UNIT II: FIRMS & MARKETS

UNIT II: FIRMS & MARKETS
4/17/2017 UNIT II: FIRMS & MARKETS Theory of the Firm Profit Maximization Perfect Competition Review 7/14 MIDTERM 6/28

4/17/2017 Theory of the Firm Today we will build a model of the firm, based on the model of the consumer we developed in UNIT I. Where consumers attempt to maximize utility, firms attempt to maximize profit. We saw how changes in prices affect consumers’ optimal decisions and derived a demand function: P = f(Qd). Now we will see how changes in prices affect firms’ profit maximizing decisions and derive a supply curve: P = f(Qs). Later, we will put supply and demand together, and begin our analysis of markets and market structures.

Theory of the Firm The Good News!
4/17/2017 Theory of the Firm The Good News! In moving from the consumer to the firm, we replace the troublesome notion of utility with something nice and hard-edged: profit. Where utility is subjective and thus hard to measure, now we’ll be talking about simple, measurable quantities, physical units of inputs (tons of steel, hours of labor) and outputs, and an account for everything in dollars and cents (“the bottom line”).

Theory of the Firm The Technology of Production Short-run v. Long-run
4/17/2017 Theory of the Firm The Technology of Production Short-run v. Long-run Isoquants Returns to Scale Cost Curves Cost Minimization Profit Maximization

Profit (P) = Total Revenue(TR) – Total Cost(TC)
4/17/2017 Theory of the Firm First, we need to write down our model: Profit (P) = Total Revenue(TR) – Total Cost(TC) TR(Q) = PQ TC(Q) = rK + wL P Price L Labor Q Quantity K Capital w Wage Rate Q = f(K,L) r Rate on Capital The firm wants to maximize this difference

4/17/2017 Theory of the Firm First, we need to write down our model: Profit (P) = Total Revenue(TR) – Total Cost(TC) TR = PQ TC(Q) = rK + wL P Price L Labor Q Quantity K Capital w Wage Rate Q = f(K,L) r Rate on Capital Economic costs include opportunity costs Economic P < Normal P (accounting) If a firm earns positive profits, all factors are earning more than they could in alternative uses

4/17/2017 Theory of the Firm First, we need to write down our model: Profit (P) = Total Revenue(TR) – Total Cost(TC) TR(Q) = PQ TC(Q) = rK + wL P Price L Labor Q Quantity K Capital w Wage Rate Q = f(K,L) r Rate on Capital INPUTS The production function describes a relationship between the quantity of physical inputs (K, L) and quantity of outputs (Q).

4/17/2017 Theory of the Firm First, we need to write down our model: Profit (P) = Total Revenue(TR) – Total Cost(TC) TR(Q) = PQ TC(Q) = rK + wL P Price L Labor Q Quantity K Capital w Wage Rate Q = f(K,L) r Rate on Capital OUTPUT The production function describes a relationship between the quantity of physical inputs (K, L) and quantity of output (Q).

The Technology of Production
4/17/2017 The Technology of Production Technology: a list of all possible production plans, i.e., all the ways to transform inputs into outputs. The production function: describes a relationship between inputs and the maximum quantity of output (all inputs are used technologically efficiently). Technological constraints: Nature (& science) imposes certain physical constraints on a firm: only so much output can be created out of so much input(s). Thus the firm must limit its choice to technologically feasible production plans.

The Technology of Production
4/17/2017 The Technology of Production The Production Function Q = F(K, L), For a given technology Q Output L Labor K Capital Cobb-Douglas Production Function Q = AKaLb where A is a constant (scale).

Production in the Short-Run
4/17/2017 Production in the Short-Run We define the short-run as the period in which at least one factor of production is fixed: Total Product Function The maximum quantity of output the can be produced for a given quantity of input, holding other factors constant. TP: Q = f(L) Q L

4/17/2017 Production in the Short-Run We define the short-run as the period in which at least one factor of production is fixed: Law of Diminishing Marginal Returns As firm adds more of a variable factor (holding others constant), the increment to output will eventually decrease. Total Product Function TP: Q = f(L) Q L

4/17/2017 Production in the Short-Run Q Average Product AP = Q/L Output per unit labor (input) A ray from the origin to any point on the TP curve is AP TP L AP L

4/17/2017 Production in the Short-Run Q Average Product AP = Q/L Output per unit labor (input) AP is greatest at Point A A TP L AP L

