Suppose that a firm’s production function is given by the ...



• Suppose that a firm’s production function is given by the following relationship.

Q=2•L0.5•K0.5

Where Q=output, L=Labor input, and K=Capital input

1. Determine the percentage increase in output if labor input is increased by 10%, assuming that capital input is held constant.

• Lagrangian function [Fun Stuff again ?? !!! ]

The output of a production process is a function of two inputs (L and K) and is given by the following relationship

Q = 0.5•L•K – 0.1• L2 – 0.05•K2

The unit cost of inputs L and K are $20 and $25, respectively. The firm is interested in maximizing output subject to a cost constraint of $500.

2. Formulate the Lagrangian Function

3. Find the optimal values of L and K

4. Based on your answers to the question above, how many units of L and K should be used by the firm? What is the total output of these input combination?

Comparison between Consumption and Production

Consumption Production

• Utility: U=f(C,F) • Output: Q=f(L,K)

• Indifference Curve [F,C] • Isoquant Curve [L,K]

- Slope of Tangent Line - Slope of Tangent Line : MRS : MRTS

• Budget Line • Isocost Line

- Slope of Budget Line - Slope of Isocost Line : Relative Price Ratio : Relative Price Ratio

• MUF • (F + MUC • (C = 0 • MPL • (L + MPK • (K = 0

• Hypothesized Cost-Output Relationships

1. Cubic Total Cost Function

TC=a+bQ+cQ2+dQ3

MC=b+2cQ+3dQ2

ATC=(a/Q)+b+cQ+dQ2

2. Quadratic Total Cost Function

TC=a+bQ+cQ2

MC=b+2cQ

ATC=(a/Q)+b+cQ

3. Linear Total Cost Function

TC=a+bQ

MC=b

ATC=(a/Q)+b

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