EconS Supply and Demand

Transcription

1 EconS Supply and Demand Eric Dunaway Washington State University eric.dunaway@wsu.edu August 28, 2015 Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

2 Introduction When people talk about economics, most often, they know something about supply and demand having to be equal. There s a lot more to the picture than that. Today, we are going to talk about what factors determine how much consumers want to buy and rms want to sell. aka, Supply and Demand. Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

3 Demand What is Demand? Demand comes from the consumer (customer) side of the market. It matches a quantity of a good or service that is purchased to any given set of factors. Several factors drive consumer demand. Price Income Tastes Information Prices of other goods and services Regulations Etc. Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

4 Demand Curve We model demand using a negatively sloping curve. To keep things simple, we hold everything but price constant, and then see how changes in the price a ect the quantity demanded. It s important to note, that in a real world scenario, it s very rare that "everything else is constant." Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

5 Demand Curve Price, p 0 Quantity, q Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

6 Demand Curve Price, p Quantity, q Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

7 Demand Curve Price, p Quantity, q Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

8 Demand Curve For simplicity, we depict the shape of the demand curve as a straight line. This is not always the case. Most Demand curves are curved, bowed towards the origin. They re a lot harder to analyze though, so we ll stick to linear demand curves for this class. Price, p Quantity, q Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

9 Demand Curve What about the other factors of demand? In reality, demand curves are many-dimensional, but we can t draw or visualize that. We can model the e ect of other factors changing as shifts in the demand curve. An important distinction: A change in price is a change in quantity demanded, i.e., movement along the curve. A change in another factor is a change in demand, i.e., movement of the curve. Why? Becuase when a di erent factor changes, there is a new quantity demanded for every price! Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

10 Demand Curve Price, p Quantity, q Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

11 Demand Curve Price, p Quantity, q Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

12 Demand Curve Price, p Quantity, q Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

13 Demand Function We can express all of the ways demand is in uenced by its factors with the demand function. Let s look at an example. A discount banjo manufacturer has discovered, after years of rigorous data collection, that the demand for his banjoes are a function of their price, the average income of everyone in his town, and the price of mandolins. The demand function is D(p, Y, p m ) = p Y p m where p is the price of a banjo, Y is the average income of everyone in the town in thousands of dollars, and p m is the price of a mandolin. Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

14 Demand Function If we set Y = 20 and p m = 25, the demand function reduces to D(p, 20, 25) = 24 = p (20) (25) 6 7 p which is the same as the demand curve that has been in our previous examples. If we let income increase (a lot) to Y = 200 (A rich town), our demand curve becomes the same as in our demand shift example. Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

15 Demand Function D(p, Y, p m ) = p Y p m A few things to note: The sign of a goods own price is negative. This implies that as its own price goes up, the quantity goes down. We call this the law of demand. Theoretically, we could have a demand curve that increases with its own price (we call it a Gi en good), but nobody has ever proven that one exists. The signs on the income and price of manolins could be either positive or negative, and they tell us a lot about the relationship between those factors and banjoes. We ll be talking more about that next week. Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

16 Inverse Demand Function There is another way that we can express demand functions, known as the inverse demand function. This treats price as a function of quantity, rather than quantity as a function of price. This is particularly useful when you want to graph a demand function, as it puts the function into something more familiar. Let s simplify the notation from our previous demand function and nd its inverse 6 q D = D(p, Y, p m ) = 24 7 p Y p m 6 q D = 24 7 p Y p m Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

17 Inverse Demand Function q D = p Y p m To get the inverse demand function, all we have to do is solve the demand function for price, p. Rearranging some terms, 6 7 p = 24 q D Y p m p = q D Y p m Plugging in our values of Y = 20 and p m = 25, the inverse demand function becomes p = q D (20) (25) p = q D Note that we would have gotten the same answer had we taken our previously reduced demand function and solved it for p. Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

