Economic Analysis for Business Session XVII: Production Function and Factor Markets

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Economic Analysis for BusinessSession XVII
Production Function and Factor Markets
InstructorSandeep Basnyat 9841892281 Sandeep_basn
yat_at_yahoo.com
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Recall Profit Maximization

• As stated before,
• Firms will hire extra labour and capital until
• MRPL w and MRPK r
• PxMPL w and PxMPK r
• Dividing,
• MPL / MPK w / r
• MPL / w MPK / r ..(i)
• Equation (i) is known as efficiency condition. Or
• Least cost combination input.
• Meaning if a firm is maximizing in the above
  condition, then it is efficiently operating.

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Numerical Problems

• 1) Consider the Production function
• Q 3LK 2K
• Price per unit of K and L are 76 and 6
  respectively. Per unit selling price for output
  is 2. Find
• Amount of factors demanded
• Amount of product produced
• Amount of profit or Loss generated

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Solution Numerical Prob. (1)

• Q 3LK 2K
• MPK 3L2
• MPL 3K
• Profit Maximizing condition,
• P x MPL w and P x MPK r
• 2(3K) 6 and 2 (3L2) 76
• K 1 and L 12
• Q 3(12)(1) 2(1) 38
• Profit TR TC 2(38) 6(12) 76(1) - 72
  (Loss)

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Numerical 2

• Assume the production function
• Q 100K0.5L0.5
• If the price of labour and capital are 4 and 2
  respectively, find the efficient input
  combination (least cost combination input) for
  producing 1000 units of output.
• How would the input mix change if the price of
  capital increased to r 4 and the firm still
  wanted to produce 1000 units of output?
• Interpret the result of (b).

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Solution to Numerical 2

• a) Q 100K0.5L0.5
• MPK 50(L0.5 / K0.5)
• MPL 50(K0.5 / L0.5)
• Efficiency condition,
• MPL / MPK w / r
• K (w/r)L .(i)
• Substituting the value of K in Production
  function,
• 1000 100 ((w/r)L )0.5L0.5 100 L (4/2) 0.5
• L 7.07. Substituting the value of L in eq. (i),
  K 14.14
• b) When k 4,
• 1000 100 L (4/4) 0.5 100 L (4/4) 0.5 L 10
  and K 10
• c) The firm responded to the higher price of
  capital by substituting labour for capital

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Numerical 3

• Suppose that a firms production function is
  given by
• Q K² L. Further suppose that w 10 and r
  20a) Suppose the firm wants to produce 27,000
  units of output. What is the most efficient
  combination of labor and capital?

Solution MPL K², MPK 2KLMRTS MPL / MPK
K / 2LK / 2L 10 / 20...therefore KLTo
produce 27000 unitsK²L 27000....therefore K³
27000, so K30, L30
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Numerical 3

• Suppose that a firms production function is
  given by
• Q K² L. Further suppose that w 10 and r
  20
• b) Suppose that the firm wants to produce 27,000
  units of output in the most efficient way
  possible. How much does the firm spend?

Solution Budget constraint iswL rK (10)(30)
(20)(30) 900
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Numerical 3

• Suppose that a firms production function is
  given by
• Q K² L. Further suppose that w 10 and r
  20c) Suppose that the firm wants to produce
  27,000 units of output and has exactly 10 units
  of capital in hand. In this situation, how many
  labor has to be employed?

Solution 27000 10²L, so L 270 units of labour
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Numerical 3

• Suppose that a firms production function is
  given by
• Q K² L. Further suppose that w 10 and r
  20d)Suppose that the firm wants to spend
  exactly 1,200. What is the most efficient
  combination of labor and capital ?

Solution wL rK 1200We know that LK, w10,
r20, so (10)(L) (20)(L) 1200, therefore
L40, K40
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Numerical 3

• Suppose that a firms production function is
  given by
• Q K² L. Further suppose that w 10 and r
  20e) Suppose that the firm spends exactly
  1200 in the most efficient way possible. How
  much output can the firm produce?

Solution Substitute KL40 into production
function(40)²(40) 64000 units
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Summary of Factor Market
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Factor market
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• Derived demand derived from a firms decision
  to supply a good in another market.
• Production function- provides relationship
• MRPL/MRPK (VMPL/VMPK) curves - demand curve for
  factor market determine additional labour or
  capital hired
• Profit maximizing or efficiency condition
• VMPL P x MPL MR (or MC) x MPL W
• VMPK P x MPK MR (or MC) x MPK r

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MPL and VMPL Example
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The VMPL curve
L (number of workers)
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Supply Curve for factor market-eg. Labour
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Equilibrium in the Factor Market
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Linkages Among the Factors of Production
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• In most cases, factors of production are used
  together in a way that makes each factors
  productivity dependent on the quantities of the
  other factors.
• Example an increase in the quantity of capital
• The marginal product and rental price of capital
  fall.
• Having more capital makes workers more
  productive, MPL and W rise.

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Thank you