E321 Exam 3
List the characteristics of isoquants.
- Negative Slope - Nonintersecting - Convexity
List the conditions necessary for a market to be "perfectly competitive".
- There are many firms (sellers) in the industry (market), each firm is small relative to the total industry output. - Firms produce a similar product. - Firms and consumers have full information on the product's price and quality (full info requirement). - There is unrestricted resource mobility in/out of the industry in the LR (no barrier to entry or exit requirement).
State the equations for calculating Average Product of Labor (APL) and Marginal Product of Labor (MPL)
APL = Q/L MPL = ^Q/^L
State the equations linking MC with MPL and linking AVC with APL.
APL = Q/L MPL = ^Q/^L MC = w/MPL AVC = w/APL
What is an isocost line?
An isocost line is a line that identifies all the combinations of K and L, two factor inputs that can be produced at a given total cost.
Explain why diminishing marginal returns does not necessarily imply that an increase in labor input decreases output.
At first an increase in labor increases output. It isn't until you reach the inflection point for the MPL curve that an increase of labor marginally decreases the output.
Why could it be said that a profit maximizing firm's supply curve is positively sloped due to the law of diminishing returns?
Because of the law of diminishing returns, if L and Q go up and MPL goes down, then MC goes up because MC = w/MPL. The MC has a positive slope when MPL has a negative slope.
Explain how a perfectly competitive firm should choose a SR profit maximizing level of labor input (L*). State the specific solutions to the FOC and SOC for choosing L*.
Choose L* where FOC and SOC hold. FOC: d/Profit = d/L = 0 where VMP = W. - VMP = P* x MPL SOC: d2Profit/dL2 < 0 when dVMP/dL < 0 ... VMP curve has negative slope.
If a production function exhibits constant returns to scale, what does this imply about the shape of the LRTC, LRAC, LRMC curves? How about increasing and decreasing returns?
Constant returns to scale implies that as Q goes up, LRAC remains unchanged. Increasing returns to scale implies that as Q goes up, the LRAC goes down, so does LRMC so does LRTC eventually. Decreasing returns to scale implies that as Q goes up, the LRAC goes up, thus so do LRMC and LRTC.
If a firm is using "too much K" to produce a given output quantity at minimum possible cost, is w/r greater than or less than MRTS at this quantity?
If a firm is using "too little k", then MRTS M w/r so capital needs to be substituted for labor.
If a firm is constrained in the SR to use "too much K" to produce a given output quantity at minimum possible cost, is w/r greater than or less than MRTS at this quantity?
If a firm is using "too much k", then MRTS > w/r so labor needs to be substituted for capital.
Explain the LR adjustment process in a perfectly competitive firm.
If profit > 0 then return on resources owned > return in best alternative use. Industry attracts resource, which means entry of new firms and expansion of existing firms. This causes supply to increase and P* to drop until profit = 0 again. If profit < 0 then the return on resources owned < return in best alternative use. The industry then loses resources, firms exit and supply decreases until profit = 0 or industry disappears.
Explain the difference between implicit and explicit costs.
Implicit Costs: Opportunity costs associated with resourced already owned by the firm. Explicit Costs: Payments for resources now owned by the firm, accounting costs.
How is production in the LR different from production in the SR?
In the SR only the quantity of L can be varied in the production function. K is a fixed input. IN the LR all inputs can be varied in the production function.
Explain how a perfectly competitive firm operating in the SR could choose a profit-maximizing production quantity (Q*).
In the SR to choose a Q to maximize profit you must choose where: - P = MC (FOC) - dMC/dQ > 0. (SOC)
State the linear equation, and the slope for the isocost line.
K = TC/r - w/r Slope = -w/r
What is an isoquant?
LR production opportunities are illustrated using isoquants, which are curves of constant output in K,L space.
Explain how the basic shapes of these curves can be derived from the corresponding total curves.
MC: Because of the law of diminishing marginal returns, the marginal product of labor varies with the amount of output and, therefore, so must marginal cost. When MPL is falling, MC must be rising.
State the equations for calculating the firm's SR Marginal Cost (MC), Average Variable Cost (AVC), Average Fixed Cost (AFC), and Average Total Cost (ATC) curves.
MC: ^TVC/^Q AVC: TVC/Q AVF: TFC/Q ATC: TC/Q
How is MRTS related to MPL and MPK?
MRTS is the decrease in K that holds Q constant when L is increased by one unit in the production function. MRTS = ^K/^L
Define Marginal Rate of Technical Substitution (MRTS)
MRTS measures the extent to which L can be substituted for K in a production function holding Q constant. When the MRTS diminishes along an isoquant, the isoquant is convex.
State the two conditions must hold at a SR competitive equilibrium.
