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CSUN ECON 500 - Examination 3

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ECON 500 Examination 3 - Spring 2005 1) Does the production function 24),( LKLKF += exhibit Increasing, Decreasing, or Constant Returns to Scale? Clearly explain. (10 points) ()224)(4),( LKLKLKFλλλλλλ+=+= while ()24),( LKLKF +=λλ. For 1>λ, 2244 LKLK +>+λ which implies ),(),( LKFLKFλλλ> . This inequality implies that the production process exhibits Increasing Returns to Scale. 2) David enjoys eating hotdogs. As the price of a package of hotdogs decreases from $3.75 to $3.25, his annual consumption changes as a result of two effects, a “substitution effect” and an “income effect.” The substitution effect alone causes consumption to increase by 15 units, while the income effect alone causes consumption to decrease by 6 units. Based upon this information: a) Are hotdogs an ordinary good or Giffen good for David? Clearly explain. (6 points) As price decreases, consumption changes by 09)6()15( >+=−++. Since a decrease in price causes consumption to increase, hotdogs are clearly an ordinary good for David. b) Are hotdogs a normal good or inferior good for David? Clearly explain. (6 points) The income effect associated with this decrease in price is negative. This suggests that an increase in income (with no change in prices) would lead to a decrease in consumption. Thus, hotdogs are an inferior good.3) Suppose demand is given by ppD000,2)( = . a) Graphically illustrate Consumers' Surplus in this market at a price of 16=p (being sure to label quantity demanded at this price). (6 points) b) Graphically identify the decrease in Consumers' Surplus resulting from an increase in price from 16=p to 25=p (being sure to label quantity demanded at each of these prices). (6 points) c) Noting that the “demand curve becomes flatter” as we move to “lower price, higher quantity pairs,” place both an upper and lower bound on the decrease in Consumers' Surplus resulting from an increase in price from 16=p to 25=p . (8 points) The decrease in Consumers’ Surplus resulting from an increase in price from 16=p to 25=p must be greater than 600,3400)1625( =−, but less than 050,4)1625)(400500(600,321=−−+ . qp16500)16(=Dqp16500)16(=D25400)25(=Dd) Is demand for this product “elastic,” inelastic,” or “unit elastic”? Explain. (6 points) One way to determine if demand is “elastic,” “inelastic,” or “unit elastic” is to examine the change in “total consumer expenditures” in the market as price is changed. Total consumer expenditures can be expressed as a function of price as pppppD 000,2000,2)( == . Clearly this expression becomes larger as price is increased, suggesting that demand is inelastic. 4) Consider the production function LKKLF 20),( = . For this function LKMPL10= and KLMPK10= . a) Determine the amount of output that can be produced with )2,18(),( =KL and with )18,2(),( =KL . (6 points) 1203620)2,18( ==F and 1203620)18,2( ==F. b) State an expression for KLMRTS,. Is the Marginal Rate of Technical Substitution “Diminishing”? Explain. (8 points) LKMPMPMRTSKLLKKLKL===1010,. As K is decreased and L is increased, this expression gets closer to zero, implying that the Marginal Rate of Technical Substitution is “Diminishing.” c) Based upon your answers to parts (a) and (b), explain why the input combination )10,10(),(=KL must produce more output than )2,18(),( =KL (NOTE: base your answer on parts (a) and (b), and NOT upon a direct evaluation of ),( KLF ). (8 points) First, note that 120)18,2()2,18(==FF . Second, recognize that )10,10(),( =KL is “an average” of )2,18(),(=KL and )18,2(),( =KL (since )2()18(102121+= and )18()2(102121+=). Third, since KLMRTS, is “Diminishing” it follows that an average of any two input combinations that produce a common amount of output will produce a higher level of output. Thus, )10,10(),(=KL must produce more than 120)18,2()2,18(== FF units of output.d) Sketch the isoquant passing through the input combination )2,18(),( =KL . Illustrate the input combinations )18,2(),( =KL and )10,10(),( =KL in relation to this isoquant. (6 points) 5) Consider a market in which demand is given by the linear function illustrated below. a) Is demand “elastic,” inelastic,” or “unit elastic” at a price of $8? Briefly explain. (6 points) Recall that 1−<<∞−pε along the “top half” of any linear demand curve. For the demand curve illustrated above, this insight implies that demand is elastic at any price between )12(621= and 12 . Since 8 is within this range, it follows that demand is elastic at this price. qp12LK2 2 10 18 10 18b) Would decreasing price from $4 to $3 lead to an increase, decrease, or no change in total consumer expenditures in this market? Briefly explain. (6 points) Likewise, recall that 01<<−pε along the “bottom half” of any linear demand curve. When demand is inelastic, decreasing price will lead to a decrease in total consumer expenditures. c) What price would have to be charged in order to maximize total consumer expenditures in this market? Briefly explain. (6 points) In order for total consumer expenditures to be maximized, it must be that 1=pε. For a linear demand curve this is only the case exactly “half way down the curve.” Thus, the unique price which maximizes total consumer expenditures is )0()12(62121+=. d) If income elasticity of demand for this good is equal to 73.=Iε, would a decrease in per capita income lead to an increase, decrease, or no change in demand? Briefly explain. (6 points) 073. >=Iε implies that the good in question is a normal good. It follows that a decrease in per capita income would lead to a decrease in demand.EXTRA CREDIT - 4 points! A firm produces output using two inputs, labor and capital. Is it possible for the production process to exhibit “Increasing Returns to Scale” even if the marginal product of each input is “diminishing”? Explain. (hint: consider the production function βαLAKLKF =),( with 0>α and 0>β, for which 1−=βαβLAKMPL and βααLAKMPK1−= .) • LMP is diminishing if it decreases in value as L is increased. For βαβαββ−−==11LAKLAKMPL this is the case so long as 1<β. • Similarly, KMP is diminishing if it decreases in value as K is increased. For αββααα−−==11KALLAKMPK this


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CSUN ECON 500 - Examination 3

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