18 Inverse Demand Function Another (Simpler) Example: Consider the demand function q D = p To nd the inverse demand function, we just solve this expression for p, 1 2 p = 10 q D p = 20 2q D Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

19 Inverse Demand Function 20 p q D = 10 ½p p = 20 2q D 0 10 q Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

20 Inverse Demand Function There will be times when using the inverse demand function will be much easier than using demand function. Speci cally, when we get into pro t maximization problems later. In many cases, it does not matter which one is used (since they are mathematically equivalent) as long as the calculations are consistent. Let s look at a case where it does matter. Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

21 Aggregation In reality, every person will have their own demand function for a good. We all have di erent tastes, incomes, etc. We can, however, add together (aggregate) individual demand curves to obtain a market demand curve. For example, take two individuals with di erent demands for hotel rooms. We ll say that only the price matters to them, let D 1 (p) = 30 D 2 (p) = p 1 2 p We can (carefully) add these two demand curves together to get a market demand curve. Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

22 Aggregation 60 p D 1 (p) = 30 ½p 30 D 2 (p) = 15 ½p q Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

23 Aggregation D 1 (p) = 30 D 2 (p) = p 1 2 p First, note that the second person isn t willing to pay nearly as much for a hotel room as the rst person. In fact, when the price is above 30, person 2 does not want to buy any hotel rooms. Therefore, for the rst part of the aggregated demand curve, for all prices above 30, it s D(p) = D 1 (p) + D 2 (p) = D 1 (p) {z } =0 Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

24 Aggregation D 1 (p) = 30 D 2 (p) = p 1 2 p When price is below 30, both customers want to purchase hotel rooms, and we have D(p) = D 1 (p) + D 2 (p) = 45 p Putting these two parts together, we ll have an aggregate demand curve with a kink in it. Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

25 Aggregation 60 p D 1 (p) = 30 ½p 30 D 2 (p) = 15 ½p q Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

26 Aggregation 60 p D 1 (p) = 30 ½p 30 D(p) = 45 p q Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

27 Aggregation It s important to remember to remember who is and isn t in the market for all relevant prices when using aggregated demand curves. When we talk about equilibrium later, it might be possible that only 1 person is in the market! Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

28 Supply Let s talk about the other side of the market, Supply. Supply is the rm, or producer side of the market. It matches a quantity of a good or service that is provided to any given set of factors. Several factors drive producer supply. Price Costs Regulations Etc. Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

29 Supply Curve Like Demand, we can model Supply using a positively sloping curve. Again, we keep everything else but the price held constant, and then see how changes in price a ect the quantity supplied. Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

30 Supply Curve p q Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

31 Supply Curve p q Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

32 Supply Curve Again, like demand curves, supply curves are not typically linear. We use linear supply curves in this class since they are easier to analyze. Most supply curves are also curved, bowed to the bottom right of the graph. p 0 q Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

33 Supply Curve Once again, supply curves are multidimensional, but we simplify them so we can represent them in two-dimensions, then treat other factors as shifts in the supply curve. The important distinction: A change in price is a change in quantity supplied, i.e., movement along the curve. A change in another factor is a change in supply, i.e., movement of the curve. Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

34 Supply Curve p q Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

35 Supply Curve p q Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

36 Supply Curve p q Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

37 Supply Function We can express the total e ect on the quantity supplied by its factors by analyzing the supply function. Back to banjoes. Our discount banjo manufacturer from before also collected excellent data on his resource suppliers. He discovered that the amount of banjoes he was willing to supply is a function of their price, and the price of magic banjo wood. The supply function is S(p, p w ) = p 5p w where p is the price of the banjo and p w is the price of magic banjo wood. Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

38 Supply Function If we set p w = 2, the supply function reduces to S(p, 2) = p 5(2) 20 = p which is the same as the supply curve in the previous example. If p w increases to p w = 10 3, our supply curve becomes the same as in our supply shift example. Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