4/17/2017 Production in the Short-Run Q Marginal Product MPL=dQ/dL Increase in output from a unit increase in labor (input) The slope of TP curve is MP MP is greatest at point B MP is negative at point C C A TP B L L MP

4/17/2017 Production in the Short-Run Q Marginal Product MPL=dQ/dL Increase in output from a unit increase in labor (input) The slope of TP curve is MP MP = AP at AP max C A TP B L AP L MP

4/17/2017 Production in the Short-Run Q Average and Marginal Products In general, average will equal marginal, where average is greatest, e.g., the height of people in the room. C A TP B L AP L MP

Production in the Long-Run
4/17/2017 Production in the Long-Run In the long run, all factors of production are variable. Total Product Function TP: Q = f(K,L) Q Again, we have 3 variables… K,L

4/17/2017 Production in the Long-Run In the long run, all factors of production are variable. Total Product Function TP: Q = f(K,L) Q K L

4/17/2017 Production in the Long-Run In the long run, all factors of production are variable. The production function determines the maximum possible output for a given combination of inputs (a boundary condition). Technological efficiency. Total Product Function TP: Q = f(K,L) Q K,L

4/17/2017 Production in the Long-Run In the long run, all factors of production are variable. One particularly convenient form is the Cobb-Douglas production function Q = AKaLb Total Product Function TP: Q = f(K,L) Q K,L

4/17/2017 Production in the Long-Run Isoquant: all the possible combinations of inputs that are just sufficient to produce a given level of output. K Well-behaved isoquants are monotonic and convex Q = 20 Q = 10 L

4/17/2017 Production in the Long-Run Isoquant: all the possible combinations of inputs that are just sufficient to produce a given level of output. K Well-behaved isoquants are monotonic: More of any input produces at least as much output. MPL, MPK > 0. Q = 20 Q = 10 L

4/17/2017 Production in the Long-Run Isoquant: all the possible combinations of inputs that are just sufficient to produce a given level of output. K aK bK Well-behaved isoquants are convex: Combinations of production plans produce at least as much as either alone. 10 units of output can be produced using aL units of L and aK units of K or bL units of L and bK units of K or (aL+bL)/2 of L and (aK+bK)/2 of K or any linear combination of plans a and b Q = 20 Q = 10 aL bL L

4/17/2017 Production in the Long-Run Isoquant: all the possible combinations of inputs that are just sufficient to produce a given level of output. Marginal Rate of Technical Substitution (MRTS): The rate at which one input can be exchanged for another while keeping output constant. K Q = 20 Q = 10 L

4/17/2017 Production in the Long-Run Isoquant: all the possible combinations of inputs that are just sufficient to produce a given level of output. MRTSKL = - MPL/MPK Along an isoquant dQ = 0 dK*MPK +dL*MPL = 0 dK/dL = - MPL/MPK = slope K MRTS: The rate at which one input can be exchanged for another while keeping output constant. This is the slope of the isoquant. Q = 20 Q = 10 L

4/17/2017 Returns to Scale Constant returns: doubling all inputs doubles output. The firm can replicate production unit (e.g., build another plant). K 2K Q2 = 2Q1 Q = AKaLb a + b = 1 Q2 Q1 L 2L L

4/17/2017 Returns to Scale Increasing returns: doubling all inputs more than doubles output. (aka “Economies of scale”). K 2K Q2 > 2Q1 Q = AKaLb a + b > 1 Q2 Q1 L 2L L

4/17/2017 Returns to Scale Decreasing returns: doubling all inputs less than doubles output. Crowding (assume homogeneous factor quality). K 2K Q2 < 2Q1 Q = AKaLb a + b < 1 Q2 Q1 L 2L L

4/17/2017 Returns to Scale Decreasing returns: doubling all inputs less than doubles output. Crowding (assume homogeneous factor quality). K 2K Q2 < 2Q1 Firm should always be able to get at least constant returns by dividing production Q2 Q1 L 2L L

Returns to Scale Do any of these cases violate with the law of diminishing marginal productivity?

Cost Curves We can combine technological info about production possibilities with price info to characterize the firm’s cost structure. In the short-run, economic efficiency = technological efficiency, b/c to produce a certain level of output, Q, given K, there is a unique level of L required. This is the cheapest way to produce Q. In the long-run, all factors are variable, and the firm’s problem is to choose its optimal factor proportion.

