Perspectives in Economics Lecture 4
Production Function Perspectives in Economics
Think of producing something Assume for now we want to produce as much of something as possible We can think of any production process as a machine that takes inputs and produce outputs Rancher and Farmer example Input: Time Output: Meat or potatoes Manufacturing Input: labor, machinery, raw materials Output: cars, TVs, computers Services Input: labor, tools Output: haircuts, financial reports
Production Function We can present such a machine with a mathematical function. For example Output = F(Labor, Capital) and F is a function F Labor, Capital = Labor + Capital Looking this way, the decision of a seller/manufacturer is not that different from a individual maximizing her own utility Consumer Choice Utility (Function) Prices of Goods Producer Choice Production (Function) Input Prices
Production vs Utility Maximization There are two crucial differences though: 1. Producers generally do not maximize the amount of output as we assumed. Instead they try to maximize their profit 2. We generally do not assume producers are limited by a budget. Instead, they can borrow money from banks or raise money from the stock market, as long as they make a profit in the end So let us slightly reframe the decision process of a producer: 1. Find the least costly way to produce a given amount of output 2. Find the amount of output that maximizes profit
Inputs In economics we very often simplify the number of inputs to 2: labor and capital Labor is the amount of human input. It is often measured in number of workers number of hours per worker What are some problems with this specification? In cases where education level of workers is important, we sometimes use instead workers number of hours per worker education level of worker Capital is anything that is not human input. This includes raw material, machinery
Measuring Productivity Motorola's American Dream: unbridled customization, two-day shipping and one big Texas factory Just like an American dream, Motorola's Fort Worth facility went from zero to success story almost overnight In less than half a year's time, the 455,000-square-foot facility transformed from a vacant, anonymous building in the Alliance region of Fort Worth into a busy center of production that employs about 2,500 people and ships nearly 100,000 Moto X's per week. Suppose Motorola has hired 100 workers last week and produced 2,000 more Moto X s.
Measuring Productivity How should we measure productivity? Average product of labor is how many units of output each worker is producing on average Marginal product of labor is how many units of output the last worker is producing Let F(L,K) be output quantity given the inputs Average Product (AP) of Labor = F L,K L Marginal Product (MP) of Labor = F L, K F L 1, K
Measuring Productivity Exercise Complete the following chart Quantity of Labor Total Output Marginal Product of Labor Average Product of Labor 0 0 - - 1 200 2 175 3 450 4 70 5 115 6 43
Short Run versus Long Run You hear economists talking about these two terms a lot. What do they mean? Short Run Some Variables are unchangeable Long Run All Variables are changeable Notice the definitions have nothing to do with time The two concepts are defined as a description of whether all variables are changeable or not The best way to think of the two concepts is to take short run as sudden change and long run as planned change The economist, Maynard Keynes ( 凱恩思 ), famously said In the long run we are all dead.
