry, n*. a“: may £0405 (a ??go- 6!: 4200 \ 5,2106 gaff/1 firmjproaluas ‘ MW, n"= } 200 ...
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Midterm 2 - Econ 410: Micro Theory Spring 2010 Basak Altan...

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