TAMU ECON 323 Exam 2

What does decreasing returns to scale mean?

As inputs increase, production increases at a slower rate. 2f(L,K) > f(2L,2K) α + β < 1

What does constant returns to scale mean?

As inputs increase, production increases at the same rate. 2f(L,K) = f(2L,2K) α + β = 1

What does increasing returns to scale mean?

As inputs increases, production increase at a higher rate. 2f(L,K) < f(2L,2K) α + β > 1

What is the equation for the Cost of production q amounts of output when capital is held constant?

C(q) = rK + wL(q,K) or C(q) = F + VC(q)

What is the equation for Cost when both Labor and Capital are variable?

C(q) = rK(q;r,w) + wL(q;r,w)

Under what circumstances does a firm satisfy the Law of Decreasing Marginal Returns?

A firm is experiencing decreasing marginal returns when inputs increases but the amount of output generated from each additional input is decreasing.

What is the law of Decreasing Marginal Returns of Labor?

A firm's marginal product of labor per unit of additional labor is decreasing until additional output reaches 0 and no longer increases.

What is a firm's production function?

A function for a firm that assigned the MAXIMAL amount of output for each combination of inputs.

What does the graph of a firm's Iso-Quant look like?

A graph with labor on one axis and capital on the other. A line connects all the combinations of labor and capital that have the same value of output.

What is a firm's Iso-Cost line?

A line that connects all the combinations of labor and capital that have the same cost, C.

What is an Iso-Quant?

A line that connects all the combinations of labor and capital that produce the same amount of output.

What is the equation for a firm's Average Cost?

AC(q) = C(q)/q

What is the equation for a firm's Average Fixed Cost?

AFC(q) = AF(q)/q

What is the equation for a firm's Average Variable Cost?

AVC(q) = VC(q)/q

What makes accounting profit and economic profit different?

Accounting profit can be manipulated; Its simply numbers reported. Economic profit cannot be manipulated.

What is a firm?

An economic entity that produces and sells goods and pays a cost for its production. Takes in inputs and to create outputs.

How can you tell if a firm with a linear production function will produce with only capital or labor?

Compare the Marginal Rate of Technical Substitution with the ratio of prices: MRTS > w/r - uses labor only MRTS < w/r - uses capital only

What does the graph of Marginal Product of Labor look?

Graphs the slopes at each combination of labor and output as labor increases.

What does returns to scale mean?

How does production change when the amount of input used changes.

What is the equation for a firm's Fixed Cost?

F = rK

What is economic cost?

Economic cost is the best alternative use of resources that are being used to make the firm's revenue.

What is the equation for a firm's Marginal Cost?

MC(q) = C'(q)

What does it mean for inputs to be complements?

Production will not change unless the inputs both change in the correct proportion.

How do you find the value of wL(q,K) when capital is fixed?

Set q equal to the production function. Plug in known values. (K b/c it's fixed) Solve for L.

How do you graph the Iso-Quant of a production function?

Set the production function equal to the desired output value. Solve for K in terms of L.

What is a firm's Marginal Product of Capital?

Shows how much a firm's production changes as capital changes, assuming labor is constant. -Gives us the slope of the line tangent to the production function, with labor held constant, at a certain capital and output combination.

What does a firm's supply curve represent?

It assigns a profit-maximizing output for each value price level.

What is the goal of a firm?

To maximize economic profit.

What is the equation for a firm's Variable Cost?

VC (q) = wL(q,K)

How do you find the values of L and K when both variables are unknown?

Solve for two equations? 1) f(L,K) = q 2) MRTS(L,K) = w/r -Find the value of K after simplifying one of the equations (usually number 2) -Plug in the value of K into the other equation (usually number 1) and find your L value -Plug the value of L back into the equation for the value of K to find K. In the end, the values of L and K should only be in terms of r, w, and q, not L or K. -Can use these value to plug them back into the equation for cost, when both L and K are unknown.

What is a firm's Marginal Product of Labor?

Tells us how much a firm's production changes as labor changes, assuming capital is constant. -Gives us the slope of the line tangent to the production function, with capital held constant, at a certain labor and output combination.

What are the characteristics the production level that maximizes profit when labor and capital are variables?

p = MC(q) p >= AC(q)

What are the characteristics the production level that maximizes profit when only labor is a variable?

p = MC(q) p >= AVC

What is the equation for the Marginal Rate of Technical Substitution?

(Marginal Product of Labor)/(Marginal Product of Capital)

What is the equation for a firm's Average Product of Labor?

(Production at a combination of labor and capital)/(Labor used to make that production) f(L,K)/L

How do you find the supply curve for a firm when only labor is a variable?

It's the Marginal Cost line that is above AVC.

What does the graph of Variable Cost look like?