In Short Run When we only have labor and capital as inputs, we usually assume capital is the factor that is fixed Idea: It s easier to have workers go overtime or hire temporary workers then purchasing additional machineries Do you think productivity goes up or down as you add more labor to a fixed amount of capital? Probably lower Same for adding more capital to a fixed amount of labor Law of Diminishing Marginal Returns Holding other inputs constant, marginal product of an input goes down as you add more of it
In Long Run All inputs are variable Law of Diminishing Marginal Returns does not apply Should output double when you double all inputs? If not, why not? Examples: Workers get more experienced as workers work more Higher degree of specialization among workers More/less flexibility as production expand
Returns to Scale When input increase by c% If there is Then Output Increasing Returns to Scale Increase more than c% Constant Returns to Scale Increase c% Decreasing Returns to Scale Increase less than c% In mathematics, for any α > 1, If there is Then Output Increasing Returns to Scale F αk, αl > αf(k, L) Constant Returns to Scale F αk, αl = αf(k, L) Decreasing Returns to Scale F αk, αl < αf(k, L)
Returns to Scale Exercise For each of the following production functions, state whether it has increasing, decreasing or constant returns to scale F K, L = 2L + LK + K F K, L = AL 1 3 K 1 3 F K, L = L β K 1 β 0 < β < 1
Cost of Production Perspectives in Economics
Production and Costs Combining the production function with input prices, we can calculate the cost of producing the good Total-cost curve Relationship between quantity produced and total costs
A Production Function and Total Cost: Caroline s Cookie Factory
Caroline s Production Function and Total-Cost Curve Quantity of Output (cookies per hour) 160 (a) Production function Production function Total Cost $90 80 (b) Total-cost curve Total-cost curve 140 70 120 60 100 50 80 40 60 30 40 20 20 10 0 1 2 3 4 5 6 Number of 0 20 40 60 80 100 120 140 160 Quantity Workers Hired of Output
Various Measures of Cost Fixed costs Costs that do not vary with the quantity of output produced Variable costs Costs that vary with the quantity of output produced Total cost Fixed cost + Variable cost
A Production Function and Total Cost: Caroline s Cookie Factory
Various Measures of Cost Average fixed cost (AFC) Fixed cost divided by the quantity of output Always declines as output rises Average variable cost (AVC) Variable cost divided by the quantity of output Typically rises as output increases Because of diminishing marginal product
Various Measures of Cost Average total cost (ATC) Average total cost = Total cost / Quantity ATC = AVC + AFC ATC is the cost of a typical unit of output If total cost is divided evenly over all the units produced Shape of ATC AFC always declines as output rises AVC typically rises as output increases ATC is U-shaped Efficient scale: quantity of output that minimizes ATC
A Production Function and Total Cost: Caroline s Cookie Factory Avg. Cost
Various Measures of Cost Marginal cost (MC) Increase in total cost arising from an extra unit of production Marginal cost = Change in total cost / Change in quantity
A Production Function and Total Cost: Caroline s Cookie Factory Mrg. Cost
Various Measures of Cost Marginal cost (MC) Increase in total cost arising from an extra unit of production Marginal cost = Change in total cost / Change in quantity Rising marginal cost curve Because of diminishing marginal product
The Various Measures of Cost: Conrad s Coffee Shop
Conrad s Average-Cost and Marginal-Cost Curves Costs $3.50 3.25 3.00 2.75 2.50 2.25 2.00 1.75 1.50 1.25 1.00 0.75 0.50 0.25 MC 0 1 2 3 4 5 6 7 8 9 10 ATC AVC AFC Quantity of Output (cups of coffee per hour) This figure shows the average total cost (ATC), average fixed cost (AFC), average variable cost (AVC), and marginal cost (MC) for Conrad s Coffee Shop. All of these curves are obtained by graphing the data in the table. These cost curves show three features that are typical of many firms: (1) Marginal cost rises with the quantity of output. (2) The averagetotal-cost curve is U- shaped. (3) The marginalcost curve crosses the average-total-cost curve at the minimum of average total cost.
