Shows the max output attainable from a given amt of a fixed input (capital) as the amt of the variable input (labor) is changed.

1. to raise a power to a power you need to multiply the exponents.

1. if the negative exponents in teh numerator get moved to denominator and become positive exponents.

2. negative exponents in the denominator get moved to the numerator and become positive (only move the negative exponent)

Says that to divide two exponents with the same base, you keep the base and subtract the powers put the anser in teh numerator or denominator depending on where the higher power was located

The firm will always hire the input that is cheapest. So, the function is

If w < r, TC = wq.

If w > r, TC = rq.

If w = r, either equation works

**that with a doubling of inputs, output more than doubles.** Since average cost = TC/Outputs, this increase in inputs (increase returns) will cause the numerator to double the old value while the new denominator is more than double the old value. As a result, **long-run average cost falls** *as more output is produced.*

Profit Formula =

TC = VC+FC

AC = C/1 = AFC+AVC

AFC = F/q

AVC = VC/q

AVC or Variable Cost

AC or Averabe Cost

–is the amount by which a firm’s cost changes (or variable cost chg) if the firm produces one more unit of output; ∆*C* is the change in cost when the change in output, ∆*q, *is 1 unit.

Marginal Cost = Chg in Cost/Chg qty

MC = Chg in VC/ chg in qty

–is the rate of change of cost as we make an infinitesimally small change in output.

*MC*=*dVC*/*dq* because *dF*/*q*=0.

What is the total Variable cost in this equation? **TC(Q)=5,000+2,000Q−10Q^2+0.25Q^3**

**2,000Q−10Q^2+0.25Q^3**

What is the fixed cost in this equation?

**TC(Q)=5,000+2,000Q−10Q^2+0.25Q^3**

Calculate the firm's total cost for Q=10

**TC(Q)=5,000+2,000Q−10Q^2+0.25Q^3p**

**TC(Q)=5,000+2,000Q−10Q^2+0.25Q^3**

What is the equation for the firm's average total cost?

**TC(Q)=5,000+2,000Q−10Q^2+0.25Q^3**

**ATC=TC/Q**

**= (5000/Q) + 2,000Q/Q - 10Q^2-1/Q +0.25Q^3-1/Q**

Calculate average total cost for Q=10

**TC(Q)=5,000+2,000Q−10Q^2+0.25Q^3**

**ATC= 500+2,000 - 100 + 25= 2,425 (ATC=TC/Q=24,250/10=2,425).**

What is the equation for the firm's marginal cost?

**TC(Q)=5,000+2,000Q−10Q^2+0.25Q^3**

**MC= 2000 - 20Q +0.75(Q^2)**

Calculate marginal cost for Q=10

**TC(Q)=5,000+2,000Q−10Q^2+0.25Q^3**

**MC=2000 -200 + 75= 1,875**

What is the equation for the firm's average variable cost?

**TC(Q)=5,000+2,000Q−10Q^2+0.25Q^3**

AVC=VC/Q=

(**2,000Q - 10Q^2 + 0.25Q^3)/Q= 2,000 - 10Q +0.25Q^2.**

Calculate average variable cost for Q=10:

**TC(Q)=5,000+2,000Q−10Q^2+0.25Q^3**

**AVC= 2,000 - 100 + 25= 1,925**

Calculate average variable cost for Q=20:

**TC(Q)=5,000+2,000Q−10Q^2+0.25Q^3**

**AVC= 2,000 - 200 + 100 = 1,900**

**L" work**labor units

change in total or variable cost / change in quantity

U-shaped curve

In short Run Capital is Fixed, so the chg in variable cost as output increases by one unit, MC, is the change in the what and formula?

Change in the cost of labor, where

MC = wage*extra labor necessary to produce one more unit of output

Chg.VC/Chg.extra.labor

–is the total number of units of output produced since the product was introduced.

–If a firm is operating in the economies of scale section of its average cost curve, expanding output lowers its cost for two reasons.

1. Its average cost falls today because of economies of scale,

2. also because of learning by doing.

–A firm enjoys economies of scope if it is less expensive to produce goods how?

MR=MC (where they intersect)

MR = chg in TR (TR2-TR1)/Q inputs (Q2-Q1)

MC = chg in TC (TC2-TC1)/Q inputs (Q2-Q1)

Find profit max; given:

TC = 120 + 2Q^2

TR = 100Q

Given the following:

TR=20Q

TC=75+10Q+0.01𝑄2

a. Find Total Profit Equation

b. Find MR

c. Find MC

d. Find Profit Max point

E. Find Profit Earned

a. What is this firm's total profit equation? Profit = TR – TC = 10Q - 75 - 0.01𝑄2

b. What is the firm's marginal revenue equation? MR= 20

c. What is the firm's marginal cost equation? MC = 10 +0.02Q

d. At what level of output is total profit maximized?

MR=MC = Q = 500.

e. How much profit is earned?

Profit = $2,425

**Capital) + (Beta**Labor)

1. Capital

2. Labor

If the production function is given by Q = f (z1, z2) and all inputs are multiplied by the same positive constant (t>1), then, what are the effect of output Returns to scale based on:

1. Equals or constant

2. decreasing or less than

3. increasing or greater than

1. Will increase at exactly % increase

2. Will increase by less than % increase

3. will increase by greater than % increase

the additional cost of producing on one additional unit of output

(MC unit2 - MC unit1)

What is the formula of following:

1. Total cost?

2. Avg total cost

3. avg fixed cost

4. avg variable cost

5. marginal cost

6. total fixed cost

7. total variable cost

1. TC = TFC + TVC

2. ATC = AFC +AVC or TC/Q

3. AFC = TFC/Q (Fixed cost is constant)

4. AVC = TVC/Q

5. MC = Chg in (TC2-TC1)/chg (Q2-Q1)

6. TFC = fixed cost is independant of production and is constant

7. TVC = TC-TFC

What are the profitability formulas to define following:

1. Total Revenue

2. Profit

3. Marginal Revenue

1. TR = Profit * Qty

2. Profit = Total Revenue - Total cost

3. MR = chg in TR/chg Q, then (Profit - TR-TC)

What are the following formula's for production function:

1. Marginal Profit

2. Avg Profit

1. MP = chg of Q/chg of L

2. AP = TQ/L