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 xxxxx L x Marginal xxxxxxx of xxxxxx function xx L xxxxx Q xxxxx L x ndash x b xxxxxxx product xx labour xxxxxxxx AP x Q x L xxxxx L x The xxxxx of x that xxxxxxxxx Q xx when xx L xx equal xx zero xxxxxxxxx L xxxxx L xx L xxxxx L xx L xx as xxxx there xxxxx be xxxx output xxxx ndash x or x or x or x units x The xxxxx of x for xxxxx average xxxxxxx is xxxxxxx is xxxx AP x is xxxxx to xxxx Therefore x ndash x or x ndash x as x ne xxxx ndash x or x or x unitsAnswer x The xxxxxxxxxx elasticity xx demand xxx labor xx given xx dQ xx L x d xx A x b x b x b x Q x A x b x K x E x L x b xxxxxxxxx The xxxxxxxxxx elasticity xx demand xxx capital xxxxx is xxxxx by xx dK x Q x And xxx production xxxxxxxxxx of xxxxxx for xxxxxx is xxxxx by xx dE x Q x b xxx elasticity xx demand xxx labor xxxxxxxx how xxxxxxxxxx of xxxxxx is xxxxxxxxxx by xxxx change xx labor xxxx the xxxxx solution xx can xxx that xxx cent xxxxxx in xxxxx hour xxxx result xx per xxxx change xx output xx if xxxxxx hours xxx increased xx per xxxx next xxxx then xxxxx will xxx cent xxxxxxxx in xxxxxx unitary xxxxxx c xxxxxxxxx from xxx elasticity xx demand xxx capital xxxxx implies xxx per xxxx change xx number xx trucks xxxx result xx per xxxx change xx output xx if xxxxxx of xxxxxx decreases xx per xxxx next xxxx there xxxx be xxx cent xxxxxxxx in xxxxxx unitary xxxxxx d xxx above xxxxxxxxxx function xxxxxxxx increasing xxxxxxx to xxxxx as xxx powers xx the xxxxxx add xx to xxxx than xxxxx That xx for xxxxxxx if xxx the xxxxxx are xxxxxxxxx in xxxxx A xxxxx proportion xxxx the xxxxxx change xxxx exhibit xxxx than xxxxx A xxxxx proportion xxxxxxxxMore Articles From Economics
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