Various Measures of Cost Relationship between MC and ATC When MC < ATC: average total cost is falling When MC > ATC: average total cost is rising The marginal-cost curve crosses the average-total-cost curve at its minimum
Economies of Scale Perspectives in Economics
Returns to Scale When input increase by c% If there is Then Output Increasing Returns to Scale Increase more than c% Constant Returns to Scale Increase c% Decreasing Returns to Scale Increase less than c% Suppose input prices are constant To make things easy, we can just assume all input prices = 1 for now When 1% more input is used, input cost goes up by 1%
Implications of Returns to Scale What does returns to scale implies? When input cost increase by c%: If there is Then Output Increasing Returns to Scale Increase more than c% Constant Returns to Scale Increase c% Decreasing Returns to Scale Increase less than c% Flip the relationship around: When output increase by c% If there is Then Cost Increasing Economies Returns of Scale to Scale Increase less than c% Decreasing Diseconomies Returns of to Scale Scale Increase more than c%
Economies of Scale As output increases, do we expect to see economies of scale first or diseconomies of scale first? Remember returns to scale comes from experience, specialization, etc. These benefits probably stop increasing as output becomes bigger and bigger As output becomes really big, problems like inflexibility appears We expect economies of scale when output is small, followed by diseconomies of scale when output is high
Economies of Scale and Average Cost When output increase by c% If there is Then Cost Economies of Scale Increase less than c% Diseconomies of Scale Increase more than c% When output is rising faster than total cost, average cost Goes down When output is rising slower than total cost, average cost Goes up So if economies of scale comes before diseconomies of scale, the LR average cost curve will be U-shaped Different reason than short run here it is not about fixed cost
Economies of Scale Returns to scale is not the only way economies of scale can arise Consider the case when input prices are not fixed Case 1: Going from buying very little input to a moderate amount of input Input prices probably goes down Case 2: Going from buying a moderate amount of input to an enormous amount of input Input prices probably goes up Again, we expect economies of scale when output is small, followed by diseconomies of scale when output is high
Variable Input and Variable Cost There is a more subtle point In the long run all inputs are variable, does that mean all costs are variable? No you can have a contract where you get a variable amount of input for a fixed price Fixed-price variable quantity contracts are very common Think about your university education you have a choice of how many courses you want to take, and yet you only pay a fixed tuition So even in the long run there can be fixed cost Another reason why LR average cost curve might be U- shaped
Short Run Cost cs. Long Run Cost Perspectives in Economics
Short Run vs. Long Run Short run Some inputs cannot be changed Long run All inputs can be changed Question: Which one should have a lower cost? Which one is more flexible, long run or short run? Whatever we can do in the short run we can do in the long run, but not the other way round Cost is lower in the long run
Long Run Cost Curves Let s summarize Long run average total cost can still be U-shaped Whatever we can do in the short run we can do in the long run, but not the other way round Long run cost is lower than short run costs Combining the three, how should a graph with both LR and SR average cost curves looks like?
Average Total Cost in the Short and Long Runs Average Total Cost ATC in short run with small factory ATC in short run with medium factory ATC in short run with large factory ATC in long run you re here SR you re now here LR you re now here SR LR 0 Quantity of Cars per Day
Average Total Cost in the Short and Long Runs Average Total Cost ATC in short run with small factory ATC in short run with medium factory ATC in short run with large factory ATC in long run 0 Economies of scale Constant returns to scale (Assume per-unit input prices are constant) Diseconomies of scale Quantity of Cars per Day
Supply Curve Perspectives in Economics
Supply Curve Let s come back to the issue of supply curve Assume for now that The seller has to take the price as given When is this the case? The seller s store and machineries have to be paid for Short run How many units of the good should the seller sell?
Conrad s Average-Cost and Marginal-Cost Curves Costs $3.50 3.25 3.00 2.75 2.50 2.25 2.00 1.75 1.50 1.25 1.00 0.75 0.50 0.25 MC ATC 0 1 2 3 4 5 6 7 8 9 10 Quantity of Output (cups of coffee per hour)
Conrad s Average-Cost and Marginal-Cost Curves Costs $3.50 3.25 3.00 2.75 2.50 2.25 2.00 1.75 1.50 1.25 1.00 0.75 0.50 0.25 MC ATC 0 1 2 3 4 5 6 7 8 9 10 Quantity of Output (cups of coffee per hour)
Supply Curve As long as the price is higher than marginal cost, it is worthwhile to sell So the supply curve is given by the marginal cost curve
Supply Curve Now if The seller has to take the price as given The seller s store and machineries have to be paid for only if the seller is producing something Need to pay fixed cost only if output is bigger than 0 How many units of the good should the seller sell?
Conrad s Average-Cost and Marginal-Cost Curves Costs $3.50 3.25 3.00 2.75 2.50 2.25 2.00 1.75 1.50 1.25 1.00 0.75 0.50 0.25 MC ATC AVC AFC 0 1 2 3 4 5 6 7 8 9 10 Quantity of Output (cups of coffee per hour)
Supply Curve It is worthwhile for the seller to enter a market as long as the price is higher than marginal cost and average total cost So the supply curve is given by the marginal cost curve above the average cost curve Conclusion: Supply curve is (marginal) cost of production