question

Costs

answer

Total costs = fixed costs + variable costs

question

Short-run costs

answer

Costs = k-bar (fixed capital)

Can use production function to solve for one of the variables (K or L) in terms of quantity, and then can plug that back in

If K is fixed in the short-run, can solve for L and plug in k-bar...and then you'll arrive at a short-run cost function.

**r (rate of capital) + quantity of L**w (wage rate of L)Can use production function to solve for one of the variables (K or L) in terms of quantity, and then can plug that back in

If K is fixed in the short-run, can solve for L and plug in k-bar...and then you'll arrive at a short-run cost function.

question

Deriving short-run cost function

answer

1. You are given a production function

2. You are given the

a. Rental rate (r) of capital

b. The wage rage (w) of labor

c. The fixed level of capital

3. We know the cost function is generally of the form: c = k

We can solve the production function for one variable - normally labor in the short-run

And then can plug it into the cost function, such that we get a cost function that tells us how cost varies with quantity produced

2. You are given the

a. Rental rate (r) of capital

b. The wage rage (w) of labor

c. The fixed level of capital

3. We know the cost function is generally of the form: c = k

**r + l**wWe can solve the production function for one variable - normally labor in the short-run

And then can plug it into the cost function, such that we get a cost function that tells us how cost varies with quantity produced

question

Marginal cost

answer

The derivative of cost with respect to quantity

delta c / delta q

cost of producing the next unit

delta c / delta q

cost of producing the next unit

question

Short-run MC and relationship to MPL

answer

1. We started with a production function and solved it such that we had L = some relationship to K and quantity

2. On the other hand, we have our TC function ; if we take the derivative of cost w/ respect to labor, the capital term drops out because it's fixed ... so we get change in cost / change in quantity = wage * change in labor / change in quantity

3. We know the MPL is delta q / delta L - how quantity changes for a change in labor

4. So we can rewrite MC as w / MPL

5. This means marginal cost will be higher when wage is higher ... and lower when MPL, meaning delta q / delta L, is higher ... meaning, that you get more output from an additional worker...

6. This explains why firms want to pay productive people higher wages

MC = wage rate / MPL

2. On the other hand, we have our TC function ; if we take the derivative of cost w/ respect to labor, the capital term drops out because it's fixed ... so we get change in cost / change in quantity = wage * change in labor / change in quantity

3. We know the MPL is delta q / delta L - how quantity changes for a change in labor

4. So we can rewrite MC as w / MPL

5. This means marginal cost will be higher when wage is higher ... and lower when MPL, meaning delta q / delta L, is higher ... meaning, that you get more output from an additional worker...

6. This explains why firms want to pay productive people higher wages

MC = wage rate / MPL

question

Average costs

answer

c / q

Example: cost = 10 + 5q^2

Average cost = cost / q = 10/q + 5q

Average cost: often decreases and then increases. Why?

-Total costs = fixed costs + variable costs

-For first set of units, you are paying off your fixed costs, so as quantity increases, your costs are spread over more units, so average cost reduces

-Once you've paid off fixed costs, then your cost rises because your average variable costs rise

Example: cost = 10 + 5q^2

Average cost = cost / q = 10/q + 5q

Average cost: often decreases and then increases. Why?

-Total costs = fixed costs + variable costs

-For first set of units, you are paying off your fixed costs, so as quantity increases, your costs are spread over more units, so average cost reduces

-Once you've paid off fixed costs, then your cost rises because your average variable costs rise

question

Long-run cost curves

answer

Choosing the mix of inputs in order to minimize costs

Optimal mix may differ with quantity

1. What's the right mix of L and Q for a given quantity?

2. As the quantity varies, how does it change the optimal mix of L and Q

Steps

1. We have production function

2. We have costs

3. With costs and the knowledge of the slope of the isocost line, we can figure out the ratio of k to L

4. We can plug the info from #3 back into the production function to have a more precise production function

5. We can solve for L in terms of Q and K in terms of Q

6. We can plug #5 into our TC function in order to get how cost varies w/ production or output

...what we need is w, r, and production function

-everything comes from these 3 things

Optimal mix may differ with quantity

1. What's the right mix of L and Q for a given quantity?

2. As the quantity varies, how does it change the optimal mix of L and Q

Steps

1. We have production function

2. We have costs

3. With costs and the knowledge of the slope of the isocost line, we can figure out the ratio of k to L

4. We can plug the info from #3 back into the production function to have a more precise production function

5. We can solve for L in terms of Q and K in terms of Q

6. We can plug #5 into our TC function in order to get how cost varies w/ production or output

...what we need is w, r, and production function

-everything comes from these 3 things

question

Isocost curves

answer

A firm's budget constraint

question

Cost curves

answer

The marginal cost intersects the average costs curve at its minimum

If you have a function and you take the average, then the minimum is going to be at the derivative

If you have a function and you take the average, then the minimum is going to be at the derivative

question

MC and MPL relationship

answer

Close relationship between marginal cost and marginal product of labor

MPL = DQ / DL

-Digging a hole

-Diminishing marginal product of labor

Derivative of cost function with respect to labor

-Costs = k-bar (fixed capital)

-Delta C / Delta L = k-bar

MC of production = delta c / delta q

-Delta

MPL = DQ / DL

-Digging a hole

-Diminishing marginal product of labor

Derivative of cost function with respect to labor

-Costs = k-bar (fixed capital)

**r (rate of capital) + quantity of L**w (wage rate of L)-Delta C / Delta L = k-bar

**r**dLMC of production = delta c / delta q

-Delta

question

What happens when input prices change? Or W:R ratio changes?

answer

...

question

Isocost line budget is not fixed

answer

Isocost line is asking what mix of capital and labor required to produce a given quantity of goods at the lowest cost given the productivity of each

Budget not fixed, so minimal budget could change as we change the cost of inputs

Budget not fixed, so minimal budget could change as we change the cost of inputs

question

Long-run expansion path

answer

...

question

At what range of prices will the firm produce a positive output?

answer

The firm will supply positive levels of output in the short run as long as P = MC > AVC, or as long as the firm is covering its variable costs of production.

In my language, revenue maximized where P = MC ... so this means the revenue is greater than the average variable costs...meaning, no operating loss.

In my language, revenue maximized where P = MC ... so this means the revenue is greater than the average variable costs...meaning, no operating loss.

question

At what range of prices will the firm earn a negative profit?

answer

The firm will earn negative profit when P = MC < AC, or at any price below minimum average cost.

question

Firm's supply curve

answer

The MC curve above where MC = AVC

The firm will produce at the point where price equals MC as long as MC is greater than or equal to AVC. T

The firm will produce at the point where price equals MC as long as MC is greater than or equal to AVC. T

question

What is the lowest price at which each firm would sell its output in the long run? Is profit positive, negative, or zero at this price? Explain.

answer

In the long run profit falls to zero, which means price falls to the minimum value of AC. To find the minimum average cost, set marginal cost equal to average cost and solve for q