# 1 Q: Why is the tangent point special?. 2 A: It gives us a short cut.

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1 Q: Why is the tangent point special?

2 A: It gives us a short cut.

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?

6 Lecture 18: Consumer Choice 1

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)

12 Another budget constraint example

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

16 Indifference curves, graphically

17 Assumptions forbid intersecting indifference curves

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

21 The optimal bundle, graphically

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