3 Features of the tangency between isocost lines and isoquants. Slope of isoquants is called the Marginal Rate of Technical Substitution (MRTS) MRTS = MP L / MP K = (∆K / ∆L | Q=q) At tangency, MRTS = input price ratio MP L / MP K = w / r MP K / r = MP L / w (P* x MP K ) / r = (P* x MP L ) / w Benefits-cost ratio is equal across inputs Profit max’ing firm also sets benefits equal to cost, so r = MRP K and w = MRP L
4 Usefulness of shortcut: Finding firm’s optimal input choices Recall that MP K / r = MP L / w You will be given factor marginal products and factor prices Firm must also achieve optimum for some cost level—recall the total cost equation You will be given the target cost level Can solve two equations for two unknowns Optimal wage is even easier: one equation
5 Back to puzzle with shortcut: What happens if an input price changes? To MRTS? To input price ratio? To market price? To tangency between input price ratio and MRTS?
7 Transition: The California Wine Producers Is profit maximization a good assumption?
8 Transition: The California Wine Producers Is profit maximization a good assumption? What if your job makes you happy? As a firm owner, you have lower costs Opportunity costs are much lower because you’re doing something you like Need utility theory to save profit maximization theory here
9 Start with the bottom line: Budget constraints Consumers are simple: They consume and they work. Consumption denoted c Work denoted h Consumers have only 24 hours per day in which to consume and work. Wage for work denoted w Price for consumption denoted p Budget constraint?
10 Start with the bottom line: Budget constraints Consumers are simple: They consume and they work. Consumption denoted c Work denoted h Consumers have only 24 hours per day in which to consume and work. Wage for work denoted w Price for consumption denoted p Budget constraint? p x c = w x h if h > 0; c = 0 if h = 0
11 Budget constraints summarize tradeoffs A budget constraint in 2D can trade off any two goods Our example: consumption and leisure p x c = w x h pc = 24w – w(24 – h) ; leisure = 24 – h = z pc + wz = 24w = I max c = I max / p- (w/p)z A line! A simpler example: A gift of $120,000 can be used to pay for college ($30k/year) or to buy cars ($20k/car)
13 Budget definitions Budget constraint: Requirement that expenditure on a set of goods equal available funds (income or endowment) Budget set: All bundles of goods (points) that meet the BC, i.e. all feasible points Budget line: All bundles of goods that meet the BC with equality
14 Indifference curves Illustrate consumption bundles that give a consumer equal levels of utility Drawn in consumption good space U(c1, c2) = U(c3, c4) if the points (c1, c2) and (c3, c4) are both on the same IC Consumer is “indifferent” between any two bundles on an indifference curve because all points on an IC provide the same utility
15 Features of indifference curves Higher is better Assumption that more is always better “Local non-satiation” Downward sloping When decrease consumption of one good, must give more of the other to keep consumer happy Convex Results from diminishing marginal utility at higher levels of consumption for one good Do not cross Result of first assumption
18 Marginal rate of substitution MRS: The quantity of good 2 (y axis) that consumer must receive to remain indifferent to losing one unit of good 1 (x axis) Equal to slope of an indifference curve at a given point MRS YX = [∆Y/∆X | U = u*] = MU X /MU Y Varies with location on indifference curve Not the same as elasticity!
19 MRS varies with location on indifference curve
20 The consumer’s optimization problem Problem: Maximize utility subject to the budget constraint In other words, achieve highest level of utility (IC) that intersects the budget line Because of their curved shape, no two points on an indifference curve will be on the same budget line At optimal bundle, MRS YX = MU X /MU Y = P X /P Y
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