SR Total Product Function
4/17/2017 Cost Curves We can combine technological info about production possibilities with price info to characterize the firm’s cost structure. Q SR Total Product Function TP: Q = f(L) A firm will never choose to produce where MPL is negative. L

4/17/2017 Cost Curves We can combine technological info about production possibilities with price info to characterize the firm’s cost structure. SR Total Product Function TP: Q = f(L,K) SR Cost Function TVC = wL(Q) Q Qo $ wLo Lo L Qo Q

4/17/2017 Cost Curves We can combine technological info about production possibilities with price info to characterize the firm’s cost structure. SR Total Product Function TP: Q = f(L,K) SR Cost Functions TC = TFC + TVC TVC = wL(Q) TFC = rK Q Qo $ Lo L Qo Q The shape of cost curves come from technology

Cost Curves TC Average Cost AC = TC/Q Cost per unit output
4/17/2017 Cost Curves TC $ Average Cost AC = TC/Q Cost per unit output A ray from the origin to any point on the TC curve is AC AC min at point A A Q AC Q

Cost Curves TC Marginal Cost MC = dTC/dQ = dTVC/dQ
4/17/2017 Cost Curves TC $ Marginal Cost MC = dTC/dQ = dTVC/dQ (b/c only VC can change) = wdL/dQ = w/MPL MC min at point B B Q MC AC Q

Cost Curves TC Marginal Cost MC = dTC/dQ = dTVC/dQ
4/17/2017 Cost Curves TC $ Marginal Cost MC = dTC/dQ = dTVC/dQ (b/c only VC can change) = wdL/dQ = w/MPL AC = MC at ACmin A B Q MC AC Q

Cost Curves TC Average Fixed Cost TVC AFC = TFC/Q AVC = TVC/Q TFC MC
4/17/2017 Cost Curves TC $ Average Fixed Cost AFC = TFC/Q AVC = TVC/Q TVC A B TFC Q MC AC AVC AFC Q

Cost Curves Deriving long-run cost curves:
4/17/2017 Cost Curves Deriving long-run cost curves: 3 short-run total cost curves associated w/different levels of K. The cheapest way to produce Q1 is using SRTC1 … $ SRTC(K2) SRTC(K1) SRTC(K3) Q1 Q2 Q Q

4/17/2017 Cost Curves Deriving long-run cost curves: 3 short-run total cost curves associated w/different levels of K. If K is continuously variable, the lower envelope of all SRTCs shows the lowest cost for each quantity of output. This is the long-run total cost curve $ SRTC(K2) SRTC(K1) SRTC(K3) Q1 Q2 Q Q

4/17/2017 Cost Curves Deriving long-run cost curves: 3 short-run total cost curves associated w/different levels of K. If K is continuously variable, the lower envelope of all SRTCs shows the lowest cost for each quantity of output. This is the long-run total cost curve $ LRTC Q1 Q2 Q Q

4/17/2017 Cost Curves Deriving long-run cost curves: We can’t say much about the shape of the LRTC curve. (Shown is a cubic function, giving us s-shaped curves). Cobb-Douglas w/constant returns give us a linear (upward-sloping) curve. $ LRTC Q1 Q2 Q Q

Cost Curves Deriving long-run cost curves: 3 short-run average
4/17/2017 Cost Curves Deriving long-run cost curves: 3 short-run average cost curves associated w/different levels of K. If K is continuously variable, the lower envelop of all SRACs is the long-run average cost curve. $ SRAC3 SRAC1 SRAC2 LRAC Q1 Q2 Q Q

Cost Curves Deriving long-run cost curves: 3 short-run marginal
4/17/2017 Cost Curves Deriving long-run cost curves: 3 short-run marginal cost curves associated w/different levels of K. The long-run marginal cost curve is the locus of points along srmcs associated w/difference levels of output. $ SRMC2 SRMC3 LRMC SRMC1 Q Q Q3 Q

Cost Minimization Consider a firm that produces output according to the following production function. Q = 4K½L½ Assume that w = $18 and r = $36, and the firm currently has 16 units of capital. How much will it cost this firm to produce 10 units of output in the short-run?