Market: Qd = Qs at P* Firms: Try to profit maximize given P*.
State the three conditions that must hold at a LR competitive equilibrium.
Market: Qs = Qd at P* Firms: Profit maximize given P* Firm's Zero Economic Profit: Profit = 0 in LR when P* = min LRAC - Economic Profit = TR - Exp Costs - Imp Costs
Why is a firm said to be a "price taker"?
No one firm can unilaterally influence the price (P*), which is determined by the market supply and demand. Each firm views their selling price as the market price (P*).
State the general algebraic equation for a production function with only two inputs: Labor (L) and Capital (k).
Quantity (Q) = f (L,K)
Explain the difference between increasing, constant, and decreasing returns to scale.
RETURNS TO SCALE IS A LR CONCEPT ONLY Increasing: A proportional increase in all inputs resulting in a greater proportion of production (ex: 100 workers and 50 machines = 1,000 products; 200 workers and 100 machines = 2,500 products.) Constant: An increase in all inputs that results in the same proportion of production (ex: 100 workers and 50 machines = 1,000 products; 200 workers and 100 machines = 2,000 products.) Decreasing: A proportional increase in all inputs resulting in a proportional decrease of production (ex: 100 workers and 50 machines = 1,000 products; 200 workers and 100 machines = 1,500 products.)
Explain why the L that maximizes MPL (or APL) determines the Q that minimizes MC.
Rooted in the equations is the inverse of MPL (and APL), so when MPL (or APL) is at its maximum, MC (or AVC) must be at its minimum.
Explain how the TC curve is derived from the TVC and TFC curves.
The TC is derived from the TVC curve because TC = TVC + TFC. Since TFC is a fixed horizontal line, TFC is simply the beginning from where TVC is plotted on the $ axis.
Explain how the basic shape of the TVC curve is determined by the TP curve.
The basic shape of the TVC curve is rooted in the TP curve, but with Q on horizontal axis and units of L rescaled by W (TVC = W*L) If hiring labor is the only variable cost to the firm (SR), then the TP curve equals the TVC curve.
How can the information in the firm's EP be used to derive its LRTC curve?
The exact shape of the EP depends on returns to scale. Linearity implies constant returns to scale.
What is an expansion path (EP)?
The expansion path is a curve formed by connection the points of tangency between isocost lines and the highest respective attainable isoquants.
State in words the basic circumstances under which a firm should choose in the SR to operate a loss rather than shut down.
The firm will operate with a loss when: - Q* is where the FOC and SOC hold. - At Q*: TC > TR > TVC so Profit > TFC. - At Q*: ATC > P* > AVC
State in words the basic circumstances under which a firm should choose in the SR to shutdown.
The firm will shutdown when: - Q* = 0 - At Q*: TR = TVC = so Profit = - TFC - At the Q where FOC and SOC hold: TR < TVC and P* < AVC
Explain why the law of diminishing returns is also a law of increasing marginal cost.
The law of diminishing returns implies that the MC curve will eventually be positively sloped when MPL is negatively sloped. Same for APL and AVC.
Explain how the basic shape of the APL curve and be derived from the TP curve.
The shape of the APL curve is derived from the TP curve because at the inflection point of the TP curve, APL is at its maximum. So APL is rising until it hits the inflection point, then falls to show diminishing marginal returns.
Explain how the basic shape of the MPL curve and be derived from the TP curve.
The shape of the MPL curve is derived from the TP curve because at the inflection point of the TP curve, MPL is at its maximum. AS MPL goes down, it reflects that TP has positive slope but is decreasing due to diminishing returns.Then at the max of TP, MPL hits the X axis and begins to become negative.
How is the SR supply curve for a market constructed? You should be able to outline the logic that leads from diminishing marginal returns to positively sloped SR industry supply curve.
The slope of the SR supply curve relies on three key elements: 1) Law of diminishing returns and the firm's SR cost structure. - If L goes up, Q goes up, and MPL goes down, then MC goes up because MC = w/MPL. The MC has a positive slope when MPL has negative slope. 2) Perfect competition as the firm's revenue structure. 3) Goal of firm is to maximize profit or minimize loss.
State the formal condition for choosing L and K to minimize total cost minimize total cost for a specific production quantity.
To minimize cost, the firm should employ inputs in such a way that the marginal product per dollar spent is equal across all inputs. When MPL/w > MPK/r, a firm can increase output without increasing cost by shifting outlays from capital to labor. When MPK/r > MPL/w, a firm can increase output without increasing cost by shifting outlays from labor to capital.
Explain why either a change in the price of an input or a change in the production technology will generate a shift in the firm's EP and thus it's LRTC curve.
When w or r increase it causes a shift in the isocost line which then causes the EP curve to shift as well as when technology increases.