It's the graph of the production function, flipped axis, and labor scaled down. -One axis is output and the other is cost.

What does the graph of cost (total cost) look like?

It's the graph of variable cost, but it starts at the fixed cost level.

What is the equation for the slope of the line tangent to the Iso-Quant of a firm at (L,K)

(Change in Capital)/(Change in Labor)

What is the equation of Marginal Product of Capital?

(Change in Production)/(Change in Capital) -The derivative of the production function in terms of capital (holding Labor constant).

What is the Marginal Product of Labor equation (with explanation)?

(Change in Quantity of Production)/(Change in Labor) -The derivative of the Production Function with respect to L. (K is held constant)

What dose the graph of fixed cost look like?

Fixed cost is indecent of output. It's a straight line at whatever value it is. -One axis is output and the other is cost.

What does the graph of Average Cost look like?

Output is on the horizontal axis and cost is on the vertical axis. -It has an asymptote at 0. From there it decreases until it crosses Marginal Cost, and then increases again. It is always above Average Variable Cost

What does the graph of Average Variable Cost look like?

Output is on the horizontal axis and cost is on the vertical axis. -Line begins where marginal cost is equal to zero, or where the slope of variable cost at 0. -Decreases until it reaches q2. q2 is the point on the variable cost graph where the tangent to this point runs through (0,0). As it decreases, it is always above marginal cost.- -At q2, MC(q2) = AVC(q2) -The line crosses and increases, but underneath marginal cost.

What does the graph of Average Fixed Cost look like?

Output is on the horizontal axis and cost is on the vertical axis. A decreasing function. As more output is created, fixed cost decreases because it does not change.

What does the graph go marginal cost look like?

Output is on the horizontal axis and cost on the vertical axis. -Starts at the slope of the variable cost at 0. Can be zero, or can be positive. -Decreases until it reaches the point q1. q1 is the quantity on the variable cost graph that the slope of variable cost starts to decrease. -Marginal cost increase after this point.

What is the equation for economic profit?

Revenue (Accounting profit) - Economic costs

What do we know about a firm that is in a market that has free-entry?

The firm has constant returns to scale.

What happens when a firm's economic costs outweigh its revenues?

The firm will use their resources for the best alternative (the economic cost) and maximise its profits.

What are the characteristics of a competitive market?

-All participants are price takers. -Producers and consumers decide how much to make/buy based on observed market price. -Free-entry is not necessary.

How do you find supply curve from cost function?

-Decide if it's only labor as a variable or both capital and labor. -Solve for p=MC(q) in terms of q = -Check to see if the second rule holds at that price. If it does, then that is the supply curve.

What is special about the cost, marginal cost and average cost graphs of a firm that has constant returns to scale?

-The cost function is linear. -The Marginal Cost is equal to the Average Cost.

What is special about the cost, marginal cost and average cost graphs of a firm that has decreasing returns to scale?

-The cost graph is increasing. -The Marginal Rate line increase always above the Average Cost line.

What do you know about a firm with a production function that is linear?

It will produce either with only capital or only labor.

How do you find the supply curve for a firm when labor and capital are variable?

It's the Marginal Cost line that is above AC.

What does the revenue of a firm equal?

R(q) = pq

What does the Iso-Quant of a firm with inputs that are not substitutes or complements look like?

The Iso-Quant is a smooth curve.

What does the Iso-Quant for a firm with inputs that are complements look like?

The Iso-Quant is linear.

What is the Marginal Rate of Technical Substitution of Labor for Capital?

The amount of capital that can be replaced with one unit of labor so that production remains the same. -The slope of the iso-quant that passes through a combination of L & K, at (L,K). The slope of the line tangent to the Iso-Quant at (L,K).

How do you find the profit for a firm when labor and capital are variables, graphically?

The area between AC and P on MC.

How do you find the profit for a firm when only labor is variable, graphically?

The area between the AC and MC at price p.

What is a firms Average Product of Labor?

The average number of units produced per unit of labor.

What does Average Product of Labor look graphically?

The average product of labor is the SLOPE of the line that passes through (0,0) and (L,f(L,K))

How do you know when a firm has constant returns to scale from its cost function?

The cost function is linear.

What does the Iso-Quant for a firm with inputs that are perfect substitutes look like?

The iso-quant is linear.

What does the supply curve look like for a firm with constant returns to scale?

The supply curve is flat and equals the firm's Marginal Cost and Average Cost.

What does it mean for inputs to be perfect substitutes.

The two inputs can be substituted for each other while production remains constant.

What is the equation for a firm's profit?

π(q) = R(q) - C(q) or π(q) = pq - C(q) or π(q) = q(p- (C(q)/q)) π(q) = q(p-AC(q))