Question.3036 - Homework: Problem Sets 1. You are given the following information about the amount your company can produce per day given the number of workers it hires. Numbers of WorkersQuantity Produced 0 0 1 1 2 3 3 6 4 11 5 19 6 24 7 28 8 31 9 33 10 34 11 34 12 33a. What is the range of workers where there are increasing returns to scale? Constant returns to scale? Decreasing returns to scale? Negative returns? b. If the company wants to maximize total output, what number of workers should be hired? c. What is the number of workers that should be hired if the company wants to maximize output per worker? Hint: Use Marginal Product, and Average Product.2. Your engineering department estimated the following production function.Q = 15L 2 – 0.5L 3 a. What is the marginal product of labor function, MP L ? b. What is the average product of labor function, AP L ? c. What is the value of L that maximizes Q? d. What is the value of L at which average product is maximized? 3. The following Cobb-Douglas production function is used to describe the output generated by a local government maintenance agency. Q = αL β1 K β2 E β3 Where L represents number of worker hours, K represents number of trucks used, and E represents energy used. Statistical estimated generated the following values for α, β1, β2, and β3. Α = 0.01; β1 = 0.5, β2 = 0.4, and β3 = 0.2 a. What are the production elasticities of demand for labor, capital (trucks) and energy? b. If worker hours (labor) are increased by 10% next year, how much will output (Q) increase? c. If the number of trucks (K) decreases by 10% next year, how much will output (Q) decrease? d. What type of returns to scale is consistent with the above production function?
Answer Below:
Answer xxx following xxxxxxxxxxx about xxx amount xxx company xxx produce xxx day xxxxx the xxxxxx of xxxxxxx it xxxxx Numbers xx WorkersQuantity xxxxxxxxxxxxxxx ProductMarginal xxxxxxx - x The xxxxx of xxxxxxx for xxxxx there xx increasing xxxxxxx to xxxxx when xxxxxx of xxxxxxx rises xxxx to xxxx a xxxx increase xx workers xxxxx to x more xxxx a xxxx change xx total xxxxxx The xxxxx of xxxxxx in xxxxxx of xxxxxxx for xxxxx there xx decreasing xxxxxxx to xxxxx is xxxx to xxxx total xxxxxxx increases xx a xxxxxxxxxx rate xx number xx workers xxxxxxxx When xxxxxx workers xxx increased xxxx to xx exhibits xxxxxxxx returns xx scale xxx For xxxxxxxx returns xxx marginal xxxxxxx becomes xxxxxxxx when xxxxxxx employed xxxxx from xx b xx the xxxxxxx wants xx maximize xxxxx output xx needs xx employ xx workers xx units xx the xxxxxxx amount xx output xxx company xxx produce x The xxxxxxx can xxxxxxxx its xxxxxx per xxxxxx when xxx average xxxxxxx is xxxxxxx to xxxxxxxx product xxxxxx this xxxxx of xxxxxxxx both xxx AP xxx MP xxx increasing xxx the xx is xxxxx the xx implying xxxx a xxxxxxx can xxxxxxxx output xx increasing xxxxxx After xxx point xxxxx MP xxx AP xxxxxxxxx both xxxxxxxx start xxxxxxx and xx maximizes xxxxxx by xxxxxxxx workers xxxxx the xxxxxx of xxxxxxx that xxxxxx be xxxxx if xxx company xxxxx to xxxxxxxx output xxx worker xx where xx and xx are xxxxx - xxxxxxx Marginal xxx Total xxxxxxxxxxxxxxx ProducedAverage xxxxxxxxxxxxxxx Product xxxxxxxx ProductAnswer xx engineering xxxxxxxxxx estimated xxx following xxxxxxxxxx function x L x a xxxxxxxx product xx labour xxxxxxxx MP x Q x L x b xxxxxxx product xx labour xxxxxxxx AP x Q x L x c xxx value xx L xxxx maximizes x is xxxx MP x is xxxxx to xxxx Therefore x L xx L x as x as xxxx there xxxxx be xxxx output xxxx L xx L xx L xx L xxxxx d xxx value xx L xxx which xxxxxxx product xx maximum xx when xx L xx equal xx zero xxxxxxxxx L x or x L xx L xxxx L xx L xx L xxxxxxxxxxx a xxx production xxxxxxxxxx of xxxxxx for xxxxx is xxxxx by xx dL x Q x dL x L x K x E x L x b x L x - x b x b x Q x Similarly xxx production xxxxxxxxxx of xxxxxx for xxxxxxx truck xx given xx dQ xx K x b xxx The xxxxxxxxxx elasticity xx demand xxx Energy xx given xx dQ xx E x b x The xxxxxxxxxx of xxxxxx for xxxxx exhibits xxx production xx output xx influenced xx unit xxxxxx in xxxxx From xxx above xxxxxxxx we xxx say xxxx per xxxx change xx labor xxxx will xxxxxx in xxx cent xxxxxx in xxxxxx So xx worker xxxxx are xxxxxxxxx by xxx cent xxxx year xxxx there xxxx per xxxx increase xx output xxxxxxx method x Similarly xxxx the xxxxxxxxxx of xxxxxx for xxxxxxx truck xxxxxxx one xxx cent xxxxxx in xxxxxx of xxxxxx will xxxxxx in xxx cent xxxxxx in xxxxxx So xx number xx trucks xxxxxxxxx by xxx cent xxxx year xxxxx will xx per xxxx decrease xx output xxxxxxx method x The xxxxx production xxxxxxxx exhibits xxxxxxxxxx returns xx scale xx the xxxxxx of xxx inputs xxx up xx more xxxx unity xxxx is xxx example xx all xxx inputs xxx increased xx A xxxxxxxxxx then xxx output xxxxxx will xxxxxxx more xxxx A xxxxxxxxxx increaseMore Articles From Economics
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