Question 1

A firm faces the following total product curves depending on how much capital it employs:

K = 1 unit | K = 2 units | K = 3 units |

Quantity of Labor | Total Product | Quantity of Labor | Total Product | Quantity of Labor | Total Product |

1 | 100 | 1 | 123 | 1 | 139 |

2 | 152 | 2 | 187 | 2 | 193 |

3 | 193 | 3 | 237 | 3 | 263 |

4 | 215 | 4 | 263 | 4 | 319 |

5 | 233 | 5 | 286 | 5 | 366 |

6 | 249 | 6 | 306 | 6 | 407 |

7 | 263 | 7 | 323 | 7 | 410 |

a. Suppose that the firm currently employs 1 unit of capital and 3 of labor. Compute MRTSLK. Compute MPL. Compute MPK.

[3 marks]

Computation of MPL and MPK will be performed first prior to MRTSLK. Computation of MPL can be done using 2 methods; namely by tabulating the Figure 1.1 or by way of equation. These are to be proven as below.

Figure 1.1 shows the computation of each MPL and it clearly illustrates that MPL = 41 where it employs 1 unit of capital and 3 of labor.

K = 1 unit | K = 2 units | K = 3 units |

Quantity of Labor | Total Product | MPL | Quantity of Labor | Total Product | MPL | Quantity of Labor | Total Product | MPL |

1 | 100 | - | 1 | 123 | - | 1 | 139 | - |

2 | 152 | 52 | 2 | 187 | 64 | 2 | 193 | 54 |

3 | 193 | 41 | 3 | 237 | 50 | 3 | 263 | 70 |

4 | 215 | 22 | 4 | 263 | 26 | 4 | 319 | 56 |

5 | 233 | 18 | 5 | 286 | 23 | 5 | 366 | 47 |

6 | 249 | 16 | 6 | 306 | 20 | 6 | 407 | 41 |

7 | 263 | 14 | 7 | 323 | 17 | 7 | 410 | 3 |

Equation 1.1 shows how MPL is computed.

MPL = ∆Q / ∆L

= (193 – 152) / (3 – 2)

= 41 /1

= 41

MPK = ∆TP / ∆K

= (193 – 0) /1

= 193 /1

=193

MRTSLK = MPL / MPK

= 41 / 193

= 0.2124

Hence, MPL = 41, MPK = 193, MRTSLK = 0.2124.

b. Suppose that the firm currently employs 2 units of capital. The price of capital is $4 per unit and the price of labor is $10 per unit. What is the short-run total cost of producing 263 units of output? What is the long-run total cost of producing 263 units of output?

[3 marks]...

A firm faces the following total product curves depending on how much capital it employs:

K = 1 unit | K = 2 units | K = 3 units |

Quantity of Labor | Total Product | Quantity of Labor | Total Product | Quantity of Labor | Total Product |

1 | 100 | 1 | 123 | 1 | 139 |

2 | 152 | 2 | 187 | 2 | 193 |

3 | 193 | 3 | 237 | 3 | 263 |

4 | 215 | 4 | 263 | 4 | 319 |

5 | 233 | 5 | 286 | 5 | 366 |

6 | 249 | 6 | 306 | 6 | 407 |

7 | 263 | 7 | 323 | 7 | 410 |

a. Suppose that the firm currently employs 1 unit of capital and 3 of labor. Compute MRTSLK. Compute MPL. Compute MPK.

[3 marks]

Computation of MPL and MPK will be performed first prior to MRTSLK. Computation of MPL can be done using 2 methods; namely by tabulating the Figure 1.1 or by way of equation. These are to be proven as below.

Figure 1.1 shows the computation of each MPL and it clearly illustrates that MPL = 41 where it employs 1 unit of capital and 3 of labor.

K = 1 unit | K = 2 units | K = 3 units |

Quantity of Labor | Total Product | MPL | Quantity of Labor | Total Product | MPL | Quantity of Labor | Total Product | MPL |

1 | 100 | - | 1 | 123 | - | 1 | 139 | - |

2 | 152 | 52 | 2 | 187 | 64 | 2 | 193 | 54 |

3 | 193 | 41 | 3 | 237 | 50 | 3 | 263 | 70 |

4 | 215 | 22 | 4 | 263 | 26 | 4 | 319 | 56 |

5 | 233 | 18 | 5 | 286 | 23 | 5 | 366 | 47 |

6 | 249 | 16 | 6 | 306 | 20 | 6 | 407 | 41 |

7 | 263 | 14 | 7 | 323 | 17 | 7 | 410 | 3 |

Equation 1.1 shows how MPL is computed.

MPL = ∆Q / ∆L

= (193 – 152) / (3 – 2)

= 41 /1

= 41

MPK = ∆TP / ∆K

= (193 – 0) /1

= 193 /1

=193

MRTSLK = MPL / MPK

= 41 / 193

= 0.2124

Hence, MPL = 41, MPK = 193, MRTSLK = 0.2124.

b. Suppose that the firm currently employs 2 units of capital. The price of capital is $4 per unit and the price of labor is $10 per unit. What is the short-run total cost of producing 263 units of output? What is the long-run total cost of producing 263 units of output?

[3 marks]...