39 Supply Function More things to note: S(p, p w ) = p 5p w The sign of the goods own price is positive. This implies that as the price goes up, the quantity supplied also goes up. This is the law of supply. In this case, the price of magic banjo wood acts like a cost to the supplier. It will typically enter into the supply function negatively. Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

40 Inverse Supply Function Just like we have an inverse demand function, we can convert a supply function to an inverse supply function. We follow the same steps as before with the inverse demand function. Simplifying our notation a bit, q S = S(p, p w ) = p 5p w q S = p 5p w Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

41 Inverse Supply Function q S = p 5p w To obtain the inverse supply function, we simply solve the supply function for the price, p. Rearranging terms, 4 3 p = q S + 5p w 5 p = q S p w and letting p w = 2, we obtain p = p = q S q S (2) which is the same result we would have obtained if we solved the reduced supply function for p. Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

42 Inverse Supply Function Another Example: Consider the supply function q S = 4 + 2p If we wanted to plot this supply function, it would be easier to rst nd the inverse supply function, which we get by solving the supply function for p, 2p = 4 + q S p = q S Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

43 Inverse Supply Function p q S = 4 + 2p p = 2 + ½q S q Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

44 Inverse Supply Function Again, for the most part, it doesn t matter whether you use the supply function or the inverse supply function since they are mathematically equivalent. There will be times when one is much easier than the other. Just remember to be consistent! One of the times where it does matter is when aggregating supply curves, because adding prices together just doesn t make sense. Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

45 Aggregation Just like with aggregating individual demand curves, individual supply curves can also be aggregated to obtain a market supply curve. The same rules apply, so make sure each individual supplier would want to enter the market before adding them together! Let s look at a market with two rms, each having a di erent supply function S 1 (p) = 5 + p S 2 (p) = 1 2 p Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

46 Aggregation For some extra practice, let s convert these supply functions into inverse supply functions before we plot them. q S1 = S 1 (p) = 5 + p p = 5 + q S1 q S2 = S 2 (p) = 1 2 p p = 2q S2 Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

47 Aggregation p S 1 (p) = 5 + p p = 5 + q S1 5 0 S 2 (p) = ½p p = 2q S2 10 q Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

48 Aggregation As we can see, if the price is too low (below 5), only rm 2 wants to enter the market. Thus, when we add the supply functions together for a price below 5, we obtain S(p) = S 1 (p) +S 2 (p) = S 2 (p) = 1 {z } 2 p 0 Once the price rises above 5, however, both rms enter the market and the aggregate supply curve becomes S(p) = S 1 (p) + S 2 (p) = 5 + p p = p Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

49 Aggregation Again, to help with plotting, I can convert this into an inverse aggregate supply function by solving for p, q SA = S(p) = p 3 2 p = 5 + q SA p = q SA Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

50 Aggregation p S 1 (p) = 5 + p p = 5 + q S1 5 0 S 2 (p) = ½p p = 2q S2 10 q Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

51 Aggregation p S(p) = p p = 5 + ⅔q SA S(p) = ½p p = 2q SA 10 q Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

52 Summary Supply and Demand show us how much rms want to sell and consumers want to buy, given many di erent factors, the most important of which is price. We can manipulate the supply and demand functions for ease of graphing by taking their inverses. Individual Supply and Demand functions can be carefully added together to nd their market counterparts. Remember that you can t use inverses when you aggregate, but can still use those inverses to help with plotting. Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

53 Preview for Friday Friday, we will put supply and demand together and see how markets reach an equilibrium. Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54

54 Homework Assignment 2 1. Consider the demand function for ukeleles. q D = 100 3p + 0.2Y p l where p is the price of a ukelele, Y is average income measured in thousands, and p l is the price of a lei in Hawaii. Assume that Y = 25 and p l = 3. For parts b and c, draw a gure and explain what happens for each of the two situations. a. What is the inverse demand function? b. The average income increases from Y = 25 to Y = 35. c. The price of a lei in Hawaii increases from p l = 3 to p l = 5. Eric Dunaway (WSU) EconS Lecture 2 August 28, / 54