# Managerial Economics Study Set 8

## Quiz 7 :Production Economics

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Figure shows the annual rate of crude oil extraction of the United States was basically unchanged 2002-2012. Not so for Saudi Arabia whose production increased 33%. Explain why with special attention to the price spike in mid-2008. FIGURE Oil Price 1970-2012 and Drilling Rig with Horizontal Drilling
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From the provided information, during 2002-2012, country U is using alternate fuel i.e. natural gas as this resource availability is plentiful in the country NA.
When country U requires resources like crude oil and gasoline, country S increased the prices on gasoline. Indeed, country U applied same policy for the prices of natural gas. As a result, crude oil prices were lowered by Saudi and more oil is extracted for supply.

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Based on the production function parameter estimates reported in Table: a. Which industry (or industries) appears to exhibit decreasing returns to scale (Ignore the issue of statistical significance.) b. Which industry comes closest to exhibiting constant returns to scale c. In which industry will a given percentage increase in capital result in the largest percentage increase in output d. In what industry will a given percentage increase in production workers result in the largest percentage increase in output Table PRODUCTION ELASTICITIES FOR SEVERAL INDUSTRIES Number in parentheses below each elasticity coefficient is the standard error. *Significantly greater than 1.0 at the 0.05 level (one-tailed test). Source: John R. Moroney, "Cobb-Douglas Production Functions and Returns to Scale in U.S. Manufacturing Industry," Western Economic Journal 6, no. 1 (December 1967), Table 1, p. 46.
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The production function is:
represents the labor elasticity for production.
represents the elasticity of non-labor.
represents the capital elasticity of production.
represents the returns to scale. If
, then the production function represents increasing returns to scale. If
, then the production function represents constant returns to scale. If
, then the production function represents decreasing returns to scale.
a) Petroleum, primary metals shows decreasing returns to scale. Decreasing returns to scale occurs when
. This means that if
, L n and
are increased by 'a' times, then the increase in output is less than 'a' times.
b) Textiles represents constant returns to scale. Constant returns to scale arises when
. This means that if
,
and
are increased by 'a' times, then the increase in output is exactly equal to 'a' times.
c) This is true for primary metals. This occurs when
is largest. Higher
represents higher output elasticity for capital which means that % change in output is higher due to percentage change in capital input.
d) This is true for stone, clay, etc. This occurs when
is largest. Higher
represents output elasticity for production labor which means that percentage change in output is higher due to percentage change in production labor input.

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With interest rates at historic lows in the United States, what is the effect on the optimal rate of extraction for a Texas oilfield owner Explain the intuition that supports your answer.
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The oil field owner has two options. Firstly, more oil can be extracted once and sold at market price. Secondly, oil can be extracted when it is required. This option again depends on the two variables, i.e. oil price and interest rates.
Suppose interest rates are lower than the price of the oil. For instance, the price of the oil increases by 4 percent by year and the interest rate is only 2 percent. Then, oilfield owner would like to reduce the rate of extraction of oil. Extraction of more oil when the interest rate is low does not give good returns to the owner. Thus, oil holding underneath increases the value rather than extraction. This scenario is vice versa when interest rates are higher than the price of the oil.