Cost Minimization Consider a firm that produces output according to the following production function: Q = 4K½L½ Assume that w = $18 and r = $36, and the firm currently has 16 units of capital. With K = 16, the firm’s short-run production function is: Q = 16L½ For Q = 10, 10 = 16L½ => L = 100/256 = .39

Cost Minimization Consider a firm that produces output according to the following production function: Q = 4K½L½ Assume that w = $18 and r = $36, and the firm currently has 16 units of capital. To produce 10 units: 10 = 16L½ => L = 100/256 = .39 With K = 16, the firm’s total cost of production is: TC = rK + wL = 36(16) + 18(.39) = $583.03

TC = rK + wL = 36(16) + 18(Q/16)2 = $576 + 18(Q/16)2
Cost Minimization Consider a firm that produces output according to the following production function: Q = 4K½L½ Assume that w = $18 and r = $36, and the firm currently has 16 units of capital. More generally: Q = 16L½ => L = (Q/16)2 With K = 16, the firm’s short-run total cost function is: TC = rK + wL = 36(16) + 18(Q/16)2 = $ (Q/16)2

Cost Minimization in the Short-Run
4/17/2017 Cost Minimization in the Short-Run How much will it cost this firm to produce Q units of output in the short-run? Total Cost Function TCsr = (Q/16)2 $ Fixed Costs = rK = 36(16) = $576 Q

Cost Minimization in the Short-Run
4/17/2017 Cost Minimization in the Short-Run How much will it cost this firm to produce 10 units of output in the short-run? In the short-run, if the firm wants to produce more (or less) than 10 units, it would move along it’s short-run output-expansion path, at K =16. K K = 16 Q = 10 L = L

Cost Minimization in the Long-Run
4/17/2017 Cost Minimization in the Long-Run How much will it cost this firm to produce 10 units of output in the long-run? In the long-run, all factors are variable. Firms combine factors of production in a manner analogous to the way consumers choose a consumption bundle. K Q = 10 L

4/17/2017 Cost Minimization in the Long-Run How much will it cost this firm to produce 10 units of output in the long-run? An isoquant is all the technologically efficient combinations of K ,L to produce a certain output, Q. K Isoquant Slope = - MRTS Q = 10 L

4/17/2017 Cost Minimization in the Long-Run How much will it cost this firm to produce 10 units of output in the long-run? If we think of the all the combinations of K&L that cost a certain amount (TC), we have an isocost line: K = TC/r – (w/r)L Recall: TC = wL + rK K Isocost lines Slope = - w/r Q = 10 L

4/17/2017 Cost Minimization in the Long-Run How much will it cost this firm to produce 10 units of output in the long-run? Tangency between the isoquant and an isocost curve shows the economically efficient combination K*, L*. Hence, the condition for optimal factor proportion is: MRTS = w/r K K* Isocost lines Slope = - w/r Isoquant Slope = - MRTS Q = 10 L* L

4/17/2017 Cost Minimization in the Long-Run How much will it cost this firm to produce 10 units of output in the long-run? The condition for optimal factor proportion is: MRTS = w/r . This is LR condition! Why? Because some factors (K) are fixed in the SR. K K* Isocost lines Slope = - w/r Isoquant Slope = - MRTS Q = 10 L* L

4/17/2017 Cost Minimization in the Long-Run How much will it cost this firm to produce 10 units of output in the long-run? Another way to think about this: TC is a projection of the firm’s long-run output expansion path: the locus of optimal factor bundles (K,L) for different levels of Q. (Constant return depicted) K K* Q = 10 L* L

How much will it cost this firm to produce 10 units of output in the long-run? To find total cost in terms of Q, we use the cost minimization condition and the production function to find substitute expressions in terms of Q for K and L. Cost minimization requires that the firm produce using a combination of inputs for which the ratios of the marginal products, or the marginal rate of technical substitution, equals the ratio of the input prices: MRTS = w/r

How much will it cost this firm to produce 10 units of output in the long-run? Q = 4K1/2L1/2 w = 18; r = 36 MRTS = MPL/MPK MPL = 2K1/2L-1/2 MPK = 2K-1/2L1/2 MRTS = K/L. = w/r = 18/36 = L = 2K. The firm’s optimal factor proportion (given technology and factor prices).

