Assignment on Cost Equations

Given the following TC function:  TC = 1,500 + 300Q - 24Q²  + 1.5Q³, answer the following questions.

-         Marginal Cost (MC) = TC´ = 300 – 48Q +4.5Q²

-         Total Fixed Cost (FC or TFC) = 1500

-         Total Variable Costs (TVC) = TC – TFC = 300Q - 24Q²  + 1.5Q³

-         Average Fixed Costs (AFC) =  FC/Q = 1500/Q

-         Average Total Cost (ATC) = TC/Q = 1500/Q + 300 - 24Q + 1.5Q²

-         Average Variable Cost (AVC) = TVC/Q = 300 – 24Q  + 1.5Q²

-         Profits = Total Revenue (TR) – Total Costs (TC)

-         TR = P*Q

-         AC = (TFC + TVC)/Q = AFC + AVC

-         TC = TVC + TFC

1.     How much is the TFC.

ASNWER:

TFC = 1500

2.     Write the TVC equation.

ASNWER:

TVC = TC – TFC = 300Q - 24Q²  + 1.5Q³

3.     Write the AVC equation.

ASNWER:

AVC = TVC/Q = 300 – 24Q  + 1.5Q²

4.     At which level of output starts stage II of production (Hint: as the AP_L reaches its maximum, AVC reaches its minimum).

ASNWER:

AVC´ = -24 + 3Q

When AVC reaches its minimum → AVC´ = 0

-24+3Q = 0 → Q = 8

5.     Write the MC equation.

ASNWER:

MC = TC´ = 300 – 48Q + 4.5Q²

6.     At which level of output diminishing returns starts, (Hint: as MP_L reaches its maximum, MC reaches its minimum).

ASNWER:

MC´ = -48 + 9Q

When MC reaches its minimum → MC´ = 0

-48 + 9Q = 0 → Q = 48/9

7.     When the price of a variable input rises in the short-run, which of the following curves would shift up: AFC, AVC, MC, ATC.

ASNWER:

AVC, MC, ATC

8.     When the rent of the factory building rises, which of the following curves would shift up: AFC, AVC, MC, ATC.

ASNWER:

AFC,ATC