Question

Suppose that a firm's production function for Temoc plush toys is given by the following formula: Q=12(EO+EG)^(1/3)

where EO is the number of orange workers and EG is the number of green workers.

The wage that orange workers receive is $7, and the wage for green workers receive is $4. The price of a Temoc Plush Toy is $9.

How much profit does the firm earn?

Answer 1

As Production function can be written as

(Q/12)3 = EO + EG

So perfect Substitutes technology, hence corner solution exist, only one input is used in Production

So, MRTS = MPO/MPG = 1

Now WO/WG = 7/4

As MRTS < wO/wG

1< 7/4

​​​​​​MPO /wO < MPG/wG

only Green workers are employed

EO*= 0,

so Production function , Q= 12(EG)1/3

At eqm, P*MPG = w

9*(12/3)*EG​​​-2/3 = 4

9= EG​​​​​2/3

EG*= 27

Q*= 12*3 = 36

π= 9*36 - 4*27

= 324 - 108

= $ 216