A firm must decide how to allocate the 100 tons of some input I it
has between two production plants. The average total product curves of
the two plants are

and

If the firm optimally allocates the input between the two plants, the
first plant should get 80 (100%) tons
of the input

Correct

Comment:

We know for an optimal allocation MP of both plants need to be equal.

To calculate MP functions:

First calculate TP1 and TP2 (multiply functions by
I1 and I2 respectively)

Then just derive those functions to get MP1 and MP2:

MP1=-10(I1)

MP2=-40(I2)

MP1=MP2:

-10(I1)=-40(I2)

We also know that I1+I2=100, so I2=100-I1.

-10(I1)=-40(100-I1)

Solve and gives you I1=80

Question 2:Score 1/1

Your response

A firm produces its output using capital (K) and labor (L). The production
function is

The price of labor is given by 10, and the price is capital
by 7 .

The minimum cost of
producing Q units of output is given by: 11/2*Q (100%) .

Correct

Comment:

Leontief function:

F(K,L)=min(aK,bL)

r*(Q/a)+w*(Q/b) = Q*( (r/a)+(w/b) )

Filling above values in gives:

Q( (7/2)+(10/5) )

Solve, gives (11/2)*Q

Question 3:Score 1/1

Your response

A firm has a long-run total cost function:

The long run marginal coist function crosses
the long run average total cost function at Q equal to:

5/4 (100%)

Correct

Comment:

Two ways to solve this method:

1. You know that LRAC crosses the LRMC at its minimum,
so we can calculate derivative of LRAC and equal it to 0:

LRAC=2Q²-5Q+4 (divide LRTC by Q)

Derive it: 4Q+5

4Q+5=0

Q=5/4

2. Calculate the intersection by doing LRMC=LRAC (bit more work though):

LRAC=2Q²-5Q+4

LRMC=6Q²-10Q+4

2Q²-5Q+4=6Q²-10Q+4

Also gives Q=5/4 (also Q=0 but this is economics…)

Question 4:Score 1/1

Your
response

A firm needs to produce 90 units of a product. The firm has two
production plants. The total cost curves of the plants are :

and

If the firm allocates
optimally production across the two plants, it should produce72 (100%) units in
plant 1.

Correct

Comment:

In an optimal case MC1=MC2

You know 90=Q1+Q2, so Q2=90-Q1

MC1=2(Q1)+8

MC2=8(Q2)+8

2(Q1)+8=8(90-Q1)+8

Solve and gives you Q1=72

Question 5:Score 1/1

Your response

For any level of labor input above the maximum of the average product
curve, the marginal product curve is above the average product curve.

False (100%)
Comment:

Correct

Comment:

Question 6:Score 1/1

Your response

For any level of
production above the minimum of the average total cost curve, the
marginal cost curve is below the
average total cost curve.False (100%)