How much will it cost this firm to produce 10 units of output in the long-run? Q = 4K1/2L1/2 L = 2K => Q = 4K1/2(2K)1/2 = 4(2)1/2K Q = 4(2)1/2K => K = Q/[4(2)1/2] Q = 5.66K => K = Q/5.66 For Q =10 => K = 1.77; L = 3.54 TC = wL + rK TC(Q=10) = 36(1.77)+18(3.54) = $127.28 To produce 10 units of output, we solve for K and L in terms of Q and substitute in the total cost function. Producing 10 units costs $ At this point, the firm is using 1.77 units of capital and 3.54 units of labor.

How much will it cost this firm to produce 10 units of output in the long-run? Q = 4K1/2L1/2 L = 2K => Q = 4K1/2(2K)1/2 = 4(2)1/2K Q = 4(2)1/2K => K = Q/[4(2)1/2] Q = 5.66K => K = Q/5.66 For Q =10 => K = 1.77; L = 3.54 TC = wL + rK TC(Q=10) = 36(1.77)+18(3.54) = $127.28 Comparing this to the short-run, the cost of production is lower in the long-run, because the firm is now able to adjust K as well as L to minimize the cost of the production of a given amount of output, which is more efficient.

How much will it cost this firm to produce Q units of output in the long-run? TC = 18L + 36K = 9Q/(2)1/2 + 9Q/(2)1/2 = 18/(2)1/2(Q) = 12.73Q MC = = AC We can also solve for the firm’s long run total cost function for any level of output. .

4/17/2017 Cost Minimization in the Long-Run Graphically: Q = 4K1/2L1/2 w = 18; r = 36 TCsr = (Q/16)2 $ TClr = 12.73Q MC = 12.73 Fixed Costs = rK = $576 Q

Profit Maximization Profit (P) = Total Revenue(TR) – Total Cost(TC)
4/17/2017 Profit Maximization Profit (P) = Total Revenue(TR) – Total Cost(TC) $ To maximize profits, look for Q where distance between TC and TR is greatest. This will be where they have the same slope.. slope. TR = PQ Pmax TC Q1 Q2 Q3 Q* Q

4/17/2017 Profit Maximization Profit (P) = Total Revenue(TR) – Total Cost(TC) Marginal Analysis: If TC is rising faster than TR, reduce Q. If TR is rising faster than TC, increase Q. $ TR = PQ Pmax TC Q1 Q2 Q3 Q* Q

4/17/2017 Profit Maximization Profit (P) = Total Revenue(TR) – Total Cost(TC) Marginal Analysis: Recall: slope TR = MR slope TC = MC Hence, to maximize profits: MR = MC $ TR = PQ Pmax TC Q1 Q2 Q3 Q* Q

Profit Maximization Demand for the firm’s output is given by Q = 100 – 2P. Find the firm’s profit maximizing level of output. Q = 4K1/2L1/2 w = 18; r = 36 Q = 100 – 2P => P = 50 – 1/2Q TR = PQ = (50 – 1/2Q)Q = 50Q – 1/2 Q2 MR = 50 – Q = MC = 12.73 => Q* = 37.27; P* = 31.37

4/17/2017 4/17/2017 Profit Maximization We solved the firm’s optimization problem focusing on the profit output level, Q*, but it is important to emphasize that the optimization principle also tell us about input choices. When the firm chooses an output level Q* that maximizes P for given factor prices (w, r), the firm has simultaneously solved for L* and K*. To produce Q* = (given the production function, Q = 4K1/2L1/2, and optimal factor proportion, L = 2K), we find: L* = 6.58; K* = 3.29. Finally, P = TR–TC = PQ–12.73Q = (31.37–12.73)37.27 = $695. Later we will look at situations in which a firm may have a strategy of entry deterrence as a long-run strategy… 68

Next Time 6/30 Profit Maximization or Besanko, Ch. 8
4/17/2017 4/17/2017 Next Time 6/30 Profit Maximization Pindyck & Rubenfeld, Ch. 7. or Besanko, Ch. 8 Varian Ch. (parts of) Ch 19, 22, 23. 69

UNIT II: FIRMS & MARKETS

Similar presentations

Presentation on theme: "UNIT II: FIRMS & MARKETS"— Presentation transcript:

Similar presentations

About project

Feedback

Log in

Auth with social network:

UNIT II: FIRMS & MARKETS

Similar presentations

Presentation on theme: "UNIT II: FIRMS & MARKETS"— Presentation transcript:

Similar presentations

About project

Feedback