Find the Jacobian $\frac { \partial ( x , y ) } { \partial ( u , v ) } \text { for the following change of variables: }$

question 11

Multiple Choice

Find the Jacobian $\frac { \partial ( x , y ) } { \partial ( u , v ) } \text { for the following change of variables: }$ $x = \frac { 1 } { 4 } ( 9 u - 4 v ) , y = \frac { 1 } { 4 } ( 3 u + 3 v )$

• A) \(\frac { 27 } { 16 }\)
• B) \(- \frac { 45 } { 4 }\)
• C) \(- \frac { 27 } { 16 }\)
• D) \(\frac { 39 } { 16 }\)
• E) \(- \frac { 39 } { 16 }\)

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Definitions:

Purely Competitive Firm

A company that operates in a market where there are many sellers and buyers, the products are homogeneous, and there is free entry and exit from the market.

Vertical Axis

The y-axis in a graph, which typically shows the range of values for the variable measured.

Pure Competition

A market structure featuring a large number of small firms selling identical products, with no single firm able to influence market price.

Differentiated Products

Goods and services that are distinct from those offered by competitors due to unique characteristics, branding, quality, or features.