DOC PREVIEW
CSUN ECON 500 - Take Home Exam #3

This preview shows page 1-2 out of 6 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 6 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 6 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 6 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

Take Home Exam #3 – Answer Key. ECON 500 – Summer 2004. 1) Suppose that under current market conditions, the price elasticity of demand for oranges is 34.−=pε, while the income elasticity of demand for oranges is 58.=Iε. a. Would an increase in the price of oranges lead to an increase or decrease in total consumer expenditures on oranges? Explain. (6 points) Since 34.−=pε ( 01<<−pε), demand is inelastic. Therefore, an increase in the price of oranges will result in increased consumer expenditure on oranges. b. Would an increase in consumer income lead to an increase or decrease in demand for oranges? Explain. (6 points) Since 058. >=Iε, oranges are a normal good. As a result, an increase in consumer income will lead to an increase in demand for oranges. 2) Consider the production function 210),( LKKLF += . For this function, LMPL2= and 10=KMP . a. How much output can the firm produce with )20,10(),(=KL ? (4 points) 300100200)20,10(=+== Fq. b. Determine the functional form of KLMRTS,. (4 points) LLMPMPMRTSKLKL51,102===. c. Is the Marginal Rate of Technical Substitution “Diminishing”? Explain. (6 points) When increasing labor and decreasing capital (while maintaining the initial level of output), the value of LMRTSKL51,= will increase (not decrease). Therefore, the Marginal Rate of Technical Substitution is NOT “Diminishing.”d. Sketch the isoquant associated with 300=q units of output. (4 points) Since LMRTSKL51,= is “increasing” (not “diminishing”), each isoquant becomes stepper as one moves to “higher labor, lower capital” input combinations. Thus, the isoquant associated with 300=q units of output looks something like: 3) Suppose the demand for boxes of Franzia wine is given by the function ppD −= 6)( (for 360≤≤ p ). As a result, ppD21)(−=′. a. Derive an expression for price elasticity of demand as a function of price. (8 points) As a function of price, )()(pDppDp′=ε. Substituting ppD −= 6)( and ppD21)(−=′ leads to pppp−−=621ε. This expression can be simplified to ppp212 −−=ε. K L 0 0 30 10 20b. Is demand elastic, inelastic, or unit elastic if the price of a box of wine is 9=p ? Clearly explain. (4 points) As a function of price, ppp212 −−=ε. Thus at a price of 9=p we have 216123−=−−=pε. Since 01<<−pε, demand is inelastic at a price of 9=p . c. What price maximizes total consumer expenditures in this market? Clearly explain. (8 points) When total consumer expenditures are maximized, price elasticity of demand must be equal to -1 (that it, demand must be unit elastic). Setting 1212−=−−=pppε and solving for p, we see that demand is unit elastic only at a price of 16=p . Therefore, a price of 16=p maximizes total consumer expenditures. 4) Consider a firm operating in the long run with the production function {}KLKLF ,2min),( = . a. If the firm wishes to produce 10 units of output as inexpensively as possible, how many units of L and how many units of K should be hired? Clearly explain. (6 points) In the long run the firm can vary both the level of labor and the level of capital. In order to produce 10 units of output while minimizing rKwL+, the firm will want to choose 102==KL . That is, they should hire 5=L and 10=K . Any other combination of inputs either produces less output or costs more to hire.b. Suppose the firm wishes to produce an arbitrary level of output 0>q . Graphically illustrate the solution to the long run cost minimization problem for this firm. (4 points) c. Suppose the firm wishes to produce an arbitrary level of output 0>q . Determine the long run cost minimizing levels of labor and capital. (6 points) Using the same logic as in part (a), the firm should hire qrwqLLR21*),,( = and qrwqKLR=),,(*. d. Determine the long run cost function of this firm. (4 points) Long run costs are equal to ()rqqwrKwLLRLR+=+21**. Treating this as a function of only the level of output, we have {}qrwqc +=21)( . e. Suppose the wage rate for each unit of labor were to increase. Clearly explain how this change would this alter the long run cost minimizing level of labor, the long run cost minimizing level of capital, as well as the long run costs of producing 0>q units of output. (6 points) As w increases, qrwqLLR21*),,( = and qrwqKLR=),,(* do not change (since the firm is not able to “substitute capital for labor”). However, long run costs (given by {}qrwqc+=21)( ) will increase, as a direct result of the increased cost of hiring qrwqLLR21*),,( = units of labor. K=2L L K K* L* F(L,K)=min{2L,K}=q5) Determine if each of the following production functions exhibits Increasing, Decreasing, or Constant Returns to Scale: a. LKKLF 2),( += . (6 points) LKLKKLF 22),(λλλλλλ+=+= , while LKKLF 2),(λλλ+= . Comparing these expressions, ),(),( KLFKLFλλλ< for any 1>λ (since KKλλ< for any 1>λ). Thus, the underlying technology exhibits Decreasing Returns to Scale. b. LKJJKLF 2),,( = . (6 points) ),,(222),,(5.15.13JKLFLKJLKJJKLJKLFλλλλλλλλλ==== . For any 1>λ, ),,(),,(5.1JKLFJKLFλλ> . As a result, the underlying technology exhibits Increasing Returns to Scale. 6) Consider a firm with the production function 5.25.2),( LKLKF = . This firm is currently operating in the short run with 625=K units of capital. a. Suppose the firm wishes to produce an arbitrary level of output 0>q . Graphically illustrate the solution to the short run cost minimization problem for this firm. (4 points) K=625 K L L*SRb. Determine the short run cost minimizing level of labor. (4 points) With 625=K units of capital, the short run output of the firm as a function of L is LLLLKF 10)5)(2()625(2),(5.5.25.=== . In order to produce q units of output as inexpensively as possible, the firm should hire an amount of labor so that qLLKF == 10),( . Solving this condition for L , we have 1002*qLSR= . c. Clearly explain how the short run cost minimizing level of labor will change as the wage rate increases. (4 points) 1002*qLSR= does not depend upon w . Therefore, changes in the wage rate will have no impact on the short run cost minimizing level of


View Full Document

CSUN ECON 500 - Take Home Exam #3

Download Take Home Exam #3
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Take Home Exam #3 and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Take Home Exam #3 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?