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Partial and General Equilibrium Partial and General Equilibrium A Partial and General Equilibrium Partial and General Equilibrium a. Partial equilibrium b. Factor markets October 12 2006 c. Production possibilities frontier and profit maximization d. Indifference curves and utility maximization In this topic we examine how producers and consumers e. General equilibrium come together and interact in markets. We first return to the partial equilibrium supply-demand model. Then we examine the general equilibrium model which examines several markets together. 2 Partial Equilibrium Partial Equilibrium, cont. Once we obtain supply and demand curves for a perfectly competitive market (for the run of interest) we The model of partial equilibrium shows equilibrium in one can put them together to examine a market, taking given prices of other goods and inputs, income, etc. model of a market. price Equilibrium in the economy as a whole requires equilibrium in all Equilibrium is attained in the market demand in the way discussed earlier: the markets. Otherwise some price will change, which will affect other price rises if there is excess demand markets. There is interdependence. Why? Examples: and falls in there is excess supply. Changes in prices of substitutes, complements Equilibrium in the market occurs at E E. Changes in input prices supply We can then examine how the P* Changes in production of goods affects wage income and profit equilibrium is affected by changes of various kinds, including changes income and therefore income of consumers in government policies This makes it somewhat misleading to examine equilibrium in only Behind the supply and demand one market. So we consider general equilibrium – equilibrium in curves is the behavior of producers all markets at the same time taking into account the and consumers. Note how we now have a fuller understanding of the interdependence of markets effects of changes in income, prices We will examine a simple general equilibrium model with one of other goods, tastes, technology, input, labor, and two goods, to examine their interdependence. input prices, etc. Q* quantity It will give us the basic idea of general equilibrium analysis we will discuss later. All markets perfectly competitive – price takers 3 4 Factor Markets Factor markets Demand for labor Market for labor, only input, can be analyzed To maximize profits we have seen that firm produces at with usual supply-demand model. the output at which P = MC. What is marginal cost if labor is the only factor of Consider supply and demand for labor to a production? MC = W (DL/DQ) = additional labor particular industry. Only a brief discussion required to produce additional output multiplied by the here; more detail in next topic. cost of one unit of labor. This implies that MC = W/(DQ/DL) = W/MPL. Who demands labor? Firms or producers. How Profit maximization implies: much labor will firms demand? The quantity P = MC = W/MPL. that maximizes a firm’s profit. We can also write this condition as Who supplies labor? Households or consumers. W = P x MPL. Assume for now that there is a fixed supply of Says that the marginal cost of employing one more labor to the industry. worker (W) is equal to the marginal benefit (P x MPL). P x MPL is called the value of marginal product of labor, VMPL. 5 6 1 Factor markets Factor Markets Demand curve for labor Labor market equilibrium Profit maximization implies Assume that the supply of labor for the industry is given. Supply W = P x MPL = VMPL curve is vertical line wage, VMPL wage VMPL curve is downward sloping Demand curve for labor is a because MPL is downward downward-sloping line which sloping (diminishing returns) sums up the firm demand curves and P is fixed. (or VMPL curves). supply Given the wage, firm will decide to VMPL Equilibrium in this labor market is employ workers up to where P determined at the intersection, = VMPL. with the equilibrium wage being W* For a higher wage firm will hire For higher wages there is excess W* demand fewer workers. W1 supply of labor and the wage will VMPL curve gives the demand fall. For lower wages there is curve for labor excess demand for labor and the Add up demand curves for labor of wage will fall. all firms in the industry The total value of output for the (horizontally) – gives demand industry is given by the area curve for labor of industry. under the VMPL curve. Adds up L1 quantity of labor the value of marginal product for Downward sloping line each worker. quantity of labor 7 8 Factor Markets Factor Markets Labor markets for two sectors Labor allocation equilibrium wage wage wage wage DA D DA D PA given in B B PB given in drawing DA curve drawing DB curve WA WA DL WB WB 0A 0B 0A 0B L1 quantity of labor quantity of labor L* Total amount of labor for the economy is fixed and shown by distance 0A0B. Labor will move from sector B to sector A till wages are equalized between There are two industries, producing autos (A) and butter (B), both using labor. Draw sectors. Equilibrium labor allocation will be at L*. the labor market demand curve for B “backwards”. Suppose that initially there is 0 L amount of labor in sector A and L 0 amount in sector B. Total value of production for the two sectors is maximized at L*. At the other A 1 1 B allocation shown there is a deadweight loss of DL. Equilibrium wages in the two sectors is as shown. Where will workers wish to work assuming other conditions are same in the two sectors? 9 What happens when a price changes? Say PA increases. DA shifts up. Labor10 will move to the auto sector. Production Possibilities Frontier and Profit Production Possibilities Frontier and Maximization Profit Maximization Production Possibilities Frontier Profit maximizing production equilibrium Production possibilities for butter Take prices of the two goods to be and autos are shown with the given to price-taking firms: PA and production possibilities frontier. QB PB. PA/PB > MRPT Given prices we can draw lines with QB = MCA /MCB The slope of the PPF shows the Increase A slope - PA/PB, like budget lines. The Equilibrium amount of one good the economy lines show the value of total output production P=MC for must give up to produce more of of the two goods. Lines further out both goods the other. It is called the marginal show higher values. implies PA/PB rate of product transformation = MRPT= Profit maximizing equilibrium: or MRPT. DQB MCA /MCB where one of these lines is DQ /DQ = MRPT = - MC /MC DQA B A A B tangent to the PPF. PA/PB = Why? MRPT= MCA /MCB also where the value of output P /P < MRPT DQB/DQA =(DQB/WDLA)/(DQA/WDLA) of the two goods is highest A B = MCA /MCB = -(DQB/WDLB)/(DQA/WDLA) Also have full employment: on PPF, Increase B not inside it. production =-(WDL / DQ )/(WDL / DQ ) A A B B If P /P rises, slope of value of QA A B i = - MCA /MCB output line rises. Equilibrium Q output for B will fall and A will rise A 11 12 2 General Equilibrium Indifference Curves and Utility Equilibrium Maximization General equilibrium requires: Given the price ratio and Slope gives equilibrium price ratio production point we get the Q B Full employment of QB value of income line which is Slope = also the budget line of all resources (labor) I1 consumers: value of -PA/PB production = value of income Equal wages in both Preferences shown with sectors “community” indifference Production and curves assuming all consumers consumption have the same preferences Consumption Profit maximization by (which also satisfy some other producers conditions) Production Given the budget line Utility maximization by Equilibrium consumers choose consumers quantities consumption point to reach their highest utility level. Quantity supplied = PPF Note: we don’t need Quantity demanded for consumers to have identical both goods. This is shown preferences. But all QA Q consumers will set price ratio by having production and A equal to MRS. consumption at same point 13 14 General Equilibrium Excess demand and supply When the economy is not in equilibrium, at least one of the equilibrium conditions not QBQB satisfied. I Slope = 2 Here we find quantity supplied -PA/PB not equal to quantity demanded production for both goods, although other conditions are satisfied. There is consumption excess supply (ES) of good B and ESB DQB excess demand (ED) for good A. DQA PA will increase and PB will decrease, making the value of production line steeper. Production of B will fall and of A PPF will rise, consumption of B will rise and of A will fall. Price will adjust till the economy reaches QAQA equilibrium. EDA 15 3.
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