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Determine the percentage of the variation in output that is "explained" by the regression equation.
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Extension of the Cobb-Douglas Production Function-The Cobb-Douglas production function (Equation) can be shown to be a special case of a larger class of linear homogeneous production functions having the following mathematical form: 11 where is an efficiency parameter that shows the output resulting from given quantities of inputs; is a distribution parameter (0 1) that indicates the division of factor income between capital and labor; is a substitution parameter that is a measure of substitutability of capital for labor (or vice versa) in the production process; and is a scale parameter ( 0) that indicates the type of returns to scale (increasing, constant, or decreasing). Show that when = 1, this function exhibits constant returns to scale. [Hint: Increase capital K and labor L each by a factor of , or K* = ( )K and L* = ( )L, and show that output Q also increases by a factor of , or Q* = ( )(Q).] Equation 11 See R. G. Chambers, Applied Production Analysis (Cambridge: Cambridge University Press, 1988).
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From your knowledge of the relationships among the various production functions,complete the following table:
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Determine whether this production function exhibits increasing, decreasing, or constant returns to scale. (Ignore the issue of statistical significance.)
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Determine the labor and capital estimated parameters, and give an economic interpretation of each value.
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Lobo Lighting Corporation currently employs 100 unskilled laborers, 80 factorytechnicians, 30 skilled machinists, and 40 skilled electricians. Lobo feels that the marginal product of the last unskilled laborer is 400 lights per week, the marginal product of the last factory technician is 450 lights per week, the marginal product of the last skilled machinist is 550 lights per week, and the marginal product of the last skilled electrician is 600 lights per week. Unskilled laborers earn $400 per week, factory technicians earn$500 per week, machinists earn $700 per week, and electricians earn$750 per week. Is Lobo using the lowest cost combination of workers to produce its targeted output If not, what recommendations can you make to assist the company
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Consider the following short-run production function (where L = variable input,Q = output):Q = 10L 0.5L2 Suppose that output can be sold for $10 per unit. Also assume that the firm can obtain as much of the variable input (L) as it needs at$20 per unit. a. Determine the marginal revenue product function. b. Determine the marginal factor cost function. c. Determine the optimal value of L, given that the objective is to maximizeprofits
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Estimate the Cobb-Douglas production function Q = L 1K 2 , where Q = output; L = labor input; K = capital input; and , 1, and 2 are the parameters to be estimated.
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In the Deep Creek Mining Company example described in this chapter (Table), suppose again that labor is the variable input and capital is the fixed input. Specifically, assume that the firm owns a piece of equipment having a 500-bhp rating. a. Complete the following table: b. Plot the (i) total product, (ii) marginal product, and (iii) average product functions. c. Determine the boundaries of the three stages of production. Table TOTAL OUTPUT TABLE-DEEP CREEK MINING COMPANY
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The amount of fish caught per week on a trawler is a function of the crew size assigned to operate the boat. Based on past data, the following production schedule was developed: a. Over what ranges of workers are there (i) increasing, (ii) constant, (iii) decreasing, and (iv) negative returns b. How large a crew should be used if the trawler owner is interested in maximizing the total amount of fish caught c. How large a crew should be used if the trawler owner is interested in maximizing the average amount of fish caught per person
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Suppose that a firm's production function is given by the following relationship: Q = 2:5pffiLffiffiKffiffiffi ði:e:, Q = 2:5L:5K:5Þwhere Q = output L = labor inputK = capital input a. Determine the percentage increase in output if labor input is increased by 10 percent (assuming that capital input is held constant). b. Determine the percentage increase in output if capital input is increased by 25 percent (assuming that labor input is held constant). c. Determine the percentage increase in output if both labor and capital are increased by 20 percent.
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Test whether the coefficients of capital and labor are statistically significant.
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Consider the following Cobb-Douglas production function for the bus transportation system in a particular city: where L = labor input in worker hours F = fuel input in gallons K = capital input in number of buses Q = output measured in millions of bus miles Suppose that the parameters ( , 1, 2, and 3) of this model were estimated using annual data for the past 25 years. The following results were obtained: = 0.0012 1 = 0.45 2 = 0.20 3 = 0.30 a. Determine the (i) labor, (ii) fuel, and (iii) capital input production elasticities. b. Suppose that labor input (worker hours) is increased by 2 percent next year (with the other inputs held constant). Determine the approximate percentage change in output. c. Suppose that capital input (number of buses) is decreased by 3 percent next year (when certain older buses are taken out of service). Assuming that the other inputs are held constant, determine the approximate percentage changein output. d. What type of returns to scale appears to characterize this bus transportation system (Ignore the issue of statistical significance.) e. Discuss some of the methodological and measurement problems one might encounter in using time-series data to estimate the parameters of this model.
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Consider the following short-run production function (where L = variable input, Q = output):Q = 6L3 0.4L3 a. Determine the marginal product function (MPL). b. Determine the average product function (APL). c. Find the value of L that maximizes Q. d. Find the value of L at which the marginal product function takes on itsmaximum value. e. Find the value of L at which the average product function takes on its maximumvalue.
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Consider Exercise again. Suppose the owner of the trawler can sell all the fishcaught for $75 per 100 pounds and can hire as many crew members as desired by paying them$150 per week. Assuming that the owner of the trawler is interested in maximizing profits, determine the optimal crew size. Exercise The amount of fish caught per week on a trawler is a function of the crew size assigned to operate the boat. Based on past data, the following production schedule was developed: a. Over what ranges of workers are there (i) increasing, (ii) constant, (iii) decreasing, and (iv) negative returns b. How large a crew should be used if the trawler owner is interested in maximizing the total amount of fish caught c. How large a crew should be used if the trawler owner is interested in maximizing the average amount of fish caught per person