Economics Part 2 Harvard Case Solution & Analysis


 Explanation of Terms:

Production Function:A production function is basically defined as the function, which relates the physical output of the product to the factors of production. In simple words it relates to the maximum number of outputs of a product which could be obtained from the minimum number of inputs.

Marginal Product: Marginal product is defined as the change in the overall output from deploying one additional unit of input; for example the change in productivity by increasing labors from 5 to 6.

Isoquant Curve: This is basically a graph that depicts all possible input combinations, which result in the generation or production of the desired output level.

TRS: This is the technical rate of substitution. It is defined as the amount or quantity of the reduction in one input as a result of increasing another input.

Returns to Scale: This basically explains the rate of the increase in the firm’s output as a result of the increase in the total input or the factors of the production in the long run.

Isoprofit Line: This is basically a graph of a profit function. The word Iso means same which means the profit on the line is same.

Isocost Line: This line represents the combinations of the firms factors of production and these have the same total cost.

 Comment on Production Functions

A: The investment equal to labor would need to be made for substituting capital for labor
B: The investment equal to double of labor would need to be made for substituting capital for labor.
C: Minimum investment in capital would need to be made to replace labor for capital.
3.Yes, this production function justifies returns to scale because as the input is increased, then the output, which is the function of the x1 and x2 inputs, also increases with a higher magnitude.
4.This statement is false because if the marginal product that is the change in output as a result of increasing one unit of input, which is labor in this case, is increased, then the marginal product would increase further. Therefore, a profit maximizing firm would want to hire more labor to generate more output at lower wage rates.

Problem 1
Profit maximizing output = y= 8x^0.5
X = 8
Y = 8*(8)^0.5 – 22.62
Amount of Factor = y= 8x^0.5
Y = 22.62
SQRT(X^0.5) = SQRT(22.62/8)
X= 1.681
b). Maximum Profits
Revenue – Cost
40 –(4x^-0.5)*8
Profit = $ 15.31...........................

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