# MATHEMATICS

**Question ****5**

Hedge Fun is a landscaping firm that specializes in topiary. Last year, the firm had 30 employees and served 120 customers. This year, it had 35 employees and served 135 customers. What is the marginal product of labor?

Select one:

A. 2

B. 3

C. 4

D. 5

E. none of the above

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Marginal Product of labor =

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**Question ****6**

Whenever average product is declining with increases in input usage:

Select one:

A. marginal product is less than average product

B. total product is declining with increases in input

C. total product is increasing with increases in input

D. marginal product is greater than average product

E. total product is at a maximum

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**Question ****7**

The law of diminishing marginal returns states that:

Select one:

A. the marginal product of labor declines as all inputs are increased

B. production functions exhibit decreasing returns to scale

C. the marginal product of labor returns as more capital is used

D. the marginal product of a factor eventually diminishes as more of the input is used, holding other inputs fixed

E. the marginal product of a factor always diminishes as more of the input is used, holding other inputs fixed

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**Question ****8**

The optimal combination of two inputs, *K* and *L*, can be characterized by:

Select one:

A. *P*_{K}*MP** _{K}*=

*P*

_{L}*MP*

_{L}B. *MP** _{K}*=

*MP*

_{L}C. *P*_{L}*MP** _{K}*=

*P*

_{K}*MP*

_{L}D. *MP** _{K}*/

*MP*

*=*

_{L}*P*

*/*

_{L}*P*

_{K}E. none of the above

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**Question ****9**

The marginal rate of technical substitution between two inputs:

Select one:

A. shows the rate at which one input can be traded for another, holding output constant

B. shows the efficient combination of inputs

C. increases as we move down an isoquant

D. shows the rate at which output can be increased by using more of both inputs

E. shows the rate at which output decreases when using less of one of the inputs

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**Question ****10**

If output is produced according to *Q* = (*KL*)^{3/4}, then this production process exhibits:

Select one:

A. increasing returns to scale

B. decreasing returns to scale

C. first increasing and then decreasing returns to scale

D. constant returns to scale

E. first decreasing and then increasing returns to scale

Q(M) =

**Question ****11**

Output elasticity can be defined as the:

Select one:

A. percentage change in output divided by the (equal) percentage change in all inputs

B. change in output divided by the change in all inputs

C. change in inputs divided by the change in output

D. change in output divided by the change in one input

E. percentage change in output divided by the (average) percentage change in all inputs

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**Question ****12**

If output is produced according to *Q* = 30*L* + 12*K*, then the output elasticity is:

Select one:

A. 2

B. 0

C. 1

D. 0.5

E. 21

As the production function is linear so elasticity is 1.